mixed_strategies.bib

@article{stathakis2009many,
  title = {How many hidden layers and nodes?},
  author = {Stathakis, D},
  journal = {International Journal of Remote Sensing},
  volume = {30},
  number = {8},
  pages = {2133--2147},
  year = {2009},
  publisher = {Taylor \& Francis}
}
@article{glockner2012processing,
  title = {Processing differences between descriptions and experience: A comparative analysis using eye-tracking and physiological measures},
  author = {Gl{\"o}ckner, Andreas and Fiedler, Susann and Hochman, Guy and Ayal, Shahar and Hilbig, Benjamin E},
  journal = {Frontiers in psychology},
  volume = {3},
  year = {2012},
  publisher = {Frontiers Media SA}
}
@article{fiedler20122,
  title = {The influence of social value orientation on information processing in repeated voluntary contribution mechanism games},
  author = {Fiedler, Susann and Gl{\"o}ckner, Andreas and Nicklisch, Andreas},
  journal = {Neuroscience and the economics of decision making},
  pages = {21--53},
  year = {2012}
}
@article{franco2011applying,
  title = {Applying the decision moving window to risky choice: Comparison of eye-tracking and mousetracing methods},
  author = {Franco-Watkins, Ana M and Johnson, Joseph G},
  journal = {Judgment and Decision Making},
  volume = {6},
  number = {8},
  pages = {740},
  year = {2011},
  publisher = {Society for Judgment \& Decision Making}
}
@article{Nickerson2012,
  author = {Nickerson, Raymond S and Butler, Susan F and Nickerson, S},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/27784387.pdf:pdf},
  journal = {The American Journal of Psychology},
  number = {2},
  pages = {141--151},
  title = {{On producing random binary sequences On producing random binary sequences}},
  volume = {122},
  year = {2012}
}
@article{STEVEND.LEVITTJOHNA.LIST2010,
  abstract = {The minimax argument represents game theory in its most elegant form: simple but with stark predictions. Although some of these predictions have been met with reason- able success in the field, experimental data have generally not provided results close to the theoretical predictions. In a striking study, Palacios-Huerta and Volij (2008)pre- sented evidence that potentially resolves this puzzle: both amateur and professional soccer players play nearly exact minimax strategies in laboratory experiments. In this paper, we establish important bounds on these results by examining the behavior of four distinct subject pools: college students, bridge professionals, world-class poker players, who have vast experience with high-stakes randomization in card games, and American professional soccer players. In contrast to Palacios-Huerta and Volij’s results, we find little evidence that real-world experience transfers to the lab in these games—indeed, similar to previous experimental results, all four subject pools provide choices that are generally not close to minimax predictions. We use two additional pieces of evidence to explore why professionals do not perform well in the lab: (i) complementary ex- perimental treatments that pit professionals against preprogrammed computers and (ii) post-experiment questionnaires. The most likely explanation is that these profes- sionals are unable to transfer their skills at randomization from the familiar context of the field to the unfamiliar context of the lab.},
  author = {Levitt, Steven D and List, John A and Reiley, David H},
  doi = {10.3982/ECTA7405},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/Levitt\_et\_al-2010-Econometrica.pdf:pdf},
  issn = {0012-9682},
  journal = {Econometrica},
  number = {4},
  pages = {1413--1434},
  title = {{What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments}},
  volume = {78},
  year = {2010}
}
@article{Wooders2010,
  abstract = {Does expertise in strategic behavior obtained in the field transfer to the abstract set- ting of the laboratory? Palacios-Huerta and Volij (2008) argued that the behavior of professional soccer players in mixed-strategy games conforms closely to minimax play, while the behavior of students (who are presumably novices in strategic situations re- quiring unpredictability) does not. We reexamine their data, showing that the play of professionals is inconsistent with the minimax hypothesis in several respects: (i) pro- fessionals follow nonstationary mixtures, with action frequencies that are negatively correlated between the first and the second half of the experiment, (ii) professionals tend to switch between under- and overplaying an action relative to its equilibrium fre- quency, and (iii) the distribution of action frequencies across professionals is far from the distribution implied by minimax. In each respect, the behavior of students conforms more closely to the minimax hypothesis.},
  author = {Wooders, John},
  doi = {10.3982/ECTA7970},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/Wooders-2010-Econometrica.pdf:pdf},
  issn = {0012-9682},
  journal = {Econometrica},
  keywords = {Minimax, mixed strategy, Nash equilibrium},
  number = {3},
  pages = {1143--1154},
  title = {{Does Experience Teach? Professionals and Minimax Play in the Lab}},
  volume = {78},
  year = {2010}
}
@article{Palacios-Huerta2008,
  abstract = {We study how professional players and college students play zero-sum two-person strategic games in a laboratory setting. We first ask professionals to play a 2 × 2 game that is formally identical to a strategic interaction situation that they face in their natural environment. Consistent with their behaviour in the field, they play very close to the equilibrium of the game. In particular, (i) they equate their strategies’ payoffs to the equilibrium ones and (ii) they generate sequences of choices that are serially independent. In sharp contrast, however, we find that college students play the game far from the equilibrium predictions. We then study the behaviour of professional players and college students in the classic O’Neill 4 × 4 zero-sum game, a game that none of the subjects has encountered previously, and find the same differences in the behaviour of these two pools of subjects. The transfer of skills and experience from the familiar field to the unfamiliar laboratory observed for professional players is relevant to evaluate the circumstances under which behaviour in a laboratory setting may be a reliable indicator of behaviour in a naturally occurring setting. From a cognitive perspective, it is useful for research on recognition processes, intuition, and similarity as a basis for inductive reasoning.},
  author = {Palacios-Huerta, Ignacio and Volij, Oscar},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/4502054.pdf:pdf},
  issn = {00129682},
  journal = {Econometrica},
  keywords = {Cognition,Experience,Laboratory experiments,Minimax},
  number = {1},
  pages = {71--115},
  title = {{Experientia docet: Professionals play minimax in laboratory experiments}},
  volume = {76},
  year = {2008}
}
@article{Ashby2015,
  abstract = {Online marketplaces allow consumers to leave reviews about the products they purchase, which are visible to potential customers and competitors. While the impact of reviews on valuations of worth and purchasing decisions has been intensively studied, little is known about how the reviews themselves are attended to, and the relation between attention and valuations. In three studies we use eye-tracking methodologies to investigate attention in subjective monetary valuations of consumer goods. We find that, when evaluating consumer goods, individuals' attention to ratings are related to their frequencies, attention to positive or negative information is related to subjective valuations, and that perspective (owner vs. non-owner) influences the type of information attended to. These findings extend previous research regarding the valuations of risky prospects as implemented in abstract monetary gambles and suggest that similar cognitive processes might underlie both types of tasks.},
  author = {Ashby, Nathaniel J S and Walasek, Lukasz and Gl{\"{o}}ckner, Andreas},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ashby, Walasek, Gl{\"{o}}ckner - 2015 - The effect of consumer ratings and attentional allocation on product valuations.pdf:pdf},
  journal = {Judgment and Decision Making},
  keywords = {attention,consumer review,eye-tracking,ownership,valuation},
  number = {2},
  pages = {172--184},
  title = {{The effect of consumer ratings and attentional allocation on product valuations}},
  volume = {10},
  year = {2015}
}
@article{Barraclough2004,
  abstract = {In a multi-agent environment, where the outcomes of one's actions change dynamically because they are related to the behavior of other beings, it becomes difficult to make an optimal decision about how to act. Although game theory provides normative solutions for decision making in groups, how such decision-making strategies are altered by experience is poorly understood. These adaptive processes might resemble reinforcement learning algorithms, which provide a general framework for finding optimal strategies in a dynamic environment. Here we investigated the role of prefrontal cortex (PFC) in dynamic decision making in monkeys. As in reinforcement learning, the animal's choice during a competitive game was biased by its choice and reward history, as well as by the strategies of its opponent. Furthermore, neurons in the dorsolateral prefrontal cortex (DLPFC) encoded the animal's past decisions and payoffs, as well as the conjunction between the two, providing signals necessary to update the estimates of expected reward. Thus, PFC might have a key role in optimizing decision-making strategies.},
  author = {Barraclough, Dominic J and Conroy, Michelle L and Lee, Daeyeol},
  doi = {10.1038/nn1209},
  file = {:C$\backslash$:/Users/m3kro\_000/SkyDrive/Research/forward induction/nn1209.pdf:pdf},
  isbn = {1097-6256 (Print)$\backslash$n1097-6256 (Linking)},
  issn = {1097-6256},
  journal = {Nature neuroscience},
  number = {4},
  pages = {404--410},
  pmid = {15004564},
  title = {{Prefrontal cortex and decision making in a mixed-strategy game.}},
  volume = {7},
  year = {2004}
}
@article{Borji2014,
  abstract = {In a very influential yet anecdotal illustration, Yarbus suggested that human eye movement patterns are modulated top-down by different task demands. While the hypothesis that it is possible to decode the observer's task from eye movements has received some support (e.g., Iqbal {\&} Bailey (2004); Henderson et al. (2013)), Greene et al. (2012) argued against it by reporting a failure. In this study, we perform a more systematic investigation of this problem, probing a larger number of experimental factors than previously. Our main goal is to determine the informativeness of eye movements for task and mental state decoding. We perform two experiments. In the first experiment, we re-analyze the data from a previous study by Greene et al. (2012) and contrary to their conclusion, we report that it is possible to decode the observer's task from aggregate eye movement features slightly but significantly above chance, using a Boosting classifier (34.12{\%} correct vs. 25{\%} chance-level; binomial test, p = 1.0722e − 04). In the second experiment, we repeat and extend Yarbus' original experiment by collecting eye movements of 21 observers viewing 15 natural scenes (including Yarbus' scene) under Yarbus' seven questions. We show that task decoding is possible, also moderately but significantly above chance (24.21{\%} vs. 14.29{\%} chance-level; binomial test, p = 2.4535e − 06). We thus conclude that Yarbus' idea is supported by our data and continues to be an inspiration for future computational and experimental eye movement research. From a broader perspective, we discuss techniques, features, limitations, societal and technological impacts, and future directions in task decoding from eye movements.},
  author = {Borji, Ali and Itti, Laurent},
  doi = {10.1167/14.3.29},
  file = {:C$\backslash$:/Users/m3kro/Downloads/borji itti on yarbus.pdf:pdf},
  isbn = {1534-7362 (Electronic)$\backslash$n1534-7362 (Linking)},
  issn = {1534-7362},
  journal = {Journal of Vision},
  keywords = {Yarbus,bottom-up saliency,eye movements,free viewing,mind reading,task decoding,top-down attention,visual attention,visual search},
  number = {3},
  pages = {29--29},
  pmid = {24665092},
  title = {{Defending Yarbus: Eye movements reveal observers' task}},
  volume = {14},
  year = {2014}
}
@article{Greene2012,
  abstract = {In 1967, Yarbus presented qualitative data from one observer showing that the patterns of eye movements were dramatically affected by an observer's task, suggesting that complex mental states could be inferred from scan paths. The strong claim of this very influential finding has never been rigorously tested. Our observers viewed photographs for 10. s each. They performed one of four image-based tasks while eye movements were recorded. A pattern classifier, given features from the static scan paths, could identify the image and the observer at above-chance levels. However, it could not predict a viewer's task. Shorter and longer (60. s) viewing epochs produced similar results. Critically, human judges also failed to identify the tasks performed by the observers based on the static scan paths. The Yarbus finding is evocative, and while it is possible an observer's mental state might be decoded from some aspect of eye movements, static scan paths alone do not appear to be adequate to infer complex mental states of an observer. ?? 2012 Elsevier Ltd.},
  archiveprefix = {arXiv},
  arxivid = {NIHMS150003},
  author = {Greene, Michelle R. and Liu, Tommy and Wolfe, Jeremy M.},
  doi = {10.1016/j.visres.2012.03.019},
  eprint = {NIHMS150003},
  file = {:C$\backslash$:/Users/m3kro/Downloads/1-s2.0-S0042698912000922-main.pdf:pdf},
  isbn = {0042-6989},
  issn = {00426989},
  journal = {Vision Research},
  keywords = {Eye movements,Multivariate pattern classification,Task,Yarbus},
  pages = {1--8},
  pmid = {22487718},
  publisher = {Elsevier Ltd},
  title = {{Reconsidering Yarbus: A failure to predict observers' task from eye movement patterns}},
  volume = {62},
  year = {2012}
}
@article{Rapoport2004,
  abstract = {We consider sealed-bid, first-price, all-pay auctions with complete information, discrete strategy space, budget constraint, and symmetric players, and then construct the equilibrium solution in mixed strategies for both fixed and variable prizes. The equilibrium solution yields predictions concerning the effects of group size and value of the prize that are tested experimentally. The experimental results support equilibrium play on the aggregate but not individual level. Adaptive learning on the individual level accounts for the major trends in the aggregate expenditures over time. © 2003 Elsevier B.V. All rights reserved.},
  author = {Rapoport, Amnon and Amaldoss, Wilfred},
  doi = {10.1016/j.jebo.2002.10.003},
  file = {:C$\backslash$:/Users/m3kro\_000/SkyDrive/Research/forward induction/1-s2.0-S0167268103001409-main.pdf:pdf},
  isbn = {0167-2681},
  issn = {01672681},
  journal = {Journal of Economic Behavior and Organization},
  keywords = {Adaptive learning,All-pay auctions,Bounded rationality,Mixed strategies},
  number = {4},
  pages = {585--607},
  title = {{Mixed-strategy play in single-stage first-price all-pay auctions with symmetric players}},
  volume = {54},
  year = {2004}
}
@article{Palacios-Huerta2003,
  abstract = {The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a one-shot two-person zero-sum game. The results of the tests are remarkably consistent with equilibrium play in every respect: (i) winning probabilities are statistically identical across strategies for players; (ii) players’ choices are serially independent. The tests have substantial power to distinguish equilibrium play from disequilibrium alternatives. These results represent the first time that both implications of von Neumann's Minimax theorem are supported under natural conditions.},
  author = {Palacios-Huerta, Ignacio},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/Review of Economic Studies-2003-Palacios-Huerta-395-415.pdf:pdf},
  issn = {00346527},
  journal = {Review of Economic Studies},
  number = {2},
  pages = {395--415},
  title = {{Professionals play minimax}},
  volume = {70},
  year = {2003}
}
@article{Chiappori2002,
  abstract = {This paper develops a game-theoretic model of penalty kicks in soccer and tests the assumptions and predictions of the model using data from two European soccer leagues. The application in this paper represents one of the first attempts to test mixed-strategy behavior using data generated outside of a controlled experiment. The authors analyze the complexities that arise in testing basic hypotheses in the presence of heterogeneity across kickers and goalies. They note which hypotheses are testable when the researcher has only a limited number of kicks per goalie--kicker pair, and they introduce and test restrictions on the model that lead to a richer set of testable hypotheses given the limitations of data. Although there are clear advantages provided by a well-conducted laboratory experiment, testing game theory in the real world may provide unique insights. The penalty kick data the authors examine more closely corroborates the predictions of theory than past laboratory experiments would have led the authors to expect. This paper develops a game-theoretic model of penalty kicks in soccer and tests the assumptions and predictions of the model using data from two European soccer leagues. The application in this paper represents one of the first attempts to test mixed-strategy behavior using data generated outside of a controlled experiment. The authors analyze the complexities that arise in testing basic hypotheses in the presence of heterogeneity across kickers and goalies. They note which hypotheses are testable when the researcher has only a limited number of kicks per goalie--kicker pair, and they introduce and test restrictions on the model that lead to a richer set of testable hypotheses given the limitations of data. Although there are clear advantages provided by a well-conducted laboratory experiment, testing game theory in the real world may provide unique insights. The penalty kick data the authors examine more closely corroborates the predictions of theory than past laboratory experiments would have led the authors to expect.},
  author = {Chiappori, P. and Levitt, S. and Groseclose, T.},
  doi = {10.1257/00028280260344678},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/3083302.pdf:pdf},
  isbn = {0002-8282},
  issn = {00028282},
  journal = {American Economic Review},
  number = {4},
  pages = {1138--1151},
  title = {{Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer}},
  volume = {92},
  year = {2002}
}
@article{Nyarko2002,
  abstract = {This paper investigates belief learning. Unlike other investigators who have been forced to use observable proxies to approximate unobserved beliefs, we have, using a belief elicitation procedure (proper scoring rule), elicited subject beliefs directly. As a result we were able to perform a more direct test of the proposition that people behave in a manner consistent with belief learning. What we find is interesting. First to the extent that subjects tend to “belief learn,” the beliefs they use are the stated beliefs we elicit from them and not the “empirical beliefs” posited by fictitious play or Cournot models. Second, we present evidence that the stated beliefs of our subjects differ dramatically, both quantitatively and qualitatively, from the type of empirical or historical beliefs usually used as proxies for them. Third, our belief elicitation procedures allow us to examine how far we can be led astray when we are forced to infer the value of parameters using observable proxies for variables previously thought to be unobservable. By transforming a heretofore unobservable into an observable, we can see directly how parameter estimates change when this new information is introduced. Again, we demonstrate that such differences can be dramatic. Finally, our belief learning model using stated beliefs outperforms both a reinforcement and EWA model when all three models are estimated using our data.},
  annote = {stated beliefs of our subjects differ dramatically, both quantitatively and qualitatively, from the type of empirical or historical beliefs usually used as proxies for them. Third, our belief elicitation procedures allow us to examine how far we can be led astray when we are forced to infer the value of parameters using observable proxies for variables previously thought to be unobservable},
  author = {Nyarko, Yaw and Schotter, Andrew},
  doi = {10.1111/1468-0262.00316},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1468-0262.00316.pdf:pdf},
  issn = {0012-9682},
  journal = {Econometrica},
  keywords = {belief learning,experimental economics,game theory},
  number = {3},
  pages = {971--1005},
  title = {{An Experimental Study of Belief Learning Using Elicited Beliefs}},
  volume = {70},
  year = {2002}
}
@article{Walker2001,
  author = {Walker, Mark and Wooders, John},
  doi = {10.1257/aer.91.5.1521},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/2677937.pdf:pdf},
  issn = {0002-8282},
  journal = {The American Economic Review},
  number = {5},
  pages = {1521--1538},
  title = {{Minimax Play at Wimbledon}},
  volume = {91},
  year = {2001}
}
@article{McCabe2000,
  author = {McCabe, Kevin a. and Mukherji, Arijit and Runkle, David E.},
  doi = {10.1007/s001990050020},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/art\%3A10.1007\%2Fs001990050020.pdf:pdf},
  issn = {0938-2259},
  journal = {Economic Theory},
  keywords = {and phrases,are,bayesian learning,c72,c91,d83,dation and the accounting,experimental,experiments was provided by,financial support for the,grants from the national,jel classification numbers,nash equilibrium,research center,science foun-,the views expressed here,university of minnesota},
  number = {2},
  pages = {421--462},
  title = {{An experimental study of information and mixed-strategy play in the three-person matching-pennies game}},
  volume = {15},
  year = {2000}
}
@article{Rapoport2000,
  abstract = {$\backslash$nThe iterative elimination of strongly dominated strategies \{(IESDS)\} and mixed-equilibrium solution concepts are studied in an iterated two-person investment game with discrete strategy spaces, non-recoverable investments, and either equal or unequal investment capital. In this game, the player investing the largest amount wins the competition and receives a fixed reward; ties are counted as losses. Both cases of symmetric and asymmetric dyads are studied theoretically and experimentally. Results from two experiments provide support for the mixed-strategy equilibrium solution on the aggregate but not the individual level, and evidence for a hierarchy of bounded \{IESDS.\}},
  annote = {findings suggest that equilibrium on the aggregate level arises because players learn from experience rather than figure out equilibria by introspection},
  author = {Rapoport, Amnon and Amaldoss, Wilfred},
  doi = {10.1016/S0167-2681(00)00101-3},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0167268100001013-main.pdf:pdf},
  isbn = {0167-2681},
  issn = {01672681},
  journal = {Journal of Economic Behavior \& Organization},
  keywords = {adaptive,bounded rationality,dominated strategies,iterative deletion of strongly,mixed strategies},
  number = {4},
  pages = {483--521},
  title = {{Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge}},
  volume = {42},
  year = {2000}
}
@article{Erev1998,
  author = {Erev, Ido and Roth, Alvin E},
  file = {:C$\backslash$:/Users/m3kro\_000/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Erev, Roth - 1998 - Predicting How People Play Games Reinforcement Learning in Experimental Games with unique mixed-strategy equilibria.pdf:pdf},
  issn = {0002-8282},
  journal = {AMERICAN ECONOMIC REVIEW},
  pages = {848--881},
  title = {{Predicting How People Play Games: Reinforcement Learning in Experimental Games with unique mixed-strategy equilibria}},
  volume = {88},
  year = {1998}
}
@article{Arieli2011,
  author = {Arieli, Amos and Ben-Ami, Yaniv and Rubinstein, Ariel},
  doi = {10.1257/mic.3.4.68},
  file = {:C$\backslash$:/Users/m3kro/Downloads/mic{\%}2E3{\%}2E4{\%}2E68.pdf:pdf},
  issn = {1945-7669},
  journal = {American Economic Journal: Microeconomics},
  number = {4},
  pages = {68--76},
  publisher = {American Economic Association},
  title = {{Tracking Decision Makers under Uncertainty}},
  volume = {3},
  year = {2011}
}
@article{BLOOMFIELD1994411,
  title = {Learning a mixed strategy equilibrium in the laboratory},
  journal = {Journal of Economic Behavior and Organization},
  volume = {25},
  number = {3},
  pages = {411 - 436},
  year = {1994},
  note = {},
  issn = {0167-2681},
  author = {Robert Bloomfield}
}
@article{Brocas2014,
  abstract = {In experiments, people do not always appear to infer the information of other players from their choices. To understand this thinking process further, we use “Mousetracking” to record which game payoffs subjects look at, and for how long, in games of private information with three information states, which vary in strategic complexity. Subjects often deviate from Nash equilibrium choices, converge only modestly toward equilibrium across 40 trials, and often fail to look at payoffs which they need to in order to compute an equilibrium response. When cluster analysis is used to group subjects according to lookup patterns and choices, the clusters appear to correspond approximately to level-3, level-2 and level-1 thinking in level-k cognitive hierarchy models. Deviations from Nash play are associated with failure to look at the necessary payoffs. The connection between looking and choices is strong enough that the time durations of looking at key payoffs can predict choices, to some extent, at the individual level and at the trial-by-trial level},
  author = {Brocas, Isabelle and Carrillo, Juan D. and Wang, Stephanie and Camerer, Colin F.},
  doi = {10.1093/restud/rdu001},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Brocas et al. - 2014 - Imperfect choice or imperfect attention Understanding strategic thinking in private information games.pdf:pdf},
  issn = {1467937X},
  journal = {Review of Economic Studies},
  keywords = {Behavioral game theory,Betting games,Cognitive hierarchy,Eyetracking,Level-k,Mousetracking},
  number = {3},
  pages = {944--970},
  title = {{Imperfect choice or imperfect attention? Understanding strategic thinking in private information games}},
  volume = {81},
  year = {2014}
}
@article{Camerer01082004,
  author = {Camerer, Colin F. and Ho, Teck-Hua and Chong, Juin-Kuan},
  title = {A Cognitive Hierarchy Model of Games},
  volume = {119},
  number = {3},
  pages = {861-898},
  year = {2004},
  doi = {10.1162/0033553041502225},
  abstract = {Players in a game are “in equilibrium” if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k - 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games.},
  eprint = {http://qje.oxfordjournals.org/content/119/3/861.full.pdf+html},
  journal = {The Quarterly Journal of Economics}
}
@article{Costa-Gomes2001,
  author = {Costa-Gomes, Miguel and Crawford, Vincent P. and Broseta, Bruno},
  doi = {10.1111/1468-0262.00239},
  file = {:C$\backslash$:/Users/m3kro/Downloads/1468-0262.00239.pdf:pdf},
  issn = {0012-9682},
  journal = {Econometrica},
  number = {5},
  pages = {1193--1235},
  title = {{Cognition and Behavior in Normal-Form Games: An Experimental Study}},
  volume = {69},
  year = {2001}
}
@article{Costa-Gomes2006,
  author = {Costa-Gomes, Miguel and Crawford, Vincent P},
  doi = {10.1257/aer.96.5.1737},
  file = {:C$\backslash$:/Users/m3kro/Downloads/aer{\%}2E96{\%}2E5{\%}2E1737.pdf:pdf},
  issn = {0002-8282},
  journal = {American Economic Review},
  number = {5},
  pages = {1737--1768},
  title = {{Cognition and Behavior in Two-Person Guessing Games: An Experimental Study}},
  volume = {96},
  year = {2006}
}
@article{Cristino2010,
  author = {Cristino, Filipe and Math{\^{o}}t, Sebastiaan and Theeuwes, Jan and Gilchrist, Iain D.},
  doi = {10.3758/BRM.42.3.692},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Cristino et al. - 2010 - ScanMatch A novel method for comparing fixation sequences.pdf:pdf},
  issn = {1554-351X},
  journal = {Behavior Research Methods},
  number = {3},
  pages = {692--700},
  publisher = {Springer-Verlag},
  title = {{ScanMatch: A novel method for comparing fixation sequences}},
  volume = {42},
  year = {2010}
}
@article{Day2010,
  abstract = {A new generation of eye trackers shows us a promising alternative approach to tracing decision processes beyond the popular computerized-information-board approach. In order to exploit the eye-movement data, this study examined the validity of the Needleman–Wunsch algorithm (NWA) to characterize the decision process, and proposed an NWA-based classification method to predict which typical strategy an empirical search behavior might belong to. An eye-tracking based experiment was conducted. Our results showed that the resemblance score by NWA conformed to the assumption that the pair of information search behaviors based on the same strategy should have the closest resemblance. Moreover, with respect to our NWA-based classification method, our result showed that its overall prediction accuracy, hit-ratio, in identifying underlying strategies achieved 88{\%}, significantly much higher than that gained from chance. On the whole, the combination of eye-fixation data and our NWA-based classification method is qualified.},
  author = {Day, Rong-Fuh},
  doi = {10.1016/j.dss.2010.05.001},
  file = {:C$\backslash$:/Users/m3kro/Downloads/out (1).pdf:pdf},
  issn = {01679236},
  journal = {Decision Support Systems},
  number = {4},
  pages = {396--403},
  title = {{Examining the validity of the Needleman-Wunsch algorithm in identifying decision strategy with eye-movement data}},
  volume = {49},
  year = {2010}
}
@article{Dewhurst2012,
  abstract = {Eye movement sequences-or scanpaths-vary depending on the stimulus characteristics and the task (Foulsham {\&} Underwood Journal of Vision, 8(2), 6:1-17, 2008; Land, Mennie, {\&} Rusted, Perception, 28, 1311-1328, 1999). Common methods for comparing scanpaths, however, are limited in their ability to capture both the spatial and temporal properties of which a scanpath consists. Here, we validated a new method for scanpath comparison based on geometric vectors, which compares scanpaths over multiple dimensions while retaining positional and sequential information (Jarodzka, Holmqvist, {\&} Nystr{\"{o}}m, Symposium on Eye-Tracking Research and Applications (pp. 211-218), 2010). "MultiMatch" was tested in two experiments and pitted against ScanMatch (Cristino, Math{\^{o}}t, Theeuwes, {\&} Gilchrist, Behavior Research Methods, 42, 692-700, 2010), the most comprehensive adaptation of the popular Levenshtein method. In Experiment 1, we used synthetic data, demonstrating the greater sensitivity of MultiMatch to variations in spatial position. In Experiment 2, real eye movement recordings were taken from participants viewing sequences of dots, designed to elicit scanpath pairs with commonalities known to be problematic for algorithms (e.g., when one scanpath is shifted in locus or when fixations fall on either side of an AOI boundary). The results illustrate the advantages of a multidimensional approach, revealing how two scanpaths differ. For instance, if one scanpath is the reverse copy of another, the difference is in the direction but not the positions of fixations; or if a scanpath is scaled down, the difference is in the length of the saccadic vectors but not in the overall shape. As well as having enormous potential for any task in which consistency in eye movements is important (e.g., learning), MultiMatch is particularly relevant for "eye movements to nothing" in mental imagery and embodiment-of-cognition research, where satisfactory scanpath comparison algorithms are lacking.},
  author = {Dewhurst, Richard and Nystr{\"{o}}m, Marcus and Jarodzka, Halszka and Foulsham, Tom and Johansson, Roger and Holmqvist, Kenneth},
  doi = {10.3758/s13428-012-0212-2},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Dewhurst et al. - 2012 - It depends on how you look at it Scanpath comparison in multiple dimensions with MultiMatch, a vector-based app.pdf:pdf},
  isbn = {1342801202122},
  issn = {1554-3528},
  journal = {Behavior Research Methods},
  keywords = {a higher-,comparison,dimensional,eye movement,eye movements,level cognitive task,picture or engaged in,scanpath,sequence,similarity,we make sequences of,whether passively viewing a},
  number = {4},
  pages = {1079--1100},
  pmid = {22648695},
  publisher = {Springer-Verlag},
  title = {{It depends on how you look at it: Scanpath comparison in multiple dimensions with MultiMatch, a vector-based approach}},
  volume = {44},
  year = {2012}
}
@article{Dietterich1998,
  abstract = {This article reviews five approximate statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These test sare compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type I error). Two widely used statistical tests are shown to have high probability of type I error in certain situations and should never be used: a test for the difference of two proportions and a paired-differences t test based on taking several random train-test splits. A third test, a paired-differences t test based on 10-fold cross-validation, exhibits somewhat elevated probability of type I error. A fourth test, McNemar's test, is shown to have low type I error. The fifth test is a new test, 5 × 2 cv, based on five iterations of twofold cross-validation. Experiments show that this test also has acceptable type I error. The article also measures the power (ability to detect algorithm differences when they do exist)...},
  author = {Dietterich, Thomas G.},
  doi = {10.1162/089976698300017197},
  issn = {0899-7667},
  journal = {Neural Computation},
  number = {7},
  pages = {1895--1923},
  publisher = { MIT Press  238 Main St., Suite 500, Cambridge, MA 02142-1046 USA journals-info@mit.edu  },
  title = {{Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms}},
  volume = {10},
  year = {1998}
}
@article{Glockner2011,
  author = {Gl{\"{o}}ckner, Andreas and Herbold, Ann-Katrin},
  doi = {10.1002/bdm.684},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Gl{\"{o}}ckner, Herbold - 2011 - An eye-tracking study on information processing in risky decisions Evidence for compensatory strategies based.pdf:pdf},
  issn = {08943257},
  journal = {Journal of Behavioral Decision Making},
  keywords = {cumulative prospect theory,decision field theory,eye tracking,intuition,parallel constraint satisfaction,priority heuristic,risky decisions},
  number = {1},
  pages = {71--98},
  publisher = {John Wiley {\&} Sons, Ltd.},
  title = {{An eye-tracking study on information processing in risky decisions: Evidence for compensatory strategies based on automatic processes}},
  volume = {24},
  year = {2011}
}
@article{Grimm2012,
  abstract = {We study how players learn to make decisions if they face many different games. Games are drawn randomly from a set of either two or six games in each of 100 rounds. If either there are few games or if extensive summary information is provided (or both) convergence to the unique Nash equilibrium generally occurs. Otherwise this is not the case. We demonstrate that there are learning spillovers across games but participants learn to play strategically equivalent games in the same way. Our design and analysis allow us to distinguish between different sources of complexity and theoretical models of categorization. ?? 2012 Elsevier Inc.},
  author = {Grimm, Veronika and Mengel, Friederike},
  doi = {10.1016/j.jet.2012.05.011},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0022053112000658-main.pdf:pdf},
  issn = {00220531},
  journal = {Journal of Economic Theory},
  keywords = {Experiments,Game theory,Learning,Multiple games},
  number = {6},
  pages = {2220--2259},
  publisher = {Elsevier Inc.},
  title = {{An experiment on learning in a multiple games environment}},
  volume = {147},
  year = {2012}
}
@article{Hayes2016,
  author = {Hayes, Taylor R. and Petrov, Alexander A.},
  doi = {10.3758/s13428-015-0588-x},
  issn = {1554-3528},
  journal = {Behavior Research Methods},
  number = {2},
  pages = {510--527},
  publisher = {Springer US},
  title = {{Mapping and correcting the influence of gaze position on pupil size measurements}},
  volume = {48},
  year = {2016}
}
@article{Hayes2011,
  author = {Hayes, Taylor R and Petrov, Alexander and Sederberg, Per B},
  doi = {10.1167/11.10.10.Introduction},
  file = {:C$\backslash$:/Users/m3kro/Downloads/jov-11-10-10.pdf:pdf},
  journal = {Journal of Vision},
  keywords = {1,10,11,1167,2011,a,a novel method for,analyzing sequential eye movements,b,citation,content,doi,eye movements,hayes,http,individual differences,journal of vision,journalofvision,org,p,petrov,problem solving strategies,r,reveals strategic in fl,s advanced progressive matrices,sederberg,t,temporal-difference learning,uence on raven,www},
  number = {2011},
  pages = {1--11},
  title = {{A novel method for analyzing sequential eye movements reveals strategic in fluence on Raven's Advanced Progressive Matrices}},
  volume = {11},
  year = {2011}
}
@article{Hsu2007,
  abstract = {1538 THE AMERICAN 1 Dixit, Avinash and Nalebuff, Barry. Thinking strategically: The competitive edge in busi- ness, politics, and everyday life. New York: WW Norton, 1991. Erev, Ido and Roth, Alvin E. "Predicting How People Play},
  author = {Hsu, Shih Hsun and Huang, Chen Ying and Tang, Cheng Tao},
  doi = {10.1257/aer.97.1.517},
  file = {:C$\backslash$:/Users/m3kro/Downloads/aer{\%}2E97{\%}2E1{\%}2E517.pdf:pdf},
  isbn = {00028282},
  issn = {00028282},
  journal = {American Economic Review},
  number = {1},
  pages = {517--523},
  title = {{Minimax play at Wimbledon: Comment}},
  volume = {97},
  year = {2007}
}
@article{Johnson2002,
  abstract = {We did experiments in a three-round bargaining game where the (perfect) equilibrium offer was {\$}1.25 and an equal split was {\$}2.50. The average offer was {\$}2.11. Patterns of information search (measured with a computerized information display) show limited lookahead rather than backward induction. Equilibrium theories which adjust for social utilities (reflecting inequality-aversion or reciprocity) cannot explain the results because they predict subjects will make equilibrium offers to "robot" players, but offers to robots are only a little lower. When trained subjects (who quickly learned to do backward induction) bargained with untrained subjects, offers ended up halfway between equilibrium and {\$}2.11. Journal of Economic Literature Classification Numbers: C7, C9.},
  author = {Johnson, Eric J. and Camerer, Colin F and Sen, Sankar and Rymon, Talia},
  doi = {10.1006/jeth.2001.2850},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Johnson et al. - 2002 - Detecting Failures of Backward Induction Monitoring Information Search in Sequential Bargaining.pdf:pdf},
  isbn = {0022-0531},
  issn = {00220531},
  journal = {Journal of Economic Theory},
  keywords = {bargaining,behavioral,behavioral economics,behavioral game theory,bounded,bounded rationality,cognition,economics,experimental,experimental economics,fairness,game,limited,limited cognition,rationality,theory},
  number = {1},
  pages = {16--47},
  title = {{Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining}},
  volume = {104},
  year = {2002}
}
@article{Kang01082009,
  author = {Kang, Min Jeong and Hsu, Ming and Krajbich, Ian M. and Loewenstein, George and McClure, Samuel M. and Wang, Joseph Tao-yi and Camerer, Colin F.},
  title = {The Wick in the Candle of Learning: Epistemic Curiosity Activates Reward Circuitry and Enhances Memory},
  volume = {20},
  number = {8},
  pages = {963-973},
  year = {2009},
  doi = {10.1111/j.1467-9280.2009.02402.x},
  abstract = {Curiosity has been described as a desire for learning and knowledge, but its underlying mechanisms are not well understood. We scanned subjects with functional magnetic resonance imaging while they read trivia questions. The level of curiosity when reading questions was correlated with activity in caudate regions previously suggested to be involved in anticipated reward. This finding led to a behavioral study, which showed that subjects spent more scarce resources (either limited tokens or waiting time) to find out answers when they were more curious. The functional imaging also showed that curiosity increased activity in memory areas when subjects guessed incorrectly, which suggests that curiosity may enhance memory for surprising new information. This prediction about memory enhancement was confirmed in a behavioral study: Higher curiosity in an initial session was correlated with better recall of surprising answers 1 to 2 weeks later.},
  eprint = {http://pss.sagepub.com/content/20/8/963.full.pdf+html},
  journal = {Psychological Science}
}
@article{Krajbich2011,
  abstract = {How do we make decisions when confronted with several alternatives (e.g., on a supermarket shelf)? Previous work has shown that accumulator models, such as the drift-diffusion model, can provide accurate descriptions of the psychometric data for binary value-based choices, and that the choice process is guided by visual attention. However, the computational processes used to make choices in more complicated situations involving three or more options are unknown. We propose a model of trinary value-based choice that generalizes what is known about binary choice, and test it using an eye-tracking experiment. We find that the model provides a quantitatively accurate description of the relationship between choice, reaction time, and visual fixation data using the same parameters that were estimated in previous work on binary choice. Our findings suggest that the brain uses similar computational processes to make binary and trinary choices.},
  author = {Krajbich, Ian and Rangel, Antonio},
  doi = {10.1073/pnas.1101328108},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Krajbich, Rangel - 2011 - Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value-.pdf:pdf},
  isbn = {1091-6490 (Electronic) 0027-8424 (Linking)},
  issn = {1091-6490},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  keywords = {Choice Behavior,Choice Behavior: physiology,Decision Making,Fixation, Ocular,Food Preferences,Humans,Models, Psychological,Ocular,Psychological},
  number = {33},
  pages = {13852--7},
  pmid = {21808009},
  title = {{Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value-based decisions.}},
  volume = {108},
  year = {2011}
}
@article{Krajbich2010,
  abstract = {Most organisms facing a choice between multiple stimuli will look repeatedly at them, presumably implementing a comparison process between the items' values. Little is known about the nature of the comparison process in value-based decision-making or about the role of visual fixations in this process. We created a computational model of value-based binary choice in which fixations guide the comparison process and tested it on humans using eye-tracking. We found that the model can quantitatively explain complex relationships between fixation patterns and choices, as well as several fixation-driven decision biases.},
  author = {Krajbich, Ian and Armel, Carrie and Rangel, Antonio},
  doi = {10.1038/nn.2635},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Krajbich, Armel, Rangel - 2010 - Visual fixations and the computation and comparison of value in simple choice.pdf:pdf},
  isbn = {1546-1726 (Electronic)$\backslash$n1097-6256 (Linking)},
  issn = {1546-1726},
  journal = {Nature Neuroscience},
  keywords = {Attention,Attention: physiology,Bias (Epidemiology),Chi-Square Distribution,Choice Behavior,Choice Behavior: physiology,Computer Simulation,Dominance,Fixation,Food Preferences,Food Preferences: physiology,Humans,Likelihood Functions,Models,Ocular,Ocular: physiology,Photic Stimulation,Photic Stimulation: methods,Predictive Value of Tests,Psychological,Psychometrics,Psychometrics: methods,Reaction Time,Reaction Time: physiology,Students,Time Factors,Universities},
  number = {10},
  pages = {1292--8},
  pmid = {20835253},
  title = {{Visual fixations and the computation and comparison of value in simple choice.}},
  volume = {13},
  year = {2010}
}
@article{Marshall2007,
  abstract = {INTRODUCTION: This paper describes a new approach for identifying cognitive state by using information obtained only from the eye. Data are collected from cameras mounted on a lightweight headband. A set of eye metrics captures essential eye information from the raw data of pupil size and point-of-gaze. The metrics are easily calculated every second, so that the entire set of metrics can be computed in real time. METHODS: Three studies provide empirical evidence to test whether the eye metrics are sufficient to discriminate between two different cognitive states. The first study examines the states of relaxed and engaged in the context of problem solving. The second study looks at the states of focused and distracted attention in the context of driving. The third study inspects the states of alert and fatigued in the context of visual search. Two statistical models are used to classify cognitive state for all three studies: linear discriminant function analysis and non-linear neural network analysis. Data for the models are eye metrics computed at 1-, 4-, and 10-s intervals. RESULTS: All discriminant function analyses are statistically significant, and classification rates are high. Neural network models have equal or better performance than discriminant function models across all three studies. DISCUSSION: The seven eye metrics successfully discriminate between the states in all studies. Models from individual participants as well as the aggregate model over all participants are successful in identifying cognitive states based on task condition. Classification rates compare favorably with similar studies.},
  author = {Marshall, Sandra P.},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Marshall - 2007 - Identifying cognitive state from eye metrics.pdf:pdf},
  isbn = {0-8058-5806-7},
  issn = {00956562},
  journal = {Aviation Space and Environmental Medicine},
  keywords = {Alertness,Driving,Linear discriminant function analysis,Non-linear neural network analysis,Point-of-gaze location,Problem solving,Pupil size,Visual search},
  number = {5 II},
  pages = {165--175},
  pmid = {17547317},
  title = {{Identifying cognitive state from eye metrics}},
  volume = {78},
  year = {2007}
}
@article{Martin2014,
  abstract = {The capacity for strategic thinking about the payoff-relevant actions of conspecifics is not well understood across species. We use game theory to make predictions about choices and temporal dynamics in three abstract competitive situations with chimpanzee participants. Frequencies of chimpanzee choices are extremely close to equilibrium (accurate-guessing) predictions, and shift as payoffs change, just as equilibrium theory predicts. The chimpanzee choices are also closer to the equilibrium prediction, and more responsive to past history and payoff changes, than two samples of human choices from experiments in which humans were also initially uninformed about opponent payoffs and could not communicate verbally. The results are consistent with a tentative interpretation of game theory as explaining evolved behavior, with the additional hypothesis that chimpanzees may retain or practice a specialized capacity to adjust strategy choice during competition to perform at least as well as, or better than, humans have.},
  author = {Martin, C F and Bhui, R and Bossaerts, P and Matsuzawa, T and Camerer, C},
  doi = {10.1038/srep05182},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/srep05182.pdf:pdf},
  isbn = {2045-2322 (Electronic)$\backslash$n2045-2322 (Linking)},
  issn = {2045-2322},
  journal = {Scientific Reports},
  pmid = {24901997},
  title = {{Chimpanzee choice rates in competitive games match equilibrium game theory predictions}},
  volume = {4 . Art. No. 5182},
  year = {2014}
}
@article{Mookherjee1994,
  abstract = {Two groups containing 10 pairs of players each playing a finitely repeated matching pennies game were varied in terms of the information available to any player about past choices and payoffs of its opponent. The data reveals that presentation of such information does have a significant effect on the nature of play. For subjects without information about opponents\′ moves, there is evidence in favor of the hypothesis that past experience with different choices in the past affect current strategy. For fully informed subjects, on the other hand, choices are considerably closer to i.i.d. play. Journal of Economic Literature Classification Numbers: C72, C92.},
  author = {Mookherjee, D. and Sopher, B.},
  doi = {10.1006/game.1994.1037},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0899825684710372-main.pdf:pdf},
  isbn = {0899-8256},
  issn = {0899-8256},
  journal = {Games and Economic Behavior},
  number = {1},
  pages = {62--91},
  title = {{Learning Behavior in an Experimental Matching Pennies Game}},
  volume = {7},
  year = {1994}
}
@inproceedings{nair2010rectified,
  title = {Rectified linear units improve restricted boltzmann machines},
  author = {Nair, Vinod and Hinton, Geoffrey E},
  booktitle = {Proceedings of the 27th international conference on machine learning (ICML-10)},
  pages = {807--814},
  year = {2010}
}
@article{Neuringer1986,
  abstract = {Experimental psychologists generally maintain that people cannot behave randomly. The present experiment asked students to generate random sequences of two numbers on the keyboard of a computer terminal. At first, all subjects' sequences differed significantly from random, thereby replicating the findings of the literature. But when given feedback from 5 or 10 statistical descriptors, the subjects learned to generate sequences that were indistinguishable, according to these statistics, from computer-generated random numbers. Randomlike behavior can therefore be learned.},
  author = {Neuringer, Allen},
  doi = {10.1037/0096-3445.115.1.62},
  isbn = {0096-3445},
  issn = {0096-3445},
  journal = {Journal of Experimental Psychology: General},
  number = {1},
  pages = {62--75},
  title = {{Can people behave 'randomly?': The role of feedback.}},
  volume = {115},
  year = {1986}
}
@article{Ochs1995,
  abstract = {The results of an experiment studying the choices of subjects playing mixed extensions of three variants of simple 2 × 2 non-constant sum, strictly competitive games of the same form (Matching Pennies) are presented. Subjects exhibited a variety of behavioral, adaptive learning strategies. This heterogeneity of individual behavior produced aggregate dynamics whose estimated steady states are quite different from those predicted by the Nash equilibria of those stage games with asymmetrical payoff functions. The observed aggregative dynamics are well accounted for both by a quantal equilibrium model of McKelvey and Palfrey and by a learning model of Roth and Erev. Journal of Economic Literature Classification Number: C72.},
  author = {Ochs, Jack},
  doi = {10.1006/game.1995.1030},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0899825685710305-main.pdf:pdf},
  issn = {08998256},
  journal = {Games and Economic Behavior},
  keywords = {game theory},
  number = {1},
  pages = {202----217},
  title = {{Games with unique, mixed strategy equilibria - experimental study}},
  volume = {10},
  year = {1995}
}
@article{Okano2013,
  abstract = {We analyze the behavior of two-person teams and individuals who repeatedly play the game with a unique mixed strategy equilibrium in the laboratory. When teams play O'Neill's 4??4 game against another team, the choice frequencies are consistent with equilibrium of the game at the decision-maker level. In contrast, individuals against another individual play far from equilibrium, as previous experiments have found. The hide-and-seek game experiment reveals that teams' behavior is less heterogeneous than individuals. When teams play O'Neill's game against individuals, teams win at above the equilibrium rate in one treatment, but not in the other. ?? 2012 Elsevier Inc.},
  author = {Okano, Yoshitaka},
  doi = {10.1016/j.geb.2012.10.003},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0899825612001510-main.pdf:pdf},
  isbn = {8166877511},
  issn = {08998256},
  journal = {Games and Economic Behavior},
  keywords = {Experiment,Heterogeneity,Minimax,Team vs. individual decision making},
  number = {1},
  pages = {168--180},
  publisher = {Elsevier Inc.},
  title = {{Minimax play by teams}},
  volume = {77},
  year = {2013}
}
@article{Patalano2009,
  author = {Patalano, Andrea L. and Juhasz, Barbara J. and Dicke, Joanna},
  doi = {10.1002/bdm.661},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Patalano, Juhasz, Dicke - 2009 - The relationship between indecisiveness and eye movement patterns in a decision making informational se.pdf:pdf},
  issn = {08943257},
  journal = {Journal of Behavioral Decision Making},
  keywords = {decision strategy,eye movements,indecisiveness,individual differences,process tracing},
  number = {4},
  pages = {353--368},
  publisher = {John Wiley {\&} Sons, Ltd.},
  title = {{The relationship between indecisiveness and eye movement patterns in a decision making informational search task}},
  volume = {23},
  year = {2009}
}
@article{Polonio2015,
  abstract = {We used eye-tracking to measure the dynamic patterns of visual information acquisition in two-player normal-form games. Participants played one-shot games in which either, neither, or only one of the players had a dominant strategy. First, we performed a mixture models cluster analysis to group participants into types according to the pattern of visual information acquisition observed in a single class of games. Then, we predicted agents' choices in different classes of games and observed that patterns of visual information acquisition were game invariant. Our method allowed us to predict whether the decision process would lead to equilibrium choices or not, and to attribute out-of-equilibrium responses to limited cognitive capacities or social motives. Our results suggest the existence of individually heterogeneous-but-stable patterns of visual information acquisition based on subjective levels of strategic sophistication and social preferences.},
  author = {Polonio, Luca and {Di Guida}, Sibilla and Coricelli, Giorgio},
  doi = {10.1016/j.geb.2015.09.003},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Polonio, Di Guida, Coricelli - 2015 - Strategic sophistication and attention in games An eye-tracking study.pdf:pdf},
  issn = {08998256},
  journal = {Games and Economic Behavior},
  keywords = {Attention,C71,C72,C83,C91,D83,Eye-tracking,Game theory,Social preferences,Strategic sophistication},
  pages = {80--96},
  title = {{Strategic sophistication and attention in games: An eye-tracking study}},
  volume = {94},
  year = {2015}
}
@article{Rapoport1992,
  abstract = {A general conclusion, widely and uniformly supported by a variety of experiments, is that humans are unable to produce a random series of discrete responses, even when instructed to do so. Several arguments are advanced to show that the experimental evidence in support of this claim is plagued with logical and methodological difficulties. Using a new research paradigm, this article reports experimental results showing that people can generate binary sequences that satisfy standard tests of randomness more successfully when they participate in 2-person strictly competitive games inducing them to conceal their choices and protect themselves from their own frailty to maximize gain. The results are discussed within the framework of existing theories of cognitive biases in random-sequence generation.},
  author = {Rapoport, Amnon and Budescu, David V.},
  doi = {10.1037/0096-3445.121.3.352},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/00004785-199209000-00011.pdf:pdf},
  issn = {0096-3445},
  journal = {Journal of Experimental Psychology: General},
  number = {3},
  pages = {352--363},
  title = {{Generation of random series in two-person strictly competitive games.}},
  volume = {121},
  year = {1992}
}
@article{Rapoport1997,
  abstract = {There is ample evidence that people cannot generate random series when instructed to do so. Rather, they produce sequences with too few symmetries and long runs and too many alternations among events. The authors propose a psychological theory to account for these findings, which assumes that subjects generate nonrandom sequences that locally represent theoretical random series subject to a constraint on their short-term memory. Closed-form expressions are then derived for the major statistics that have been used to test for deviations from randomness. Results from 3 experiments with 2 and 3 equiprobable alternatives support the model on both the individual and group levels. (PsycINFO Database Record (c) 2012 APA, all rights reserved)},
  address = {US},
  author = {Rapoport, Amnon and Budescu, David V},
  doi = {10.1037/0033-295X.104.3.603},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/00006832-199707000-00008.pdf:pdf},
  issn = {1939-1471(Electronic);0033-295X(Print)},
  journal = {Psychological Review},
  keywords = {*Choice Behavior,*Cognitive Processes,*Decision Making,*Short Term Memory,Group Decision Making,Models},
  number = {3},
  pages = {603--617},
  publisher = {American Psychological Association},
  title = {{Randomization in individual choice behavior.}},
  volume = {104},
  year = {1997}
}
@article{Reutskaja2011,
  author = {Reutskaja, Elena and Nagel, Rosemarie and Camerer, Colin F and Rangel, Antonio},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Reutskaja et al. - 2014 - Search Dynamics in Consumer Choice under Time Pressure An Eye- Tracking Study.pdf:pdf},
  issn = {00028282},
  journal = {The American Economic Review},
  number = {2},
  pages = {900--926},
  publisher = {American Economic Association},
  title = {{Search Dynamics in Consumer Choice under Time Pressure: An Eye- Tracking Study}},
  volume = {101},
  year = {2011}
}
@article{Richstone2010,
  abstract = {OBJECTIVE: Currently, surgical skills assessment relies almost exclusively on subjective measures, which are susceptible to multiple biases. We investigate the use of eye metrics as an objective tool for assessment of surgical skill. SUMMARY BACKGROUND DATA: Eye tracking has helped elucidate relationships between eye movements, visual attention, and insight, all of which are employed during complex task performance (Kowler and Martins, Science. 1982;215:997-999; Tanenhaus et al, Science. 1995;268:1632-1634; Thomas and Lleras, Psychon Bull Rev. 2007;14:663-668; Thomas and Lleras, Cognition. 2009;111:168-174; Schriver et al, Hum Factors. 2008;50:864-878; Kahneman, Attention and Effort. 1973). Discovery of associations between characteristic eye movements and degree of cognitive effort have also enhanced our appreciation of the learning process. METHODS: Using linear discriminate analysis (LDA) and nonlinear neural network analyses (NNA) to classify surgeons into expert and nonexpert cohorts, we examine the relationship between complex eye and pupillary movements, collectively referred to as eye metrics, and surgical skill level. RESULTS: Twenty-one surgeons participated in the simulated and live surgical environments. In the simulated surgical setting, LDA and NNA were able to correctly classify surgeons as expert or nonexpert with 91.9{\%} and 92.9{\%} accuracy, respectively. In the live operating room setting, LDA and NNA were able to correctly classify surgeons as expert or nonexpert with 81.0{\%} and 90.7{\%} accuracy, respectively. CONCLUSIONS: We demonstrate, in simulated and live-operating environments, that eye metrics can reliably distinguish nonexpert from expert surgeons. As current medical educators rely on subjective measures of surgical skill, eye metrics may serve as the basis for objective assessment in surgical education and credentialing in the future. Further development of this potential educational tool is warranted to assess its ability to both reliably classify larger groups of surgeons and follow progression of surgical skill during postgraduate training.},
  author = {Richstone, Lee and Schwartz, Michael J and Seideman, Casey and Cadeddu, Jeffrey and Marshall, Sandra and Kavoussi, Louis R},
  doi = {10.1097/SLA.0b013e3181e464fb},
  issn = {1528-1140 (Electronic)},
  journal = {Annals of Surgery},
  keywords = {Clinical Competence,Discriminant Analysis,Eye Movements,Humans,Neural Networks (Computer),Surgical Procedures, Operative,standards},
  language = {eng},
  number = {1},
  pages = {177--182},
  pmid = {20562602},
  title = {{Eye metrics as an objective assessment of surgical skill.}},
  volume = {252},
  year = {2010}
}
@article{Roth1998,
  author = {Roth, Alvin and Erev, Ido},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/117009.pdf:pdf},
  journal = {American Economic Review},
  number = {4},
  pages = {848--881},
  title = {{Prediction how people play games: Reinforcement learning in games with unique strategy equilibrium}},
  volume = {88},
  year = {1998}
}
@article{Rubaltelli2012,
  abstract = {We employed simple gambles to investigate information processing in relation to the compatibility effect. Subjects should be more likely to engage in a deliberative thinking strategy when completing a pricing task rather than a rating task. We used eye-tracking methodology to measure information acquisition and processing in order to test the above hypothesis as well as to show that losses and alternatives with uncertain outcomes are more likely than gains and alternatives with sure outcomes to be processed through a deliberative thinking process. Results showed that pupil dilations, fixation duration and number of fixations increased when subjects evaluated the gambles with a pricing task. Additionally, the number of fixations increased as the gamble outcome became increasingly negative and when the outcome was uncertain (vs. sure). Fixations were also predictive of subjects' final evaluations of the gambles. We discuss our results in light of the cognitive processes underlying different response modes in economic preferences.},
  author = {Rubaltelli, Enrico and Dickert, Stephan and Slovic, Paul},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Rubaltelli, Dickert, Slovic - 2012 - Response mode, compatibility, and dual-processes in the evaluation of simple gambles An eye-trackin.pdf:pdf},
  journal = {Judgment and Decision Making},
  keywords = {compatibility effect,dual-process theory,gambles,loss aversion,risk,uncertainty},
  number = {4},
  pages = {427--440},
  title = {{Response mode, compatibility, and dual-processes in the evaluation of simple gambles: An eye-tracking investigation}},
  volume = {7},
  year = {2012}
}
@article{Schulte-Mecklenbeck2011,
  abstract = {The aim of this article is to evaluate the contribution of process tracing data to the development and testing of models of judgment and decision making (JDM). We draw on our experience of editing the " Handbook of process tracing methods for decision research " recently published in the SJDM series. After a brief introduction we first describe classic process tracing methods (thinking aloud, Mouselab, eye-tracking). Then we present a series of examples of how each of these techniques has made important contributions to the development and testing of process models of JDM. We discuss the issue of large data volumes resulting from process tracing and remedies for handling those. Finally, we argue for the importance of formulating process hypotheses and opt for a multi-method approach that focuses on the cross-validation of findings.},
  author = {Schulte-Mecklenbeck, Michael and K{\"{u}}hberger, Anton and Ranyard, Rob},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Schulte-Mecklenbeck, K{\"{u}}hberger, Ranyard - 2011 - The role of process data in the development and testing of process models of judgment a.pdf:pdf},
  journal = {Judgment and Decision Making},
  keywords = {decision making,model building,process tracing},
  number = {8},
  pages = {733--739},
  title = {{The role of process data in the development and testing of process models of judgment and decision making}},
  volume = {6},
  year = {2011}
}
@article{Scroggin2007,
  author = {Scroggin, Steven},
  doi = {10.1016/j.jet.2005.11.001},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/felix szkola/1-s2.0-S0022053105002474-main.pdf:pdf},
  issn = {00220531},
  journal = {Journal of Economic Theory},
  keywords = {behavioral economics,bounded rationality,experimental economics,game theory,local representativeness},
  number = {1},
  pages = {219--235},
  title = {{Exploitable actions of believers in the 'law of small numbers' in repeated constant-sum games}},
  volume = {133},
  year = {2007}
}
@article{Shachat2002,
  author = {Shachat, Jason M.},
  doi = {10.1006/jeth.2001.2915},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0022053101929151-main.pdf:pdf},
  issn = {00220531},
  journal = {Journal of Economic Theory},
  keywords = {experiments,minimax,mixed-strategy},
  number = {1},
  pages = {189--226},
  publisher = {Elsevier Science (USA)},
  title = {{Mixed Strategy Play and the Minimax Hypothesis}},
  volume = {104},
  year = {2002}
}
@book{shelling,
  author = {Schelling, Thomas C.},
  title = {The strategy of conflict },
  publisher = { Harvard University Press Cambridge },
  pages = { 309 p. },
  year = { 1960 },
  type = { Book },
  language = { English },
  subjects = { Negotiation.; Games of strategy (Mathematics) },
  life-dates = { 1960 -  }
}
@article{Stewart2016,
  author = {Stewart, Neil and G{\"{a}}chter, Simon and Noguchi, Takao and Mullett, Timothy L.},
  doi = {10.1002/bdm.1901},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Stewart et al. - 2016 - Eye Movements in Strategic Choice.pdf:pdf},
  issn = {08943257},
  journal = {Journal of Behavioral Decision Making},
  keywords = {accumulator models,cognitive hierarchy,dove,drift diffusion,experimental games,eye tracking,gaze bias effect,gaze cascade effect,hawk,level‐k,normal‐form games,prisoner's dilemma,process tracing,stag hunt},
  number = {2-3},
  pages = {137--156},
  title = {{Eye Movements in Strategic Choice}},
  volume = {29},
  year = {2016}
}
@article{VanEssen2015,
  author = {{van Essen}, Matt and Wooders, John},
  doi = {10.1016/j.geb.2015.02.014},
  file = {:C$\backslash$:/Users/m3kro\_000/Downloads/1-s2.0-S0899825615000378-main.pdf:pdf},
  issn = {10902473},
  journal = {Games and Economic Behavior},
  number = {6},
  pages = {186--206},
  publisher = {Elsevier Inc.},
  title = {{Blind Stealing : Experience and Expertise in a Mixed-Strategy Poker Experiment}},
  volume = {91},
  year = {2015}
}
@book{von2007theory,
  title = {Theory of games and economic behavior},
  author = {{von Neumann}, John and Morgenstern, Oskar},
  year = {1944},
  publisher = {Princeton university press}
}
@article{Rubinstein1991,
  abstract = {The paper is a discussion of the interpretation of game theory. Game theory is viewed as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict and not as an attempt to predict behavior. The first half of the paper deals with the notion of "strategy." Its principal claim is that the conventional interpretation of a "strategy" is not consistent with the manner in which it is applied, and that this inconsistency frequently results in confusion and misunderstanding. In order to prove this point, the term "strategy" is discussed in three contexts: extensive games in which players have to act more than once in some prespecified order, games normally analyzed using mixed strategies, and games with limited memory. The paper endorses the view that equilibrium strategy describes a player's plan of action, as well as those considerations which support the optimality of his plan rather than being merely a description of a "plan of action." Deviation from the perception of a strategy as a mere "plan of action" fits in well with the interpretation of the notion "game" which is discussed in the second half of this paper. It is argued that a good model in game theory has to be realistic in the sense that it provides a model for the perception of real life social phenomena. It should incorporate a description of the relevant factors involved, as perceived by the decision makers. These need not necessarily represent the physical rules of the world. It is not meant to be isomorphic with respect to "reality" but rather with respect to our perception of regular phenomena in reality.},
  author = {Rubinstein, Ariel},
  doi = {10.2307/2938166},
  file = {:C$\backslash$:/Users/mkrol1@swps.edu.pl/Downloads/2938166.pdf:pdf},
  isbn = {00129682},
  issn = {0012-9682},
  journal = {Econometrica},
  number = {4},
  pages = {909--924},
  title = {{Comments on the Interpretation of Game Theory}},
  volume = {59},
  year = {1991}
}
@article{Aumann1995,
  abstract = {Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe--about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When n ≥ 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight.},
  author = {Aumann, Robert J and Brandenburger, Adam},
  doi = {10.2307/2171725},
  file = {:C$\backslash$:/Users/mkrol1@swps.edu.pl/Downloads/2171725.pdf:pdf},
  isbn = {00129682},
  issn = {0012-9682},
  journal = {Econometrica},
  keywords = {NE,Nash equilibrium,belief,belief systems,common knowledge,common prior,conjectures,epistemic conditions,equilibrium,game theory,interactive belief systems,knowledge,mixed strategies,mutual knowledge,rationality,strategic equilibrium,strategic games},
  number = {5},
  pages = {1161--1180},
  pmid = {367764},
  title = {{Epistemic Conditions for Nash Equilibrium}},
  volume = {63},
  year = {1995}
}
@article{Reny2004,
  abstract = {We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern's classical concealment role of mixing, as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, IG, in which each player's type is the probability he assigns to the event that his mixed strategy in G is "found out" by his opponent. We show that, generically, any regular equilibrium of G can be approximated by an equilibrium of IG in which almost every type of each player is strictly optimizing. This leads us to interpret i's equilibrium mixed strategy in G as a combination of deliberate randomization by i together with uncertainty on j's part about which randomization i will employ. We also show that such randomization is not unusual: for example, i's randomization is nondegenerate whenever the support of an equilibrium contains cyclic best replies. ?? 2004 Elsevier Inc. All rights reserved.},
  author = {Reny, Philip J. and Robson, Arthur J.},
  doi = {10.1016/j.geb.2003.09.009},
  file = {:C$\backslash$:/Users/mkrol1@swps.edu.pl/Downloads/10.1.1.198.7814.pdf:pdf},
  issn = {08998256},
  journal = {Games and Economic Behavior},
  pages = {355--384},
  title = {{Reinterpreting mixed strategy equilibria: A unification of the classical and Bayesian views}},
  volume = {48},
  year = {2004}
}
@article{aumann87,
  issn = {00129682, 14680262},
  abstract = {Correlated equilibrium is formulated in a manner that does away with the dichotomy usually perceived between the "Bayesian" and the "game-theoretic" view of the world. From the Bayesian viewpoint, probabilities should be assignable to everything, including the prospect of a player choosing a certain strategy in a certain game. The so-called "game-theoretic" viewpoint holds that probabilities can only be assigned to events not governed by rational decision makers; for the latter, one must substitute an equilibrium (or other game-theoretic) notion. The current formulation synthesizes the two viewpoints: Correlated equilibrium is viewed as the result of Bayesian rationality; the equilibrium condition appears as a simple maximization of utility on the part of each player, given his information. A feature of this approach is that it does not require explicit randomization on the part of the players. Each player always chooses a definite pure strategy,with no attempt to randomize; the probabilistic nature of the strategies reflects the uncertainty of other players about his choice. Examples are given.},
  author = {Robert J. Aumann},
  journal = {Econometrica},
  number = {1},
  pages = {1-18},
  publisher = {The Econometric Society},
  title = {Correlated Equilibrium as an Expression of Bayesian Rationality},
  volume = {55},
  year = {1987}
}
@article{neillo1987,
  title = {Nonmetric test of the minimax theory of two-person zerosum games},
  author = {O'Neill, Barry},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {84},
  number = {7},
  pages = {2106--2109},
  year = {1987},
  publisher = {National Acad Sciences}
}
@article{Wang2010,
  abstract = {We conduct laboratory experiments on sender-receiver games with an incentive for biased transmission (such as security analysts painting a rosy picture about earnings prospects). Our results confirm earlier experimental findings of “overcommunication”—messages are more informative of the true state than they should be, in equilibrium theory. Furthermore, we used eyetracking to show that senders look much less at receiver payoffs compared to their own payoffs. At the same time, the senders’ pupils dilate when they send deceptive messages, and dilate more when the deception is larger in magnitude. Together, these data are consistent with the hypothesis that figuring out how much to deceive another player is cognitively difficult. Using a combination of sender messages, lookup patterns, and pupil dilation, we can predict the true state about twice as often as predicted by equilibrium. Using these measures would enable receiver subjects to earn 6-8 percent more than they actually do.},
  author = {Wang, Joseph and Spezio, Michael and Camerer, Colin F},
  doi = {10.1257/aer.100.3.984},
  file = {:C$\backslash$:/Users/mkrol1@swps.edu.pl/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wang, Spezio, Camerer - 2010 - Pinocchio ' s Pupil Using Eyetracking and Pupil Dilation To Understand Truth-telling and Deception in Ga.pdf:pdf},
  isbn = {00028282},
  issn = {0002-8282},
  journal = {The American Economic Review},
  pages = {984--1007},
  title = {{Pinocchio's Pupil : Using Eyetracking and Pupil Dilation To Understand Truth-telling and Deception in Games}},
  volume = {3},
  year = {2010}
}
@article{Venkatraman2014,
  abstract = {When faced with multi-outcome gambles involving possibilities of both gains and losses, people often use a simple heuristic that maximizes the overall probability of winning (Pwin). Across three different studies, using choice data as well as process data from eye tracking, we demonstrate that the Pwin heuristic is a frequently used strategy for decisions involving complex (multiple outcome) mixed gambles. Crucially, we show systematic contextual and individual differences in the use of Pwin heuristic. We discuss the implication of these findings in the context of the broader debate about single versus multiple strategies in risky choice, and the need to extend the study of risky decision making from simple to more complex gambles.},
  author = {Venkatraman, Vinod and Payne, John W. and Huettel, Scott A.},
  doi = {10.1016/j.obhdp.2014.06.003},
  issn = {07495978},
  journal = {Organizational Behavior and Human Decision Processes},
  number = {2},
  pages = {73--87},
  title = {{An overall probability of winning heuristic for complex risky decisions: Choice and eye fixation evidence}},
  volume = {125},
  year = {2014}
}
@article{rosenthal90,
  issn = {00129682, 14680262},
  abstract = {In this paper, we re-examine the data from O'Neill's experiment involving a repeated, two-person, constant-sum game. We find that there is less evidence in support of the minimax hypothesis than indicated by O'Neill. There is strong evidence of serial correlation in players' choices, with several players displaying statistically significant dependence on the past moves of their opponents. We interpret this finding as evidence that the players themselves rejected minimax play as the appropriate model for their opponents' behavior. We find no evidence that players' behavior approached minimax behavior as players became more experienced.},
  author = {James N. Brown and Rosenthal, Robert W.},
  journal = {Econometrica},
  number = {5},
  pages = {1065-1081},
  publisher = {The Econometric Society},
  title = {Testing the Minimax Hypothesis: A Re-Examination of {O'Neill's} Game Experiment},
  volume = {58},
  year = {1990}
}
@article{shotter02,
  author = {Nyarko, Yaw and Schotter, Andrew},
  title = {An Experimental Study of Belief Learning Using Elicited Beliefs},
  journal = {Econometrica},
  volume = {70},
  number = {3},
  publisher = {Blackwell Publishers Ltd},
  issn = {1468-0262},
  doi = {10.1111/1468-0262.00316},
  pages = {971--1005},
  keywords = {belief learning, game theory, experimental economics},
  year = {2002}
}
@article{Spiliopoulos2013,
  abstract = {Belief models capable of detecting 2- to 5-period patterns in repeated games by matching the current historical context to similar realizations of past play are presented. The models are implemented in a cognitive framework, ACT-R, and vary in how they implement similarity-based categorization-using either an exemplar or a prototype approach. Empirical estimation is performed on the elicited-belief data from two experiments (Nyarko and Schotter, 2002; Rutstr??m and Wilcox, 2009) using repeated games with a unique, albeit significantly different, stage mixed-strategy Nash equilibrium. Model comparisons are performed by cross-validation both within and between these two datasets, and using data from completely unrelated non-strategic tasks. Subjects' beliefs are best described by 2-period pattern detection. Parameter estimates exhibited considerable instability across the two belief-elicitation datasets, and surprisingly, using median values from a wide variety of unrelated studies led to better predictions. ?? 2013 Elsevier Inc.},
  author = {Spiliopoulos, Leonidas},
  doi = {10.1016/j.geb.2013.04.005},
  file = {:C$\backslash$:/Users/mkrol1@swps.edu.pl/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Spiliopoulos - 2013 - Beyond fictitious play beliefs Incorporating pattern recognition and similarity matching.pdf:pdf},
  isbn = {0899-8256},
  issn = {08998256},
  journal = {Games and Economic Behavior},
  keywords = {ACT-R,Behavioral game theory,Beliefs,Cognitive models,Learning,Memory,Pattern recognition,Repeated games},
  number = {1},
  pages = {69--85},
  publisher = {Elsevier Inc.},
  title = {{Beyond fictitious play beliefs: Incorporating pattern recognition and similarity matching}},
  volume = {81},
  year = {2013}
}
@article{Rutstrom2009616,
  title = {Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test },
  journal = {Games and Economic Behavior },
  volume = {67},
  number = {2},
  pages = {616 - 632},
  year = {2009},
  note = {},
  issn = {0899-8256},
  doi = {10.1016/j.geb.2009.04.001},
  author = {E. Elisabet Rutstrom and Nathaniel T. Wilcox},
  keywords = {Stated beliefs},
  keywords = {Inferred beliefs},
  keywords = {Repeated games},
  keywords = {Experimental methods },
  abstract = {Belief elicitation in game experiments may be problematic if it changes game play. We experimentally verify that belief elicitation can alter paths of play in a two-player repeated asymmetric matching pennies game. Importantly, this effect occurs only during early periods and only for players with strongly asymmetric payoffs, consistent with a cognitive/affective effect on priors that may serve as a substitute for experience. These effects occur with a common scoring rule elicitation procedure, but not with simpler (unmotivated) statements of expected choices of opponents. Scoring rule belief elicitation improves the goodness of fit of structural models of belief learning, and prior beliefs implied by such models are both stronger and more realistic when beliefs are elicited than when they are not. We also find that “inferred beliefs” (beliefs estimated from past observed actions of opponents) can predict observed actions better than the “stated beliefs” from scoring rule belief elicitation. }
}
@article{Wang2011,
  abstract = {(from the chapter) A video-based eye-tracker (e.g., the mobile Eyelink II or Eyelink Remote of SR Research, Osgoode, Ontario, Canada) uses video cameras to record the eye position of human subjects, and hence record pupil dilation and eye movements. The eye-tracker puts video cameras and infrared illuminators in front of the eye to record the position of the eye, cornea reflections, and the size of the pupil. Using the movements of one's pupil (with respect to cornea reflections), the eye-tracker tracks the movement of one's eyes, which is then mapped into locations on the screen by calibration and adjustments for head movements. With the eye-tracker, we can measure gaze locations, the time length of fixations, and pupil dilation. Hence, using the eye-tracker, we can investigate how fixations (looking at the same place for a while), saccades (fast eye movements), and pupil dilation responses (changes in pupil sizes) are related to the information on the screen and behavioral choices during an experiment. Understanding the relationship between these observables can help us to understand how human behavior in the economy can be affected by what information people acquire, where their attention is focused, what emotional state they are in, and even what brain activity they are engaged in. This is because fixations and saccades (matched with information shown on screen) indicate how people acquire information (and what they see), time lengths of fixations indicate attention, and pupil dilation responses indicate emotion, arousal, stress, pain, or cognitive load. This chapter attempts to demonstrate how these measures in pupil dilation and eye tracking can help to study human decision making processes. First we introduce video-based eye tracking and then we review the literature on pupil dilation responses and discuss issues regarding interpretation. Finally we discuss applications of pupil dilation in various tasks of decision making and conclude with a list for further reading. There is also an appendix documenting the "standard operational procedure" of performing eye-tracking studies using either the Eyelink II or Eyelink Remote eye-tracker, intended as a guide for readers who are interested in conducting their own eye-tracking research. (PsycINFO Database Record (c) 2012 APA, all rights reserved) (chapter)},
  author = {Wang, Jt},
  file = {:C$\backslash$:/Users/m3kro/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wang - 2011 - Pupil dilation and eye tracking.pdf:pdf},
  isbn = {978-1-84872-864-6; 978-0-203-87529-2},
  journal = {A handbook of process tracing methods for decision research},
  pages = {1--33},
  title = {{Pupil dilation and eye tracking}},
  year = {2011}
}

This file was generated by bibtex2html 1.98.