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\title{Commitment-enhancing tools in Centipede games: Evidencing European–Japanese differences in trust and cooperation}

\author{
Eva M. Krockow\thanks{Department of Neuroscience, Psychology and Behaviour,
University of Leicester, Leicester LE1 7RH, U.K. E-mail: emk12@le.ac.uk.}
\and
Masanori Takezawa\thanks{Centre for Experimental Research in Social Sciences
and Department of Behavioral Science, Hokkaido University.}
\and
Briony D. Pulford\thanks{Department of
Neuroscience, Psychology and Behaviour, University of Leicester.}
\and
Andrew M. Colman\footnotemark[3]
\and
Samuel Smithers\thanks{Department of Economics, University of
Leicester.}
\and
Toshimasa Kita\thanks{Department of Behavioral Science, Hokkaido
University.}
\and
Yo Nakawake\footnotemark[5]
}

\date{} % leave empty
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\newcommand{\jhead}{Judgment and Decision Making, Vol.~13, No.~1}
\newcommand{\jdate}{January 2018}
\pagestyle{myheadings} \markright{\protect\small \href{\jref}{\jhead},
  \jdate \hfill Commitment-enhancing tools in Centipede games \qquad}
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\href{\jref}{\jhead}, \jdate, pp.\ 61-72
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{\small \href{\jref}{\jhead}, \jdate, pp.\ 61--72}
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\maketitle

%\begin{latexonly}
\vspace{-3mm}
\begin{onecolabstract}
%\end{latexonly}
Theories of trust distinguish general trust in situations of social
uncertainty from assurance-based trust in committed, long-term
relationships. This study investigates European-Japanese differences
using the Centipede game, in which two players choose between
cooperation and defection. The game models repeated reciprocal
interactions, necessitating assurance-based trust to sustain
cooperation. We included game conditions offering players the option of
purchasing commitment-enhancing tools to increase social certainty.
Japanese participants were more cooperative than Europeans, confirming
higher assurance-based trust, and also purchased more
commitment-enhancing tools, demonstrating their preferences for social
certainty. Purchase of commitment-enhancing tools improved
cooperativeness in both groups. However, if co-players refused tool
purchase, the Japanese appeared to interpret this as non-cooperative
intent and cooperativeness in the respective games decreased.

\smallskip
\noindent
Keywords: centipede game; cooperation; cross-cultural differences; trust; reciprocity
%\begin{latexonly}
\end{onecolabstract}\bigskip
]
%\end{latexonly}

{\renewcommand{\thefootnote}{}

\footnotetext{

We are grateful to the Leicester Judgment and Decision Making Endowment
Fund (Grant RM43G0176) and Friedrich-Naumann-Foundation for Freedom for
support in the preparation of this article, and to Anke Gerber for
sharing z-Tree software used for related experiments. 

Copyright: \copyright\ 2018.
The authors license this article under the terms of the
\href{http://creativecommons.org/licenses/by/3.0/}{Creative Commons
  Attribution 3.0 License.}
}}

\saythanks

\section{Introduction}

Cross-cultural differences in trust and cooperation — despite their
importance for international business partnerships and global human
interaction — remain to be fully understood (Krockow, Takezawa, Pulford,
Colman \& Kita, 2017). Of particular interest are differences between
countries with comparable industrial development but contrasting
cultural and religious backgrounds, such as Northern European countries
compared with East Asian nations such as Japan.

Previous cross-cultural research has differentiated between
\textit{assurance-based trust} and \textit{general trust} (Yamagishi
\& Yamagishi, 1994). Japanese society was suggested to be high in
assurance-based trust, the type of trust necessary in relationships of
high social certainty and an expectation of repeated future
interactions with the same other.\footnote{The concept of
  “assurance-based trust” appears to be related to what Russel Hardin
  (2002) described as “encapsulated trust”. However, for the purpose
  of consistency across the manuscript, we will use the terminology
  originally introduced by Yamagishi and Yamagishi (1994).} Examples
include historically close family bonds, tight business groups
(so-called \textit{keiretsu}), and life-long employment with the same
company (e.g., Kim, Hoskisson \& Wan, 2004; Spencer \& Qiu 2001).
Western societies (particularly North America), on the other hand,
were characterized by general trust, with low social certainty when
interacting with strangers in the face of incentives for dishonesty or
defection. Examples of North American society requiring high levels of
general trust include more liberal attitudes to family
responsibilities and regular staff change-over in business firms in
order to maintain flexibility and innovation. General trust is
arguably also required in ordinary commerce with strangers, especially
between individuals who do not expect to meet again.

Empirical literature supporting this trust theory is provided by
Krockow, Takezawa, Pulford, Colman and Kita. (2017), demonstrating
that Japanese participants, compared to Western participants, (a)
cooperated more frequently in decision situations with higher sense of
control; (b) showed higher levels of reciprocity and trustworthiness;
and (c) exhibited more trust towards a familiar co-player. This lends
support to Yamagishi and Yamagishi’s (1994) theory postulating
assurance-based trust to be more prevalent in Japan than in Western
cultures.

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig1.eps}
\caption{Standard Centipede game.}
\end{figure}

Only one experimental study to date has investigated Japanese decision
making within the stable, reciprocal partnerships claimed to be
characteristic of Japanese society (Krockow et al.\ 2017). That study
and the present research use Rosenthal’s (1981) Centipede game as a
research paradigm (Figure 1). This game involves two players making
alternating choices either to continue horizontally through a GO move
or to STOP the game and follow the vertical line down to an exit point
with an immediate payoff. Player A chooses at odd-numbered decision
points or \textit{nodes} and Player B at even-numbered nodes. The
payoffs, representing monetary units — including British Pounds
Sterling and Japanese Yen — are shown at the bottom of the diagram
with Player A’s payoffs above Player B’s. The number of decision nodes
is limited to eight but could be extended indefinitely to model longer
relationships.

As shown in the payoff function, every GO move increases the players’
combined payoffs by 6 monetary units. GO increases the co-player’s
payoff by 11 units while decreasing the GO-chooser’s personal payoff
by 5. Hence, a GO move can be interpreted as cooperative action
benefitting both the dyadic team and the co-player, while risking a
personal disadvantage should the co-player decide to STOP at the
following node. A STOP move, on the other hand, always terminates the
game with a higher personal payoff than the co-player and can
therefore be interpreted as defection. The Centipede game provides a
dynamic model of the reciprocal human relationships typical of
Japanese society requiring commitment and assurance-based trust to be
maintained.

Interestingly, the rational strategy to employ in the Centipede game —
according to conventional game theory — is for Player 1 to terminate
the game at the very first decision node, the \textit{subgame perfect
  Nash equilibrium}. This solution, which appears to be paradoxical
given the higher payoffs tempting from later exit points in the game,
is derived from mathematical backward induction reasoning (Aumann,
1995; 1998; Broome \& Rabinowicz, 1999; Colman, Krockow, Frosch \&
Pulford, 2017). Starting the analysis at the final decision node (Node
8), Player B has to choose between GO, leading to the game’s natural
end and a personal payoff of 27, and STOP, terminating the game with a
payoff of 32. Since 32 is higher than 27, any rational payoff
maximizer should choose STOP at Node 8. Moving backward to Node 7,
Player A has to decide between GO, which would immediately and
foreseeably be followed by a STOP move of Player B, thus yielding a
personal payoff of 24, or STOP, resulting in immediate game
termination with a payoff of 29. Again, any rational agent would
decide to STOP at this point. This type of reasoning, requiring
step-wise perspective-taking, can be continued to the very beginning
of the game where it mandates immediate and unconditional defection by
Player A at Node 1.

In contrast with the backward induction argument, the bulk of research
on the Centipede game suggests that human decision makers cooperate
frequently (e.g., Levitt, List \& Sadoff, 2011; Krockow, Pulford \&
Colman, 2015; Krockow, Colman \& Pulford, 2016b; McKelvey \& Palfrey, 1992). Across experiments, many
games reached the natural end — an outcome dependent on Player B’s
altruistic GO move at the last decision node. In an experiment by
Bornstein, Kugler and Ziegelmeyer (2004) as many as 16.5\% of games
reached the final exit point.

However, only one Centipede study using a Japanese sample (Kawagoe \&
Takizawa, 2012), and one cross-cultural experiment (Krockow et al.,
2017) have been published (see Krockow, Colman \& Pulford, 2016a, for a
review). The current study aimed to build on earlier research by using
a modified game version, enabling a more advanced investigation of
trust and relationship commitment. Specific objectives included
providing a further test of the hypothesized Japanese preference for
social certainty and their strong reliance on assurance-based trust
compared to Western samples. Our design was based on a research
paradigm originally developed by Gerber and Wichardt (2010). Their
experiment included Centipede game conditions with optional tools to
improve players’ commitment and payoff certainty.

The \textit{bonus tool} involved offering the co-player an incentive,
at a personal cost \textit{b,} for not ending the game. This incentive
was deducted from the payoff of any player who used the tool and added
to the co-player’s payoff whenever the player with the tool chose
STOP. The \textit{insurance tool} required an initial monetary
sacrifice at cost \textit{c}, deducted from all payoffs to a player
who used this tool but reimbursed if the co-player chose to STOP at
any point in the game.  Both tools were designed to remove the other
player’s fear that the tool-user would rationally quit, and
consequently, the other player’s reason for quitting herself. Hence,
the tools’ costs reflected the financial price that players had to pay
for this disincentive to stop.  Rather than paying the cost from a
personal endowment, the respective monetary units were deducted from
the overall payoffs to be earned in the games. Even though both
instruments were effective, the bonus tool required lower levels of
iterated reasoning for participants to understand its benefits. In
line with Gerber and Wichardt’s (2010) predictions, participants chose the
comparatively simpler bonus tool more frequently than the insurance
tool, but the use of either tool resulted in later game exits (greater
cooperation). The authors interpreted the findings as evidence for
limited reasoning skills and as an explanation for cooperation in the
Centipede game.

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig2.eps}
\caption{Bonus condition: Changes to the standard payoff
function if Player A decides to purchase the bonus tool.}
\end{figure}  

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig3.eps}
\caption{Insurance condition: Changes to the standard payoff
function if Player A decides to purchase the insurance tool.}
\end{figure}  

However, whereas usage of the above tools could indeed inform about
backward induction reasoning skills, other-regarding preferences — for
example considerations of commitment and social certainty — may also play
a role. This is because the purchase of either tool requires an initial
commitment in the form of voluntary reductions of personal payoffs at
particular decision nodes, while it increases social certainty in the
game through the disincentive to defect. Hence, it is possible to
conceptualize tool use as a voluntary institution or a prosocial
mechanism supporting cooperation in dyadic relationships. The present
study employed Gerber and Wichardt’s (2010) research paradigm to study
cross-cultural differences in commitment and cooperation. In addition
to the standard Centipede game, we included a bonus condition and an
insurance condition, where tools could be purchased by the players at
the beginning of each game. Figures 2 and 3 illustrate the effects on
payoff functions of typical combinations of tool use (i.e., in the
event that only Player A opts for the bonus or the insurance
respectively). For each figure, the top part shows the original
Centipede game. The game in the center shows the payoffs when only
Player A purchases a tool. Finally, the bottom part displays the new
payoff function after applying the changes caused by Player A’s tool
purchase. 

In line with Gerber and Wichardt’s (2010) original design, our bonus
tool involves offering the co-player an incentive at a personal cost
\textit{b} for not stopping the game. In our experiment, \textit{b} =
7, meaning that 7 monetary units are taken from the individual who
purchases the tool and added to the co-player’s payoff only in the
event of that individual’s STOP move (at odd-numbered exit nodes). The
consequent changes to the payoff function show that both players’
payoffs are affected by Player A’s purchase of the bonus and, as a
result, both players’ payoffs strictly increase from one decision node
to the next until reaching Node 8. This change to the payoff function
also alters the game’s equilibrium solution: Applying backward
induction reasoning, neither player has a rational reason to terminate
the game before the 8th decision node. 

In the insurance condition, tool purchase involves an initial monetary
sacrifice deducted from all personal payoffs in the game of the player
who chose the tool. To match the cost of the bonus tool, we set
\textit{c} = 7. Consequently, 7 monetary units are deducted from all of
Player A’s payoffs; see Figure 3. The tool further includes
reimbursement of the insurance cost in case of a STOP move by the
co-player. This is reflected in the repayment of 7 units to Player A at
all even-numbered nodes (nodes where Player B could terminate the
game). Only Player A’s payoffs are affected by tool purchase in this
condition, resulting in a strict increase from one node to another. As
in the bonus condition, these changes alter the game’s equilibrium
solution. Player A no longer has an incentive to defect, thus mandating
cooperation until Node 8. As a result, Player B no longer needs to fear
that Player A will defect rationally. With this fear lifted, Player B’s
reason for defection — the pre-emption of Player A’s possible STOP
move — is removed, too. Consequently, both players are rationally
expected to cooperate in the altered game version.

Both tools require an initial commitment, because their purchase
involves voluntarily reducing personal payoffs at certain decision
nodes in the game. Moreover, they have similar consequences: they
change the payoff function and create higher social certainty. The new
game-theoretic solutions prescribe cooperation until the near-end in
both cases and thus foster reciprocal GO moves. Given the obvious
benefits of choosing GO in the altered Centipede games, the co-players’
intentions are also easier to predict. Nevertheless, whereas the bonus
tool affects both players’ payoffs, yielding easily observable
consequences that do not require any perspective-taking, this is not
the case for the insurance tool. Buying insurance affects only the
payoffs of the insured player and leaves the co-player’s payoffs
unchanged. To recognize the benefits of the insurance tool, the
co-player has to perform iterated reasoning, taking into account the
insured player’s incentives and likely intentions. 

To sum up, the use of either tool indicates commitment and preference
for social certainty. Furthermore, in addition to the tools’ direct
influences on the payoff functions, the mere choice of purchasing a
tool might signal cooperativeness to the other player, thereby leading
to higher levels of overall assurance-based trust and cooperation.
These aspects could be of particular importance to Japanese
participants, who are historically used to close, committed
relationships with low uncertainty. However, only the insurance tool
requires higher cognitive reasoning skills. This also entails the
tool-user’s assumption that the co-player possesses similar skills to
recognize tool purchase as insurance in the game. Comparing the bonus
and the insurance conditions can therefore expose variations in
cognitive abilities. We hypothesized that in both Japan and Europe, the
simpler bonus tool would be chosen more frequently than the insurance
tool. For both samples, both tools were expected to increase
cooperation relative to games without tool purchases. Due to the higher
need for social certainty attributed to the Japanese participants, we
further hypothesized that the Japanese would purchase significantly
more commitment-enhancing tools than the Europeans. 

Finally, to assess the effects of individual difference variables
other than assurance-based trust itself, this study included the same
personality questionnaires assessing social value orientation (SVO),
general trust and risk-taking as used in Krockow et al.’s (2017)
earlier experiment. On the basis of our previous research in the area,
we did not anticipate significant differences between Japan and Europe
in SVO. However, we hypothesized that Japanese participants would
score lower than European participants on measures of risk-taking and
— possibly — general trust, and that individual differences in SVO,
risk-taking and trust could correlate significantly with
cooperativeness in the Centipede game, because of earlier findings
(Pulford, Colman, Lawrence \& Krockow, 2016; Pulford, Krockow, Colman
\& Lawrence, 2016).

\section{Method}

\textbf{Subjects.} The sample comprised 60 Japanese nationals from
Hokkaido University in Japan and 54 European subjects from the
University of Leicester in the UK. All subjects were undergraduate
students. The study was advertised on established online recruitment
systems for participation in psychology experiments at the respective
universities, and subjects could sign up electronically. In Japan,
the sample comprised 34 males, 25 females and one of unknown gender,
with a mean age of 18.81 years (\textit{SD} = 0.71). The sample in the
UK included 9 males, 44 females and one of unknown gender, with a mean
age of 18.65 years (\textit{SD} = 0.94). In both countries, a
between-subjects random lottery incentive system was used to
incentivize choices in the games (see Bolle, 1990, and Cubitt, Starmer
\& Sugden, 1998, for a discussion of this incentive scheme). In
particular, from each of the 6 testing sessions (three sessions in
Japan and three in the UK), one subject was randomly chosen to win
a payoff from a randomly selected played game. The games’ payoffs were
converted into Japanese Yen and British Pounds Sterling at rates of
242.32 and 1.36 respectively, to result in comparable stakes and
consequent payments. In Japan, the three lottery winners received an
average of ¥5173.3 (US\$43.78), and in the UK, they won an average of
£28.3 (US\$40.32). 

\textbf{Design.} The experiment was based on a 2 (Sample) × 3
(Condition) design. The subjects of both samples (Japanese and
European) were randomly assigned to one out of three game conditions:
(a) Standard Centipede game (Condition 1); (b) Centipede game with
bonus tool (Condition 2); (c) Centipede game with insurance tool
(Condition 3). The main dependent variable to compare cooperativeness
in the games across testing sessions was the mean exit point of the 20
game rounds an individual completed during the course of the
experiment, with higher scores showing later exiting (i.e., higher
cooperation levels), and lower scores earlier exiting (i.e., lower
cooperation levels). Additionally, to measure the level of commitment
and preference for social certainty of an individual, the total number
of tool purchases was calculated. A maximum score of 20 indicated very
high commitment and strong preference for social certainty whereas
lower scores suggested accordingly lower levels of commitment. 

\textbf{Materials.} The testing sessions were conducted in large
laboratories equipped with computer desks separated with dividing
walls. Subjects saw the other subjects when entering the
laboratories. It is possible that some subjects knew each other.
However, once they sat down, they were shielded by the dividing walls,
and could no longer observe other subjects. At no time were they
aware of what the co-player in any particular game looked like. Hence,
even if they got partnered with a known person by chance, they were
unaware of this fact. All subjects received colorfully illustrated
instruction booklets — in Japanese or in English — with detailed
explanations of example situations in the games. They interacted in the
games through z-Tree software (Fischbacher, 2007) on their computers,
which provided real-time feedback about the co-players’ choices and the
outcome of the current as well as previous games. The Japanese
subjects were presented with a fully translated version of the
software. To assess individual differences, paper copies of the
following questionnaires were distributed: (a) six-item SVO slider
measure (Murphy, Ackermann \& Handgraaf, 2011); (b) 30-item
Domain-specific risk-taking (DOSPERT) scale and respective
risk-perception scale (Blais \& Weber, 2006); and (c) the first five
items of Yamagishi and Yamagishi’s (1994) scale on general trust. 

\textbf{Procedure.} Six testing sessions were conducted, comprising 20
subjects each in Japan and 18 subjects each in the UK. Each
testing session lasted between 60 and 75 minutes. After filling in the
consent form, the subjects read through the instruction booklets in
their own time. Then, the subjects were given a short comprehension
test that the experimenters checked for any misunderstandings. Once
everybody had fully understood the instructions, the computerized
experiment was started. The program randomly assigned each subject
a player role (Player A or B) retained for the whole experiment. The
subjects completed 20 rounds of the Centipede game with random and
anonymous re-pairings after every round. This random matching scheme,
where subjects were paired randomly but could encounter the same
co-player more than once, was used as the closest possible alternative
to a fully rotating matching scheme (perfect stranger matching scheme),
where no co-player is encountered more than once. In the game
conditions with either bonus or insurance tool, the players were given
the option to purchase a tool before the start of each round. The
choices of both players were subsequently revealed on the screen and
the game payoffs incorporating any changes due to tool purchases were
displayed. All subjects were compensated for their time with a
show-up fee or course credits, and the randomly chosen lottery winner
in that session additionally received the payoff from a randomly
selected game they completed in the experiment. 

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig4a.eps}

\includegraphics[clip=true,width=\columnwidth]{fig4b.eps}

\includegraphics[clip=true,width=\columnwidth]{fig4c.eps}
\caption{Percentages of game terminations per exit point
across game conditions and samples.}
\end{figure}  

\section{Results}

\textbf{Analysis of exit points.} Overviews of game terminations per
exit node for the three game conditions are depicted in Figure
4. Striking differences between Japan and Europe are evident, with
Japanese subjects generally cooperating much more frequently than
Europeans. Some differences across conditions are also noticeable in
the graphs, but any interpretation has to be treated with caution due
to comparatively small sample sizes for each condition per country.
In Condition 1 (standard game), the exit points of the Japanese
subjects are skewed toward the right, indicating late game exits,
with the two most frequent exits points being Node 6 and, notably, the
game’s natural end (Node 9) — almost 30\% of games each terminated at
those exit points. Not a single game exited at Node 1. In contrast,
the European sample produced much earlier game exits with the data
skewed toward the left. The two most frequent exit points, with
approximately 20\% of game terminations each, were Nodes 2 and 3, and
not a single game reached the natural end.

%Table 1
\begin{table*}[t]\centering
\caption{Mean exit points, standard deviations, and 95\% confidence intervals per
sample and game condition.}
\begin{tabular}{lc@{\quad}c@{\quad}c@{\quad}c}\toprule
 & C1: Standard condition & C2: Bonus condition & C3: Insurance condition & Total\\\midrule
Japan & 7.23 (0.84) [6.82, 7.65] & 7.27 (1.34) [6.86, 7.70] & 5.92
(0.64) [5.51, 6.34] & 6.81 (1.15) [6.57, 7.05]\\
Europe & 3.76 (0.92) [3.32, 4.20] & 5.18 (0.86) [4.74, 5.62] & 5.12
(0.88) [4.68, 5.56] & 4.69 (1.10) [4.43, 4.94]\\
Total & 5.59 (1.96) [5.19, 5.80] & 6.28 (1.54) [5.92, 6.53] & 5.54
(0.86) [5.22, 5.83] & 5.80 (1.55) [5.57, 5.92]\\\bottomrule
\end{tabular}
\end{table*}

In Condition 2 (bonus game), completely different exit patterns were
found. In both samples, game terminations show a wide spread across
exit nodes. The Japanese data feature a large spike at Node 9, with a
remarkable 62.5\% of games reaching this natural end. For the UK, Nodes
5 and 6 show the highest percentages of game exits with 16.1\% and
17.2\% respectively but this condition also yielded a substantial
percentage of games reaching the natural end (12.2\%).

Condition 3 (insurance game) again yielded wide data spreads for both
samples. Over 90\% of Japanese games ended at Nodes 4–8, and only 3.5\%
reached the natural end. The European sample produced very mixed
results, with the most frequent exit points being Nodes 4, 6, and 8
(all between 16.5\% and 19\%) and very few games terminating at Node 9
(1.7\%).

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig5a.eps}

\includegraphics[clip=true,width=\columnwidth]{fig5b.eps}
\caption{Percentage of games where no, one or two players
purchased tools across the bonus and the insurance game conditions and
the two samples.}
\end{figure}

A two-way ANOVA tested for effects of sample and game conditions on
mean exit points. Descriptive statistics are displayed in Table
1. There was a significant main effect of sample: the mean exit point
of the Japanese sample (\textit{M }= 6.81; \textit{SD }= 1.15) was
significantly higher than that of the European sample (\textit{M }=
4.69; \textit{SD }= 1.1), \textit{F}(1, 108) = 145.153, \textit{p}
{\textless} .001, $\eta_p^2$ = .57. Another main effect was found for
the game condition, \textit{F}(2, 108) = 7.359, \textit{p} {\textless}
.005, $\eta_p^2$ = .12. For both samples taken together, the insurance
condition produced the lowest exit points (\textit{M }= 5.54;
\textit{SD }= 0.86), followed by the standard game condition
(\textit{M }= 5.59; \textit{SD }= 1.96), and then the bonus condition
(\textit{M }= 6.28; \textit{SD }= 1.54). Post-hoc comparisons using
Tukey HSD tests indicated significant differences between the bonus
condition and both other game conditions (\textit{p} {\textless}
.005). However, these results have to be interpreted with caution, as
the two factors also interacted significantly, \textit{F}(2, 108) =
19.217, \textit{p} {\textless} .001, $\eta_p^2$ = .26, indicating that
the effect of the game condition depended on the sample. In Japan, the
first two conditions produced similar mean exit points, but the mean
for the insurance condition was significantly lower (\textit{p
}{\textless} .001). In Europe, the standard game produced
significantly lower exit points than both the bonus and the insurance
game, (\textit{p }{\textless} .001).

To check for any confounding gender effects in the context of different gender proportions across the two samples, a three-way ANOVA was carried out, investigating the effects of gender in addition to those of the sample and game condition on mean exit points. No significant main effect of gender was found, \textit{F}(1, 100) = 2.152, \textit{p} = .145, nor any two-way or three-way interactions including gender. To test
for learning effects, temporal exit patterns across the 20 game rounds
were examined, but non-significant results from time series analysis
indicated no significant behavioral adaptation based on experience. 

% What were the gender correlations.

%Table 2 
\begin{table*}[t]\centering
\caption{Mean numbers of tools purchased, standard deviations, and 95\% confidence intervals per sample and game condition.}
\begin{tabular}{lc@{\quad}c@{\quad}c}\toprule
 & C2: Bonus condition & C3: Insurance condition & Total\\\midrule
Japan & 7.90 (8.57) [5.21, 10.59] & 4.80 (6.13) [2.11, 7.49] & 6.35
(7.52) [4.45, 8.25]\\
Europe & 2.44 (3.81) [$-$0.39, 5.28] & 4.17 (3.93) [1.33, 7.00] & 3.31
(3.91 [1.30, 5.31]\\
Total & 5.32 (7.21) [3.22, 7.13] & 4.50 (5.15) [2.53, 6.44] & 4.91
(6.24) [3.45, 6.21]\\\bottomrule
\end{tabular}
\end{table*}

\textbf{Analysis of tool purchase.} Figure 5 reveals large differences
in the bonus condition: in Japan less than a third of all games
(32.5\%) were played without a bonus purchase of either player. For
most games, only one player purchased this tool, but in many games
(11.5\%) both players purchased the bonus. In the UK, the percentage of
games with no bonus purchases was more than twice as high as in Japan
(76.1\%), and in only 23.3\% of games did one player choose the bonus
tool. In only one game out of 180, did both players purchase the tool. 

For the insurance condition, cross-cultural differences were absent. In
both samples, most games were completed without an insurance tool
purchase, and 40\% of games where played following tool purchase by one
player. The proportion of games in which both players purchased a tool
was very low in both samples (${\leq}$ 5\%).

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig6a.eps}

\includegraphics[clip=true,width=\columnwidth]{fig6b.eps}
\caption{Proportion of players who purchased a tool in each
game round in the bonus and insurance conditions across samples.}
\end{figure}  

A two-way ANOVA investigated the effects of sample and game condition
on the number of tools purchased per subject. Means, standard
deviations and 95\% confidence intervals are displayed in Table 2. The
mean number of tools purchased in Japan (\textit{M }= 6.35; \textit{SD
}= 7.52) was significantly higher than in Europe (\textit{M }= 3.31;
\textit{SD }= 3.91), \textit{F}(1, 72) = 4.83, \textit{p} {\textless}
.05, $\eta_p^2$ = .063. No main effect was found for the game
condition, \textit{F}(1, 72) = 0.247, \textit{p} = .62, and the
interaction was also non-significant, \textit{F}(1, 72) = 3.029,
\textit{p} = .086. Even though the two-way ANOVA found non-significant
differences between treatments, a separate t-test for the Bonus
condition alone showed particularly large differences between the
numbers of bonus tools purchased in Europe (\textit{M} = 2.44;
\textit{SD} = 3.81) and Japan (\textit{M} = 7.90; \textit{SD} = 8.57),
\textit{t} (36) = 2.486, \textit{p} {\textless} .05, \textit{d} =
0.808.

Temporal patterns in tool purchase are shown in Figure 6. Time series
analysis revealed a learning curve of the Japanese subjects in the
Insurance condition, with the number of tool purchases increasing
across rounds. An exponential smoothing Holt model provided the best
fit, indicating a significant linear increase in tool purchase. An
estimate of the model’s goodness of fit yielded a value of
\textit{R}\textsuperscript{2} = .32, hence the model explains more
than 30\% of the data variance. The Ljung-Box statistic \textit{Q }was
calculated to test whether the model was correctly specified, and
\textit{Q}(16) = 7.17, (\textit{p} = .97) showed that no significant
patterns in the data set were unaccounted for by the Holt linear
model. Analysis revealed~no~significant learning patterns pertaining
to tool purchase in any other game condition.

\begin{figure}[t!]
\includegraphics[clip=true,width=\columnwidth]{fig7a.eps}

\includegraphics[clip=true,width=\columnwidth]{fig7b.eps}

\includegraphics[clip=true,width=\columnwidth]{fig7c.eps}
\caption{Percentages of game terminations per exit node when
no tools were purchased.}
\end{figure}
 
\begin{figure*}[t!]\centering
\includegraphics[clip=true,width=\columnwidth]{fig8a.eps}\quad%
\includegraphics[clip=true,width=\columnwidth]{fig8b.eps}

\includegraphics[clip=true,width=\columnwidth]{fig8c.eps}\quad%
\includegraphics[clip=true,width=\columnwidth]{fig8d.eps}
\caption{Percentages of game terminations per exit node when
tools were purchased.}
\end{figure*}

Additional analyses were conducted to compare the exit points of games
in which no player, one player or both players purchased
tools. Figures 7 and 8 show the percentages of games terminating at
each exit point across game conditions and samples, and it appears
that games in which no player purchased a tool (zero-tool games),
yielded different results from the standard game (without the option
to purchase a tool) and the two conditions with tools
purchased.\footnote{The Japanese data, skewed to the right in the
  standard game condition, are skewed more to the left in the
  zero-tool instances of the bonus and insurance game conditions. In
  the UK, the opposite can be observed, with overall higher exit
  points in the tool conditions compared to the standard Centipede
  game. A two-way (Sample × Game condition) ANOVA examining the
  effects on exit points of zero-tool games confirmed these
  observations, but results need to be interpreted with caution due to
  small sample sizes. Overall, the Japanese sample produced
  significantly higher exit points (\textit{M }= 5.76; \textit{SD }=
  1.36) than the European sample (\textit{M }= 4.3; \textit{SD }=
  1.03), \textit{F}(1, 104) = 68.209, \textit{p} {\textless} .001,
  $\eta_p^2$ = .40. On the whole, the standard game produced
  significantly higher mean exit points (\textit{M }= 5.59; \textit{SD
  }= 1.96) than the zero-tool games of the bonus condition (\textit{M
  }= 4.66; \textit{SD }= 0.96) and the insurance condition (\textit{M
  }= 4.84; \textit{SD }= 0.84), \textit{F}(2, 104) = 9.108, \textit{p}
  {\textless} .001, $\eta_p^2$ = .15.  Finally, there was a
  significant interaction, \textit{F}(2, 104) = 38.785, \textit{p}
  {\textless} .001, $\eta_p^2$ = .43, suggesting that the effect of
  the game condition on mean exit points of zero-tool games differed
  between samples. In Japan, the standard game produced significantly
  higher mean exit points than the bonus and insurance games,
  \textit{p }{\textless} .001. The European sample yielded
  significantly lower mean exit points in the standard game than the
  bonus and insurance games, \textit{p }{\textless} .05.}

%Table 3
\begin{table*}[t]\centering
\caption{Mean exit points, standard deviations, and 95\% confidence intervals per
sample, differentiating between zero-tool games and games with one or
two tool purchases.}
\begin{tabular}{llc@{\quad}c@{\quad}c}\toprule
 &  & C2: Bonus condition & C3: Insurance condition & Total\\\midrule
Zero-tool Games & Japan & 4.74 (0.94) [4.29, 5.18] & 5.09 (0.58) [4.68,
5.50] & 4.93 (0.78) [4.61, 5.22]\\
 & Europe & 4.59 (1.00) [4.16, 5.01] & 4.55 (1.00) [4.13, 4.97] & 4.57
(0.98) [4.27, 4.86]\\
 & Total & 4.66 (0.96) [4.36, 4.97] & 4.83 (0.84) [4.53, 5.11] & 4.74
(0.90) [4.53, 4.95]\\\midrule
Games with Tool Purchase & Japan & 8.45 (0.85) [7.86, 9.05] & 6.94
(0.74) [6.40, 7.49] & 7.63 (1.09) [7.30, 8.10]\\
 & Europe & 6.79 (1.69) [6.23, 7.35] & 5.82 (1.22) [5.26, 6.38] & 6.31
(1.54) [5.91, 6.70]\\
 & Total & 7.57 (1.59) [7.21, 8.03] & 6.40 (1.14) [5.99, 6.77] & 6.96
(1.48) [6.72, 7.29]\\\bottomrule
\end{tabular}
\end{table*}

Additionally, we examined effects of tool purchase on the game
outcomes. In Figure 8, it is obvious that tool purchase drastically
changed exit points. Across both samples and game conditions, tool
purchase increased cooperation. This is most visible in the Japanese
bonus condition, with over 90\% of all games reaching the final end.
However, the extreme results of the European samples for games with
tool purchases by both players (in the bonus condition, 100\% reached
Node 9, and in the insurance condition, 75\% reached Node 8) need to
be interpreted with caution, as these data were based on only a single
case in the bonus condition and 4 cases in the insurance condition.

To provide a statistical test of the visual differences outlined
above, we combined data from games in which either one or two players
had purchased tools. Then we conducted a mixed
(within/between-subject) ANOVA comparing the subjects’ mean exit
points for zero-tool games and games in which one or two players had
chosen tools, while testing for differences between the two samples
and game conditions (bonus and insurance) — see Table 3. The analysis
showed a significant difference between mean exit points of games with
and without tools, \textit{F}(1, 67) = 191.855, \textit{p} {\textless}
.001, $\eta_p^2$ = .74; zero-tool games yielded a mean exit point of
4.74 (\textit{SD }= 0.90), and games with tool purchase a mean of 6.96
(\textit{SD }= 1.48). There was also a significant interaction between
the within-subjects factor (games with or without tool purchase) and
the sample, \textit{F}(1, 67) = 10.216, \textit{p} {\textless} .01,
$\eta_p^2$ = .13, indicating that in Japan, the differences between
the mean exit points of zero-tool games (\textit{M} = 4.93;
\textit{SD} = 0.76) and games with tool purchases (\textit{M} = 7.63;
\textit{SD} = 1.09) were significantly larger than the differences
observed in Europe (zero-tool games: \textit{M} = 4.56; \textit{SD} =
0.98; games with tool purchases: \textit{M} = 6.31; \textit{SD} =
1.54). Additionally, the results demonstrated a significant
interaction: for the bonus game condition, the differences between the
mean exit points of zero-tool games and those of games with tool
purchases were significantly larger than the differences observed in
the insurance game condition, \textit{F}(1, 67) = 18.244, \textit{p}
{\textless} .001, $\eta_p^2$ = .21. No significant three-way
interaction was found for the variables of interest. Finally, we
conducted a detailed analysis of the individual difference variables
SVO, risk taking and general trust, which is reported in the
\href{http://journal.sjdm.org/17/17824a/supp.pdf}{supplement}.

\section{Discussion}

This study focused on cross-cultural differences in trust and
cooperation between Japanese and European nationals using the Centipede
game as a behavioral decision task. In particular, we tested previous
concepts of trust proposed by Yamagishi and Yamagishi (1994) that
differentiated between two types of trust: general trust in situations
of low social certainty with higher prevalence in US/Western
subjects and assurance-based trust in prolonged relationships of
higher social certainty with higher prevalence in Japanese
subjects. Our research followed up on an initial study by Krockow
et al.\ (2017), in which Japanese subjects cooperated more
frequently than European subjects in the sequential the Centipede
game, a decision task with repeated opportunities for repeated mutual
reciprocity and assurance-based trust. This finding was replicated by
the present study: whereas both samples recurrently deviated from the
Nash equilibrium solution in the standard Centipede game (STOP at Node
1), the Japanese subjects exited significantly later than the
Europeans. The percentage of Japanese games reaching the natural end
was unusually high (almost 30\%). Hence, cultural background certainly
appears to be important, given that the perfect cooperation amongst the
Japanese sample was almost twice as frequent as in Bornstein et al.’s
(2004) study of Centipede games played by Western subjects. The
high cooperation levels of Japanese subjects may be linked to
higher levels of assurance-based trust. 

\textbf{Use and effects of commitment-enhancing tools.} This study
further included two game conditions offering tools designed to enhance
social certainty and commitment. Gerber and Wichardt (2010), who
introduced these tools, argued that both enhanced the players’ welfare
by inducing higher cooperation and delaying defection. The simpler
bonus tool involves offering the co-player a bonus for not exiting the
game, whereas the insurance tool requires initial payment in order to
receive an insurance compensation if the co-player terminates the game.
Both can be interpreted as types of contracts of cooperation between
players of repeated games. In real-life examples where people are
involved in repeated exchanges of favors with the same other individual
(e.g., manual labor followed by financial rewards, or alternating
emotional support in romantic relationships), commitment-enhancing
tools include employment contracts that specify working hours and
guarantee payments and certificates of marriage/civil partnerships that
bind two individuals together in life-long reciprocal relationships.
The introduction of tools to this study adds a more specific test for
the preference for social security in the game, complementing an
earlier cross-cultural comparison of the Centipede game (Krockow et
al., 2017).

We predicted that tool purchase would occur more frequently in the bonus
condition than in the insurance condition. However, whereas in Japan
bonus purchase was more frequent than insurance purchase — 67.5\% of
games in the bonus condition were completed with at least one player
having purchased the tool compared to 43\% in the insurance
condition — this difference was not statistically significant. In Europe,
no significant differences were found, and the insurance tool was used
more often than the bonus tool. However, tool purchase rates in general
were lower: 76.1\% of games in the bonus condition and 60.1\% in the
insurance condition were played without any tool purchases. These
findings contrast with previous results of Gerber and Wichardt (2010),
who found striking differences. Our non-significant results could be
explained by our detailed and illustrated instruction materials, which
presented the subjects with all possible payoff scenarios resulting
from their tool purchase. Also, our software included an automatic
update of the game’s payoff function to reflect any tool purchases by
the respective players. This payoff update was not available in Gerber
and Wichardt’s original software, and its presence in our study could
have reduced the subjects’ cognitive load — particularly in the more
difficult insurance condition — yielding a less pronounced difference in
tool usage.

Little learning was evident in tool use. The only exception was a linear
increase in the use of the insurance tool in Japan, suggesting that
Japanese subjects gradually learned its benefits. For the European
sample, no temporal patterns were found.

In line with expectations, opting for either the bonus or the insurance
tool significantly increased cooperation relative to games where no
tool was chosen. This was observed in both Japan and Europe, suggesting
that both tools’ benefits were recognized by the subjects, leading
to an improvement of commitment and social certainty. However, the
purchase of commitment-enhancing tools led to larger increases of
cooperation in Japan than Europe. Furthermore, the bonus tool was more
effective in increasing cooperation than the insurance tool, suggesting
that its benefits were easier to comprehend. This corroborates Gerber
and Wichardt’s (2010) theoretical analysis, pointing out that only the
insurance tool requires subjects to use backward induction
reasoning in order to understand its benefits. 

Our hypothesis of lower cooperation in the standard game condition
than the bonus and insurance conditions was partly confirmed. In
Europe, the control condition yielded significantly lower cooperation
levels than the two tool conditions, but the bonus and the insurance
conditions did not differ significantly from one another. In Japan,
cooperation in the standard game produced similar mean exit points to
the bonus condition, and both the standard and the bonus conditions
yielded significantly higher cooperation than the insurance
condition.\footnote{Additional statistical analyses were conducted,
  but need to be interpreted with caution due to small sample sizes:
  Comparing the standard Centipede game with the zero-tool games (in
  which tools were available but not used) showed significant
  differences in cooperativeness in the Japanese subjects between
  all three conditions, with the standard condition being the most
  cooperative, followed by the insurance condition, and lastly, the
  bonus condition.  Given that the payoff structures of these games
  were identical, these results are surprising. A possible explanation
  could be that the refusal to purchase a tool was interpreted as a
  refusal to commit and a sign of likely defection early in the
  game. As a result, assurance-based trust may have been lowered for
  these zero-tool games, particularly in the simpler bonus
  condition. However, despite the low levels of cooperativeness in
  zero-tool games of the bonus condition, the condition produced
  similar mean exit points compared to the standard game
  condition. This can be explained by the high number of bonus choices
  that led to significantly later exit points. Overall, the very high
  cooperation levels of the games with bonus choices balanced out the
  very low cooperation levels of the games with the bonus tool
  available but not chosen, consequently producing mean exit points
  seemingly similar to the standard game condition.}

In the insurance condition, tool choices were less frequent, and the
insurance tool — despite improving cooperation compared to zero-tool
games — was significantly less effective than the bonus. Hence, the games
with insurance choices failed to balance out the low cooperativeness of
the games with the insurance tool available but not chosen, therefore
producing significantly lower mean exit points overall compared to the
standard and the bonus conditions.

One interpretation could be that offering commitment-enhancing tools in
Japan to increase security in the game can increase cooperation, but
only if at least one player actually opts to purchase the
tool.\footnote{It is also possible that those who did not
purchase the tool differed from those who did in their tendency to
cooperate spontaneously. Due to the between-subjects design, we can
only speculate how non-users of available tools would have behaved in
the no-tool (control) condition.} Failure to do so could be interpreted
as a signal of non-cooperation, ultimately resulting in earlier game
exits. These findings are in contrast with the study by Gerber and
Wichardt (2010) in which no differences between the exit points of the
control condition and the zero-tool games were reported for both bonus
and insurance conditions.

The same comparison of zero-tool games was conducted for the European
sample and produced almost opposite results: the zero-tool games in the
bonus and insurance conditions yielded significantly higher cooperation
levels than the standard game condition. Again, interpretation is
somewhat speculative due to the complex between-subjects design with
relatively small numbers per condition. One interpretation could be
that in Europe, the mere offer of a commitment-enhancing
tool — regardless of whether players actually chose it — led to more
committed and more cooperative strategies in the game. This finding
could be explained by priming effects: instructions about
commitment-enhancing tools and the recurrent offers of tool purchase
may have primed the subjects to exhibit more commitment in the
decision tasks that followed.

\pagebreak

As predicted, tool purchase was significantly more frequent in Japan
than in Europe. This main finding corroborates previous trust theories
(Kiyonari, Yamagishi, Cook \& Cheshire, 2006; Yamagishi \& Yamagishi,
1994; Yuki, Maddux, Brewer \& Takemura, 2005) and suggests
a greater need of social certainty and commitment among the Japanese
subjects.

\textbf{Conclusions.} The results reported in this article are among the
first to enable a cross-cultural comparison of trust and cooperation in
Japanese and European samples. They corroborate and extend the findings
of previous investigations into trust among Japanese and North American
samples (e.g., Krockow, et al.\ 2017; Yamagishi \& Yamagishi, 1994)
while employing and improving an interesting new research paradigm
using bonus and insurance tools introduced by Gerber and Wichardt
(2010). Our study confirmed that Japanese subjects cooperated more
frequently than European subjects. This supports previous trust
theories that stated the Japanese tend to exhibit more assurance-based
trust and thus cooperativeness than Western subjects in close,
sequential relationships (Yamagishi \& Yamagishi). 

The introduction of commitment-enhancing tools yielded very different
results in Japan and Europe. Japanese subjects opted more
frequently for commitment-enhancing tools than Europeans, thus
confirming their higher need for social certainty. Also, across both
samples, the use of commitment-enhancing tools was found to increase
cooperation relative to games where no tools were available. However,
the most interesting evidence was provided by those games where tools
were available but were not chosen. In Japan, these games showed
significantly less cooperation than the control condition without
tools. This was explained by signaling effects, with the refusal to opt
for a tool suggesting a lack of commitment and likely defection in the
game. In Europe, the opposite effect was observed: even in games where
neither subject chose a commitment-enhancing tool, cooperation was
significantly higher than in the control condition. These findings
point to priming effects of the available tools, making commitment more
salient to the European subjects. Hence, whereas the mere offer of
commitment-enhancing tools improved mutual cooperation in Europe, more
complex effects were found in Japan, where tools increased cooperation
only if they were chosen by the subjects, and otherwise decreased
cooperation. 

Finally, this experiment assessed a number of individual difference
variables (e.g., SVO and risk-taking attitudes) identical to those
reported by Krockow et al., (2017). These variables did not offer any
new insights beyond the contribution reported in the earlier article.
We have therefore excluded these variables from the Discussion in this
article, but all findings are discussed in the
\href{http://journal.sjdm.org/17/17824a/supp.pdf}{supplement}.

If applied to real life decision making, the results suggest large
differences in trust and cooperation between individuals from Japanese
and Europe. In relationships characterized by a repeated exchange of
favors with another individual, Japanese people appear to show greater
loyalty and reciprocity as based on higher levels of assurance-based
trust than Europeans, reflected (for example) in close, long-term
business partnerships. When faced with optional instruments to enhance
commitment in repeated relationships, while the mere availability of
such options increases cooperation in Europeans, the Japanese might be
more sensitive to rejection (refusals to choose these options),
ultimately lowering their trust and increasing their defection.

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