DP2013-13

A Cash Effect in Ultim atum Gam e
Experiments
Junyi SHEN
Hiromasa TAKAHASHI
April 2, 2013

A cash effect in ultimatum game experiments
JUNYI SHEN*
Research Institute for Economics & Business Administration, Kobe University, Japan
andHIROMASA TAKAHASHI
Faculty of International Studies, Hiroshima City University, Japan

Abstract
This paper reports two experiments involving an ultimatum game, conducted in Japan. There
were two treatments in our experiments. One was called a cash session and the other was called apoint session. The cash session means introducing cash into the ultimatum game. In other words, in acash session, subjects bargained money in cash but not points or tokens as most prior experiments
did. We found that compared to those in the point sessions, proposers offered more and responders
rejected less in the cash sessions. These evidences imply that a cash effect does exist in theultimatum game experiments.

Keywords: Cash effect; Ultimatum game; Cost-loss discrepancy; Experimental design

JEL classification: C72, C91* Corresponding author. Research Institute for Economics & Business Administration, Kobe

University. 2-1 Rokkodai, Kobe, Hyogo 6578501, Japan. Tel/Fax: +81-78-8037013. E-mail address:
shen@rieb.kobe-u.ac.jp
11. Introduction
Standard economic models of human decision-making have typically minimized or ignoredinfluence of emotions on people’s decision-making behavior, idealizing the decision-maker as aperfectly rational cognitive machine. However, in recent years this assumption has been challenged
by behavioral economists, who have identified additional psychological and emotional factors that
influence decision-making. One of the experimental games that produced very convincing evidence
in this regard is the ultimatum game. In this game one player (i.e., the proposer) proposes to thesecond player (i.e., the responder) the division of a sum of money. If the responder accepts thedivision, then both players earn the specified amounts. If the responder rejects it, they both get
nothing.
The backwards induction prediction of the ultimatum game is so simple that the proposer offers
any amount more than zero and the responder accepts. However, being encouraged by Güth et al.
(1982), which is the first experimental study of the ultimatum game, many experimental studies
observed evidences that deviate from this theoretical prediction (e.g., Andersson et al., 2010; Bolton
and Zwick, 1995; Cameron, 1999; Croson, 1996; Eckel and Grossman, 2001; List and Cherry, 2000;
Rankin, 2005; Roth et al., 1991; Ruffle, 1998; Schotter et al., 1996; Slonim and Roth, 1998;
Tompkinson and Bethwaite, 1995). In experiments, although average offers and rejection rates
varied across studies, proposers normally offer an average of 40% of the money and responders
reject small offers of 20% or so half the time. In a detailed survey of many studies on ultimatum
game, Camerer (2003) listed five variables that might have effects on the experimental results. They
are methodological variable (e.g., repetition, stakes, anonymity), demographic variables (e.g., gender,
race, academic major, age), culture, descriptive variable (e.g., labeling, context), and structuralvariable (e.g., identity, communication, competitive pressure, information). However, we feel thatbesides these variables there might be one extra issue (i.e., creating a cash environment in theultimatum game experiments) possibly affecting the experimental results. Reviewing the ultimatum
game experiments conducted in previous studies, almost no study introducing cash into theprocedure of the experiments. Instead, during the experiments subjects played the games with points
or tokens and after the experiments these points or tokens earned by the subjects were then changed
into cash according to a certain exchange rate. 1
Creating a cash environment in the ultimatum game experiments refers to the situation that bothproposers and responders face the real money (i.e., cash) but not points or tokens written on paper orappeared on the computer screen. In our view, introducing cash into the ultimatum game
experiments is important because the issue of cash versus point or token could be considered a case
1

There were several studies asking the subjects to split the pie within a certain amount of money.
However, even the pie was in the unit of money (e.g., 10 USD or 1000 JPY), it was still not in cash.
2

of cost-loss discrepancy. 2 Under this consideration, a split of the pie in cash can be viewed as adirect loss for both the proposer and responder if the split is rejected by the responder. On the other
hand, since an offer in point or token rejected by the responder is not a direct loss as in cash, it canbe viewed as a cost for both players to earn money in the next rounds or periods of the experiment.
Therefore, we believe that in a cash environment both proposers and responders would be morecautious in making an offer and rejecting an offer.
In the current study, we conducted two laboratory experiments to examine the cash effect in theultimatum game. Our prediction of the cash effect is twofold. First, introducing cash into theexperiments may induce proposers to make relatively higher offers, because they would be moreafraid of being rejected by responders than in a point or token environment. Second, receiving offers
in cash may cause responders to hesitate to reject, therefore, rejection rates in a cash environment
will be lower than in a point or token environment. An additional note should be given that, to ourknowledge, there is almost no published literature examining such a cash effect on participants’experimental behaviors. Therefore, our study could be viewed as a first attempt on this issue. 3
The remainder of the paper is organized as follows. Section 2 describes the issues related to theexperiment. The results of the experiment are presented in Section 3. Finally, Section 4 discusses theresults and suggests several possible directions for future study.

2. Experimental issues
We conducted two ultimatum game experiments at Hiroshima City University. Sixty four
students participated in the first experiment (hereinafter, “Experiment 1”) in December 2011 andsixty students joined in the second experiment (hereinafter, “Experiment 2”) in May 2012. We
confirmed in advance that all the subjects participated in Experiment 2 had not participated inExperiment 1 before. In each experiment, subjects were evenly divided into two sessions, which we
called one as the cash session and another as the point session. There were six rounds in each session.
Each subject was randomly assigned to be a proposer or responder, and a subject played the samerole throughout six rounds. To keep anonymity between proposers and responders, they werearranged at different classrooms separately. In each classroom, subjects received written instructions,
The cost-loss discrepancy suggests that there exists a discrepancy in people’s preferences on costand loss. See Thaler (1980), Smelser and Gerstein (1986), and Tversky and Kahneman (1991) for
more detailed discussions on this issue.
3
One study (i.e., Hoffman et al., 1996) did apply cash in dictator game experiments. However, theirdesign did not allow them to examine how introducing cash into the experiments affects subjects’
behaviors, compared to those in the point or token conditions. In addition, several studies
investigated the effects of the credit card and cash on spending behavior (e.g., Prelec and Simester,
2001; Raghubir and Srivastava, 2008). They found that credit card payments would increase
consumers’ purchase likelihood and willingness to pay.
2

3

which were first read individually by the subjects and then read aloud by a Japanese-speaking
experimenter.
In both sessions of Experiment 1, every proposer was randomly matched with one different
responder in each round. In each round of the cash session, the proposer received an envelope
containing 1000 JPY in cash (i.e., one 500-yen coin, four 100-yen coins, one 50-yen coin, and five10-yen coins) and had to decide how much to offer to the responder. After deciding the amount, theproposer was asked to put the offering money in another envelope provided by the experimenter.
Then, an experimenter brought these envelopes to responders’ classroom and distributed them to thecorresponding responders. The responder learned the proposer’s offer and could either accept or
reject it. In case of acceptance, the responder’s payoff in that round was the amount of the offer, andthe proposer’s payoff in that round was 1000 JPY minus his/her offer. In case of rejection, bothsubjects earned 0 in that round. The proposers and responders were asked to put the envelopes
containing money in their bags if the offer was accepted. In contrast, the experimenters would collectthese envelopes if the offer was rejected. The subjects’ total payoff in the experiment was the sum of
the payoff earned in each round. There was no show-up fee in our experiments.
The experimental procedure of the point session in Experiment 1 was almost the same as that of
the cash session except that (i) instead of deciding how much to offer in cash, the proposers in the
point session had to decide how many points between 0 to 1000 to offer to the responders; 4 (ii)instead of being paid directly in cash once the proposers’ offers were accepted in each round,subjects in the point session would be paid after all the rounds finished; and (iii) there was no any
envelope appeared in the point session. Instead, all the decisions of proposers and responders were
written in the recording sheets, and an experimenter was in charge of conveying these decisions tothe corresponding subjects by filling in their recording sheets.
In Experiment 2, most of proposers’ and responders’ tasks, experimental procedures, andpayment rules remained the same as those in Experiment 1 except that proposers in both cash andpoint sessions were, unbeknown to responders, given only two options each round to choose from.
There were six combinations of options including (900,100) and (100,900), (800,200) and (200,800),(700,300) and (300,700), (900,100) and (500,500), (800,200) and (500,500), and (700,300) and(500,500). 5 Each proposer randomly faced one different combination in each round, and thefrequencies of each combination appeared over rounds (i.e., fifteen times) were set up to be same
within and between sessions. 6
4

In a manner consistent with that in the cash session, the pie in the point session was 1000 points
and proposed divisions were made in units of 10 points (0, 10, 20,…990, 1000). The exchange rate
for 10 points was 10 JPY.
5
The option of (900,100) stands for a proposer keeping 900 and offering 100. The same logic
applies in explaining all other options.
6
A note on the reason of conducting Experiment 2 is that the rejection rates in both sessions ofExperiment 1 were so low (5/96 in the cash session and 10/96 in the point session) that some4Including payment, each session of both two experiments lasted for about 90 minutes, andparticipants earned, on average, 2582 JPY (about 32.28 USD if 1 USD = 80 JPY). The average
payoffs of proposers and responders differed a little across sessions and experiments, due to thedifferences in proposers’ offer and responders’ rejection rate between the cash and point sessions. 7

3. Results
Tables 1a and 1b describe proposer and responder behavior aggregating across rounds inExperiment 1 and Experiment 2, respectively. Table 1a can be read as: consider the offer range 210 –
300, which signifies proposer offered responder between 21% and 30% of the pie. In the cash
session, 14.58% (14/96) of all offers were in this range, and 7.14% (1/14) of these offers were
rejected. Similarly, offers in this range accounted for 28.13% (27/96) of the offer in the point session,and 7.41% (2/27) of these offers were rejected. In addition, Table 1b can be read as: consider theoffer 300, which means proposer chose the option of (700, 300) when also given another option as(300, 700) or (500, 500) to be chosen. 16.67% (15/90) and 21.11% (19/90) of all offers were thisamount in the cash session and point session, respectively. The rejection rates on this offer were 20%(3/15) and 31.58% (6/19) in the cash session and point session, respectively.

3.1. Proposer behavior
To understand the results in Tables 1a and 1b more visually, we present proposer behavior in
Figures 1a and 1b. From the figures, we can find out that in both experiments, high offers (i.e., morethan or equal to half of the pie) appear more frequently in the cash session than in the point session.
In contrast, the frequency of extremely low offers (i.e., no more than 100 in Experiment 1 and 100 inExperiment 2) is relatively lower in the cash session than in the point session.
In Experiment 1, average offers over rounds are 404 and 323 in the cash and point sessions,
respectively. Both one-tailed t test (t = 4.802, p = 0.000) and Wilcoxon rank sum test (z = 4.962, p =0.000) suggest that proposers offer more in the cash session than in the point session. In addition, in
Experiment 2, the proportion of proposers offering 500 or more increases from 46.67% in the point
session to 53.33% in the cash session. One-tailed proportion test indicates that this increase ismarginally significant (z = 1.329, p = 0.092).
The second and third columns from the left side of Table 2 report the results of regressions ofscholars may doubt the power of the cash effect found in the current study. For detailed results anddiscussions, see the next section.
7
Proposers/responders earned, on average, 3334/2353 JPY and 2747/2247 JPY in the cash sessionsof Experiments 1 and 2, and 3569/1784 JPY and 2547/2027 JPY in the point sessions ofExperiments 1 and 2, respectively.
5offers in Experiments 1 and 2. The dependent variables are the shares of proposers’ offer inExperiment 1 and a dummy variable defined as 1 for offers no more than 300 and 0 otherwise inExperiment 2, respectively. 8 The common independent variables in both regressions are CashSession (i.e., a dummy variable equals 1 if the subjects participated in the cash session and 0 if thesubjects participated in the point session) and Round (i.e., equals 1 for round 1, equals 2 for round 2,
and so on). Additional two independent variables in the regression of Experiment 2 are Option_500(i.e., a dummy variable equals 1 if another option of offers faced by the proposer was (500,500) and
0 otherwise) and Cash*Option_500 (i.e., an interaction term of Cash Session and Option_500). As
shown in the columns, given the condition that proposers could offer any amount from 0 to 1000 in
unites of 10 (i.e., Experiment 1), the proposers in the cash session significantly offer more than thosein the point session. However, this effect is not significantly found under the environment ofExperiment 2 that proposers were asked to choose the offer from two options. We doubt that this isdue to first, the difference in proposers’ offering rules between Experiments 1 and 2, and second, theoffer ratios no more than 300 in the two sessions of Experiment 2 differed marginally (42/90 in the
cash session and 48/90 in the point session).
An interesting result is obtained from the Logit regression in Experiment 2. When anotheroption that proposers faced is (500,500), a wholly equal option to both proposers and responders, theprobability that they offer no more than 300 will be decreased in both sessions. Furthermore, thisdecrease may be stronger in the cash session. Our data revealed that in the cash session, the numbersof offering 100, 200, and 300 without and with another option of (500,500) decreased from 10/15,
12/15, and 11/15 to 2/15, 3/15,and 4/15, respectively, while in the point session the corresponding
numbers decreased from 11/15, 10/15, and 12/15 to 4/15, 4/15, and 7/15, respectively. It is to saythat proposers’ choices of (900,100) or (800,200) or (700,300) were influenced by combining these
options with an option of the equal split (500,500), compared to the conditions that anotheralternative was (100,900) or (200,800) or (300,700).9

3.2. Responder behavior
Figures 2a and 2b provide visual descriptions of rejection behaviors on the offers no more than
400.

10

As shown in the figures, smaller offers are more likely to be rejected in both sessions and

8

The regression of offers in Experiment 1 is a Tobit regression because the offer ratio is bounded
between 0 and 1, and the regression of offers in Experiment 2 is a Logit regression.
9 This evidence partly supports the result of Falk et al. (2003), which reported that proposers offered(8,2) only a third of the time when the alternative was the equal-split (5,5) and offered (8,2) most of
the time in the other conditions such as (2,8) or (10,0).
10
There were three unusual rejections occurred in the experiments. One was in the cash session ofExperiment 1 by one subject for offer of 510 and the other two were in the point session ofExperiment 2 by another subject for offers of 900 and 500. Both subjects expressed clearly in a6

offers more than 300 are never rejected in the cash session but are rejected 10.53% (4/38) of the timein the point session of Experiment 1.
Over all offers, in Experiment 1 the rejection rate decreases from 10.42% in the point session to
5.21% in the cash session, while in Experiment 2 the same decreasing tendency is observed (i.e.,from 24.44% in the point session to 16.67% in the cash session). One-tailed proportion test
marginally supports these evidences (in Experiment 1: z = 1.345, p = 0.089; in Experiment 2: z =1.291, p = 0.098).
The column from the right side of Table 2 presents the results of the Logit regression of
rejection behavior in Experiments. The dependent variable in the regression is a dummy variable that
equals 1 if the proposer’s offer was rejected and 0 otherwise. The definitions of Cash session andRound are the same as in the regression of proposer behavior. Offer300 is a dummy variable definedas 1 for proposers’ offers no more than 300 and 0 otherwise. Cash*Offer300 is an interaction term of
Cash Session and Offer300, and Experiment 2 is a dummy variable equaling to 1 for Experiment 2
and 0 for Experiment 1. As show in the column, Cash Session is estimated with significant andnegative sign, which indicates that although marginally the responders in the cash session
significantly reject less than those in the point session. In addition, the significantly positive estimateof Offer300 and insignificant estimate of Cash*Offer300 suggest that offers no more than 30% of thepie would be likely to be rejected and this is not differential between the cash and point sessions.
Combining the latter evidence with the result of Cash Session just described above, we may make aconjecture that the cash effect influences responders’ behavior most likely in the situation that they
face offers above 30% of the pie. Finally, Experiment 2 is estimated with significant and positive
sign, implying that the probability of rejection is higher in Experiment 2. This result reflects the factobserved from the raw data that rejection rates are 7.81% (15/192) in Experiment 1 and 20.56%(37/180) in Experiment 2.

4. Discussion
In the current paper, we conducted two experiments in Japan to examine how introducing cash
into the ultimatum game experiments affects both proposers’ and responders’ experimental behavior.
We found that in our experiments, the proposers offered more in the cash sessions than those in the
non-cash sessions. Meanwhile, compared to those under the non-cash environment, the responders
rejected less when they faced offers in cash. In our view, these evidences could be explained by the
cost-loss discrepancy discussed in Thaler (1980), Smelser and Gerstein (1986), and Tversky andpost-experiment questionnaire that their reason rejecting these offers was due to dislike earning more
upon the loss of their partners, therefore, we did not treat these data as missed. It should be notedthat dropping these data does not have any essential influences on the reported results of statisticaltests and regression.
7

Kahneman (1991). It is to say that relative to considering a loss as the Cost, a loss regarded as the
Loss leads people to feel more disappointed. Thus, both proposers and responders would be morecautious in making decisions under the cash environment.
Investigating the influence of cash on subjects’ behavior gives us a fresh insight not only into
the ultimatum game experiment but also into other economic experiments such as Prisoners’
Dilemma experiment, Public Goods experiment, and Auction experiment. Considering that if the
cash effect is a universal phenomenon in economic experiments, shall we start to introduce cash into
the procedures of future experiments from now on? Of course, we cannot draw such a conclusion
without examining whether a cash effect exists in other experiments. Hence, we leave this question
open and welcome any efforts to further explore this issue at much deeper extent.

Acknowledgements
The authors would like to thank the Japanese Ministry of Education, Culture, Sports, Scienceand Technology for its financial support through the Grant-in-aid for Scientific Research on Priority
Areas 19046002. All of the views expressed in this paper and any errors are the sole responsibility of
the authors.

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9Figure 1a. Proposer behavior in Experiment 1 (total observation = 96)
40

Number of offer

35
30
25
20

cash session

15

point session

1050<=100 110-200 210-300 310-400 410-490
Offer range

500

>500

Figure 1b. Proposer behavior in Experiment 2 (total observation = 90)40Frequency of offers

35
30
25
20

cash session

15

point session

10
5
0

100

200

300

500
Offer

700

10

800

900

Figure 2a. Rejection rates in Experiment 1
50%

Rejection rates

40%
30%
cash session

20%

point session

10%
0%

<=100

110-200
210-300
Offer range

310-400

Figure 2b. Rejection rates in Experiment 2
80%

Rejection rates

70%
60%
50%
40%

cash session

30%

point session

20%
10%
0%

100

200
Offer

300

11

Table 1a. Summary of Ultimatum Game – Experiment 1
Cash Session
Offer Ranges (pie = 1000 JPY)
> 500
= 500
410 – 490
310 – 400
210 – 300
110 – 200<= 100All Offers
Offers < 500
Average Offer

Point Session% Offer% Rejected% Offer% Rejected

5.21

20.00

0.00

0.00

(5)

(1)

(0)

(0)

37.50

0.00

9.38

0.00

(36)

(0)

(9)

(0)

10.42

0.00

3.13

0.00

(10)

(0)

(3)

(0)

20.83

0.00

39.58

10.53

(20)

(0)

(38)

(4)

14.58

12.50

28.13

7.41

(14)

(1)

(27)

(2)

7.29

14.29

12.50

16.67

(7)

(1)

(12)

(2)

4.17

50.00

7.29

28.57

(4)

(2)

(7)

(2)

100.005.21

100.00

10.42

(96)

(5)

(96)

(10)

57.29

7.27

90.63

11.49

(55)

(4)

(87)

(10)

404

323

Notes: The number in parentheses below each % offer is the number of offers made in the range and the number inparentheses below % rejected is the number of offers rejected in the range.

12

Table 1b. Summary of Ultimatum game – Experiment 2
Cash Session
Offers (pie = 1000 JPY)

Point Session% Offer% Rejected% Offer% Rejected

900

5.55

0.00

4.44

25.00

(5)

(0)

(4)

(1)

800

2.22

0.00

5.55

0.00

(2)

(0)

(5)

(0)

700

5.55

0.00

3.33

0.00

(5)

(0)

(3)

(0)

500

40.00

0.00

33.33

3.33

(36)

(0)

(30)

(1)

300

16.67

20.00

21.11

31.58

(15)

(3)

(19)

(6)

200

16.67

33.33

15.56

21.43

(15)

(5)

(14)

(3)

100

13.33

58.33

16.67

73.33

(12)

(7)

(15)

(11)

All Offers

100.0016.67

100.00

24.44

(90)

(15)

(90)

(22)

46.67

35.71

53.33

41.67

(42)

(15)

(48)

(20)

Offers < =300
Average Offer

403

386

Notes: The number in parentheses below each % offer is the number of offers made for the amount and the number inparentheses below % rejected is the number of offers rejected for the amount. Average offer in each session is
calculated as the expectation value of the offer.

Table 2. Regression Results of Proposer and Responder Behaviors
Proposer Behavior

Responder Behavior

Experiment 1

Experiment 2

Constant

0.344***

1.186

Cash session

0.081**－0.108－0.006**

0.095

Round

Constant－3.583***

Cash session－2.014*

Offer300

2.251***

Option_500－2.523***

Cash*Offer300

1.885

Cash*Option_500－3.478***Experiment 2

1.005*

Round－0.124

Wald chi2

10.000(2)***33.780(4)***

Wald chi2

28.390(5)***Observations

192

180

Observations

372

Notes: *p < 0.10, **p < 0.05, ***p < 0.01.

13