HIAS-E-139

Charity Fraud: An Experimental Study of the Moral
Hazard Problem in the Charity Market

Hiroki Kato(a), Youngrok Kim (b)(a) Hitotsubashi University(b) University of Hyogo

April 2, 2024

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

Abstract
Donors entrust their resources to charitable organizations, which use these to carryout activities that contribute to society. Thus, the donation market carries the potential
for moral hazard on the part of charitable organizations. However, empirical insights
into the negative consequences of this problem are scarce. This study creates a uniquegame by incorporating elements of principal-agent relationships into the dictator
game, in order to quantitatively examine the consequences of moral hazard in the
donation market through laboratory experiments. The results reveal that moral-hazard
environments hinder the average donation amount from donors and, furthermore,decrease recipients’ average payoffs. To address this negative outcome, non-bindingpromises are introduced to inform donors beforehand of the actions to be taken bycharitable organizations. Although these promises succeed in offsetting the decreasein donation amounts, they do not sufficiently improve recipient welfare.
Keywords: Charity market; Dictator game; Fraud; Hidden action; Promise
JEL codes: C71; C92; D64; D82

2

1

Introduction

Despite charitable organizations prioritizing transparency, the charity market harbors apotential moral hazard problem. Sharing asymmetric characteristics with corporations(shareholders-managers), donors may be unaware of the consequences of their donations
to charitable organizations. Consequently, the donation market faces a potential, classicalprincipal-agent problem. Although this point is by no means a new perspective (e.g.,
Rose-Ackerman, 1996), however, a scarcity of insights exists into this issue’s negative
consequences.
The key difference with classic principal-agent relationships is that charitable organizations do not pursue donors’ economic interests. Shareholders entrust some of their funds
to managers, who utilize the funds to generate profits and return them to the shareholders(Jensen and Meckling, 1976). Conversely, donors entrust some of their funds to charitableorganizations, which utilize these funds to benefit society.
Given this difference, principals (shareholders or donors) invest with different motives.
Shareholders invest with selfish motives, whereas donors invest with altruistic motives
contributing to society. A similarity is that agents, exploiting the hidden action environment
where principals cannot observe or verify agent actions, can pursue private benefits. Somecharitable organizations may aim not only for social contribution but also for private gain.
In such a structure, fraud can occur even in nonprofit organizations where collected
funds are misused. Archambeault et al. (2015) found that 17% of scandals involving
nonprofit organizations in the United States fall into such categories. In severe instances,charity fraud—such as masquerading as fundraising for disaster relief or humanitarian
aid—frequently occur. Hence, charitable organization activities become hidden actions
that are unobserved or unverified by donors, creating a potential for moral hazard in the
donation market.
The risk of potential charity fraud negatively impacts the donation behavior of principals.
Previous economic research has reported that some donors care about the manner in whichcharitable funds are utilized.1 For instance, Caviola et al. (2014) and Gneezy et al. (2014)
1

This problem is recognized not only in economics research but also in general. A public opinion survey
by the Japanese Cabinet Office revealed that 37% of individuals who choose not to donate to nonprofit
organizations cite “difficulty in seeing the effect of donations” as a reason for their donation decision. Since3have revealed the phenomenon of overhead aversion, where donors seek to avoid their
donations being used for overhead expenses by charitable organizations. This behavior
suggests that donors are motivated by a desire to make a positive social impact with their
donations. Karlan and Wood (2017) demonstrates that scientific information about thesocial impact of donations encourages donation behavior among those who have previously
made significant donations. Moreover, Null (2011) and Metzger and Günther (2019)highlight the demand for information on the social impact of donations.2 These studies
suggest that charity frauds, which reduce the social impact of donations, negatively affectdonation behavior.
We aim to understand the nature of charity fraud in terms of donation behavior andwelfare of recipients by a laboratory experiment. We have developed a simple and uniquegame that incorporates elements of hidden action environment into the standard dictator
game, in order to examine the impact of such environments on donation behavior andrecipient welfare. In the standard dictator game, the dictator sends a portion of their initialendowment to the receiver. However, we introduce a twist to this game: the introductionof an intermediary (referred to as the deliverer) between the dictator and the receiver. Theintermediary represents charitable organizations in real charity markets.
In this game, the dictator and deliverer make sequential decisions. First, the dictator
sends a portion of their initial endowment to the deliverer. Then, the deliverer divides theirinitial endowment and the funds received from the dictator between themselves and thereceiver.3 Since the dictator’s payoff does not depend on the deliverer’s actions, in thisgame, the dictator cannot observe and infer the deliverer’s behavior. Thus, the deliverer’s
actions become hidden actions. The differences with related games will be discussed indetail in Section 2.
We have two concrete research questions about nature of charity fraud. First, what
multiple answers are allowed, the possibility of self-serving bias is small. See the Cabinet Office’s “Public
Opinion Survey on NPOs” (conducted in 2013, in Japanese). https://survey.gov-online.go.jp/h25/h25npo/index.html
2Duncan (2004) has developed theoretical models concerning donors who care about social impact,
providing theoretical insights.
3
More precisely, the deliverer decides the percentage of the funds received from the dictator to send to
the receiver. The deliverer can choose from 0% to 200% in increments of 1%. If the deliverer chooses anallocation ratio higher than 100%, they transfer all the funds received from the dictator, along with a portionof their initial endowment to the receiver.

4

are the implications of the hidden action environment on the dictator’s decision to giveand the welfare of recipients after the transaction? To answer it, this study applied twotreatments to this game. First, the dictator can specify their own actions as well as thoseof the deliverer (enforcement treatment). This treatment enables the dictator to observeand verify the deliverer’s actions, eliminating the possibility of moral hazard. Second, thegame described earlier is played as usual (hidden action treatment). This treatment entails
the potential for moral hazard by the deliverer. By comparing these two treatments, we
elucidate the manner in which asymmetric information situations affect donation behavior
and recipient payoffs.
Second research question examines the breakdown of pledges on the agent side, which
is typical of charity fraud.4 To do so, we introduced a third treatment (promise treatment).
Following Charness and Dufwenberg (2006) and Vanberg (2008), which investigated
non-binding pre-play promises in a classical principle-agent relationship, before playing
the game, the deliverer decides, in advance, how to share the pie with the receiver, andpresents the same to the dictator. Then, similar to the hidden action treatment, the normal
game is played. Therefore, the deliverer once again chooses the manner in which the pie isto be allocated, which determines the payoffs for each player.
The experiment’s results reveal that the hidden action environment hinders the dictator’s
donation behavior and significantly decreases the receiver’s welfare. Compared to theenforcement treatment, the hidden action treatment reduces the average donation amountby 35% for the dictator and decreases the receiver’s average payoff by 85%.
Additionally, in a hidden action environment, non-binding promises by the deliverer
offset the decrease in average donation amount to some extent. Nevertheless, the promises
do not sufficiently improve the receiver’s average payoff. Compared to the enforcement
treatment, the promise treatment only reduces the average donation amount by 4% but stilldecreases the average payoff of the receiver by 71%. Furthermore, 56% of deliverers breaktheir promises (choosing a lower share of the pie than promised). If all deliverers wereto keep their promises, the average payoff for the receiver would double compared to thepromise treatment. However, the amount would still not reach the average payoff without
4

Some studies examine the effect of pledges on donors (principals) on altruistic behavior (see Andreoni
and Serra-Garcia, 2021; Meyer and Tripodi, 2021).

5

information asymmetry. Taken together, contrary to Charness and Dufwenberg (2006) and
Vanberg (2008), non-binding promises cannot fully resolve the negative consequences of
the hidden action environment.
Our research complements studies on sequential contributions. When some donors
are not aware of the quality of nonprofit activities, the contributions of early donors canserve as signals of this quality (Vesterlund, 2003; Andreoni, 2006). To examine thispossibility, several studies have conducted games where multiple donors invest in public
goods sequentially (Potters et al., 2005). The fact that the quality of donations is uncertain
is a common starting point with our research. However, our focus differs from thesestudies. Sequential public goods games focus on the function of initial donations as
signals in such environments, disregarding how the quality of donations is determined.
Our research focuses on how the quality of donations depends on the manner in whichcharitable organizations utilize funds, and is determined under hidden action environment.5
Our research also contributes to the study of charity fraud. While empirical research on
charity fraud in nonprofit organizations is quite limited, some studies have focused on socialeconomic attributes (Goel, 2020) and organizational characteristics (Gibelman and Gelman,
2001; McDonnell and Rutherford, 2018). These studies examine the factors that contributeto charity fraud under the assumption of information asymmetry. We quantitatively examine
the negative impact of information asymmetry, thereby complementing a series of studies
by once again demonstrating the importance of moral hazard in the charity market.6
The rest of the paper is structured as follows: In Section 2, we introduce the game usedin our experiment and discuss the differences from related games. Section 3 provides an
overview of the experiment. We present the experimental results in Section 4 and discussthem in Section 5. Finally, the conclusion is given in Section 6.
5

The quality of donations in our experiment is represented by the deliverer’s allocation ratio.
Economic research on fraud is famously rooted in the study of credence goods initiated by Darby andKarni (1973). In credence goods markets, consumers do not know the quality of the goods they desire,
while suppliers can ascertain the quality through diagnosis. Moreover, consumers can only observe theutility obtained from the traded goods (and may not even observe that). Dulleck et al. (2011) verifies theinefficiencies (under-treatment, over-treatment, overcharging) in credence goods markets through laboratory
experiments. The charity market may differ slightly from typical credence goods markets. The quality of
donations can be defined by the social impact of how much the donations have improved society. Charitableorganizations may not easily discern the social impact truly desired by donors. Instead, donors may be theones who know it.
66

Dictator (D)01𝑥Deliverer (E)

0

𝜋𝐷
𝜋𝐸
𝜋𝑅

𝑠
1−𝑥
1− 𝑠−1 𝑥𝑠𝑥

2Figure 1: Game Tree. Notes: 𝜋𝑖 is payoff of each player.

2

Dictator Game with Hidden Actions

2.1

The GameOur game consists of a dictator (𝐷), a deliverer (𝐸), and a receiver (𝑅). The dictator anddeliverer have an initial endowment of 𝐼 tokens, while the receiver has no initial endowment.
The dictator and deliverer sequentially make decisions to determine the payoffs for all
three players.
The dictator is the first mover, and decides how much of their initial endowment to send
to the deliverer. Let the amount sent by the dictator be denoted as 𝑥. The second moveris the deliverer. The deliverer decides the percentage of tokens funded by the dictator
to be sent to the receiver. The deliverer can choose a percentage ranging from 0% to200% in 1% increments. Here, the allocation ratio chosen by the deliverer is denoted as𝑠 ∈ {0, 0.01, 0.02, … , 0.99, 1, 1.01, … , 1.98, 1.99, 2}.
The deliverer transfers 𝑠𝑥 tokens to the receiver, and this becomes the receiver’s payoff.
7

If 𝑠 < 1, the deliverer sends a portion of the sent amount from the dictator to the receiver,keeping the remaining (1 − 𝑠)𝑥 tokens as their own payoff. If 𝑠 > 1, the deliverer adds theshortfall (𝑠 − 1)𝑥 tokens to the amount sent by the dictator from their initial endowment
and sends it to the receiver. Therefore, the deliverer’s payoff is 𝐼 − (𝑠 − 1)𝑥 tokens.
However, since the actions of the deliverer do not influence the dictator, the dictator’s
payoff is 𝐼 − 𝑥 tokens. Our game tree is summarized in Figure 1.

2.2

Comparison with Related Games2.2.1

Dictator Game

Our game represents a natural extension of the standard dictator game (e.g., Forsythe et al.,1994). In the dictator game, a player with an initial endowment chooses to transfer someof it to another player. In our game, when the deliverer transfers 100% of the dictator’stransfer amount (𝑠 = 1) to the receiver, the final payoffs for the dictator and the receiver are

𝐼 − 𝑥 and 𝑥 tokens, respectively. These payoffs mirror the outcomes of the dictator game.
Assuming a player who is only concerned with their own payoff, on the Nash equilibrium
path of our game, the dictator does not send anything, and the deliverer chooses 𝑠 ∈ [0, 2].
Therefore, in equilibrium, 𝜋𝐷 = 𝐼, 𝜋𝐸 = 𝐼, and 𝜋𝑅 = 0, resembling the equilibrium of
the dictator game. Thus, as in standard dictator games, the motive for dictators to send
depends on pure/impure altruism (Andreoni, 1989, 1990; Andreoni and Miller, 2002) anddistributional preferences (e.g., Fehr and Schmidt, 1999; Charness and Rabin, 2002).
Additionally, to examine rationality and preferences of altruistic behavior, some studies
have conducted a dictator game with an exogenous price 𝑝 in the form of a budget constraint,
represented as 𝜋𝐷 + 𝑝𝜋𝑅 = 𝐼, where 𝜋𝐷 and 𝜋𝑅 are the dictator’s and receiver’s payoffs,
respectively (Andreoni and Miller, 2002; Fisman et al., 2007). In our game, the allocation
ratio 𝑠 of the deliverer can be interpreted as the price. The budget constraint for the dictatorin our game is 𝜋𝐷 + (1/𝑠)𝜋𝑅 = 𝐼. In other words, as the allocation ratio increases, thecost of the transfer decreases.7
7

An increase in the allocation ratio not only leads to a decrease in price but also introduces substitutability
between the sent amount and the allocation ratio. Given 𝑠, the dictator maximizes 𝑈(𝐼 − 𝜋𝑅 /𝑠, 𝜋𝑅 ) by∗choosing 𝜋𝑅 . In this case, the optimal sent amount is 𝑥∗ = 𝜋𝑅
/𝑠. Hence, as the allocation ratio increases,
the sent amount decreases. Similarly, matching donations have both a positive effect due to price reduction

8However, the standard dictator game does not reflect the hidden action environment
in the charity market. Some studies have examined dictator games in which recipientsare actual charitable organizations, thereby providing important insights into donation
behavior.8 Nevertheless, such games do not examine the extent to which recipient welfare
improves through donations. By introducing an intermediary between the dictator and therecipient, our game can simultaneously assess donation behavior and recipient welfare,including moral hazard issues.
2.2.2

Trust Game

Our game is also related to trust games (Berg et al., 1995; Dufwenberg and Gneezy, 2000).
In this game, the trustor entrusts a portion of their initial endowment to the trustee, whichis then multiplied by a constant factor. The trustee decides the amount to be returned.
In our game, the dictator (trustor) entrusts a portion of their initial endowment to thedeliverer (trustee), who then shares 𝐼 + 𝑥 tokens with the receiver. Thus, the dictator’stransfer amount is multiplied by (𝐼 + 𝑥)/𝑥 (a decreasing function of 𝑥) and entrusted tothe deliverer. A significant difference from the trust game lies in who the trustee shares thebenefits with. In the trust game, the trustee shares the benefits with the trustor. Therefore,
a direct reciprocity towards the trustor is often observed in the trustee’s behavior (Berget al., 1995; Dufwenberg and Gneezy, 2000; McCabe et al., 2003). However, in our game,the deliverer shares the benefits with the receiver, and not with the dictator. So, direct
reciprocity is not a motivating factor for the deliverer.9
Charness and Dufwenberg (2006) incorporates the essence of hidden action into thetrust game. In this experiment, the trustor decides whether to send all of their initialand a negative effect due to substitutability in individual contributions (Hungerman and Ottoni-Wilhelm,2021). Thus, the deliverer’s allocation ratio is a form of matching donation.
8
Umer et al. (2022) conducted a recent meta-analysis on the dictator game, comprehensively examining
various elements in the dictator game. See Umer et al. (2022) for the impact of recipient differences (students
versus charitable organizations).
9
Indirect reciprocity might be a motivating factor for the deliverer. This involves a person who has beentreated kindly engaging in altruistic behavior towards an unrelated group. Strang et al. (2016) and Li et al.
(2020) examine this motive, using a two-stage dictator game in which Player A shares a pie with Player B in
the first stage, and then Player B shares another pie with Player C in the second stage. The results reveal that
as Player A’s transfer amount increases, Player B’s transfer amount increases as well. In our game, as the
dictator’s transfer amount increases, the size of the pie shared between the deliverer and the receiver also
increases. Therefore, deliverers with indirect reciprocity may increase the receiver’s share of the pie.

9

endowment to the trustee. The trustee, in turn, decides to either (1) keep the entire amountsent by the trustor or (2) multiply the amount sent by a constant factor and return only theadditional portion to the trustor. Importantly, when the trustee selects option (2), whether
the amount sent is multiplied by a constant factor (resulting in additional return to thetrustor) is probabilistic. As a result, the trustor cannot infer the trustee’s actions from theirown payoff. Thus, the trustee’s choice becomes a hidden action, leading to potential moral
hazard. Since the dictator’s payoff does not depend on the deliverer’s actions, in our game,even without introducing stochastic elements, the deliverer’s choice constitutes a hidden
action.
Charness and Dufwenberg (2006) and Vanberg (2008) demonstrated that in a hidden
action environment, pre-communication (non-binding promises by the trustee) encourages
trust behavior (the trustor sends money, and the trustee generates returns and sends themback to the trustor). In light of these findings, we investigate whether promises are effective
in a hidden action environment in the charity market. Specifically, we examine whether nonbinding promises by the deliverer promote the dictator’s transfers and enhance receiver’s
payoffs.

2.3

Treatments

In order to examine the consequences of moral hazard in the charity market and the effects
of non-binding promises, we used three treatment groups. The first two treatments focus
on whether the deliverer’s actions are hidden.
• Enforcement treatment: Stage 1: the dictator determines both 𝑥 and 𝑠. Stage 2: thedeliverer must choose 𝑠 prescribed by the dictator.
• Hidden action treatment: Stage 1: the dictator decides 𝑥. Stage 2: the deliverer
decides 𝑠.
In the enforcement treatment group, the dictator can observe and verify the allocation
ratio. However, in the hidden action treatment group, the dictator cannot observe theallocation ratio. Thus, we compare the dictator’s sent amount and receiver’s payoff
between the two treatment groups, in order to investigate the impact of moral hazard in the10charity market on donation behavior and the welfare (payoff) of the receiver. Hoppe andSchmitz (2018) has also examined the effects of hidden action with similar treatments. The
third treatment introduces promises from the deliverer in situations where moral hazard
occurs.
• Promise treatment: Stage 0: the deliverer chooses a non-binding allocation ratio

𝑠0 and discloses it to the dictator. Stage 1: the dictator determines 𝑥. Stage 2: thedeliverer decides 𝑠. The payoffs of all three players are determined by 𝑠 rather than𝑠0 .
We compare the dictator’s sent amount and receiver’s payoff between the hidden action
treatment and promise treatment groups. This comparison aims to examine the impactof the deliverer’s promise on donation behavior and the welfare of the recipient in thepresence of moral hazard in the charity market.

3

Experimental Design

In December 2023, we conducted experiments at the Research Institute for Socionetwork
Strategies (RISS) at Kansai University, with participants from RISS’s subject pool via
ORSEE (Greiner, 2015). We obtained approval from the Institutional Review Board of the
Research Institute for Socionetwork Strategies at Kansai University (Approval Number:
2023003).
The experiment consisted of eight sessions lasting 90 minutes each. Treatment assignments were as follows: initially, we evenly assigned the hidden action and promise
treatment groups at the session level. Then, for sessions assigned to the hidden action
treatment group, we assigned the enforcement treatment group to all groups in either odd
or even rounds (assigning hidden action treatment group to the remaining rounds).10
The session procedure was as follows. First, participants took a quiz on the gamestructure and received explanations via a computer, in order to enhance their understanding.
Next, participants played a one-shot game consisting of 14 rounds.11 Groups were randomly
1011

Whether to assign enforcement treatment group in odd rounds was equally allocated at the session level.
A calculator was provided to players during decision-making to predict the payoffs of all three players.

11formed again, and roles were reassigned in each round. As an initial endowment, we
provided 100 tokens to both the dictator and deliverer (𝐼 = 100). Additionally, participants
were tasked with guessing each others’ actions and beliefs.12 The dictator decided the sent
amount and guessed the deliverer’s action (first-order belief). The deliverer determined
the allocation ratio and guessed on the dictator’s expectations regarding the deliverer’s
action (second-order belief). Meanwhile, the receiver guessed the deliverer’s action when
the dictator and deliverer were engaged in decision-making. After playing the game,participants took a survey on personal attributes and altruistic preferences. They did notreceive feedback on game results after each round but could only review their own earnings
in a summary table after survey. The experiment was computerized using oTree (Chenet al., 2016).13
Participants’ experiment rewards consisted of participation fees (1,000 JPY) and performance fees (0 to 3,200 JPY) combined. Performance fees were determined as follows: foreach participant, we randomly selected two rounds out of 14 and calculated the total tokens
earned in both the game and the guess task, converting them at 5 JPY per token. Following
Costa-Gomes et al. (2014), we adopted the quadratic scoring rule for the guess task for2
incentive compatibility.14 Earnings in tokens were determined by 120−30((𝑦 − 𝑦)/100)
̂,

where 𝑦 ̂ is the predicted value, and 𝑦 is the realized value of the target of prediction.15
The number of participants in the hidden action treatment and the enforcement treatmentgroups was 105 people (35 groups). Seven rounds were held per session for both the hidden
action treatment and the enforcement treatment groups. Therefore, the total number ofobservations for the hidden action treatment and the enforcement treatment groups was
245. The number of participants in the promise treatment group was 90 people (30 groups).
12

There was no guess task in the enforcement treatment group.
You can find oTree source code and instructions at GitHub repository. See https://github.com/KimKato-Lab/pdg-otree.
14
Haaland et al. (2023) points out that with complex incentive structures, respondents may misunderstand,leading to the potential of not obtaining accurate reports. They suggest informing participants that “honest
answers maximize earnings” and designing an interface where only interested participants can grasp the
precise rules. We followed their suggestion and presented detailed scoring rule information on the web
screen in a collapsible format with toggle buttons.
15
Assume that participants believe the value of the predicted target 𝑌 follows a cumulative distribution
𝐹 (𝑦). If the participant is risk-neutral, they would choose 𝑦̂ to maximize the expected payoff of 120 −2
30 ∫((𝑦 − 𝑦)/100)
̂𝑑𝐹 (𝑦). The first-order condition is −(60/100)[∫ 𝑦𝑑𝐹 (𝑥) − 𝑦]̂ = 0. Therefore,
the optimal response is 𝑦̂ = ∫ 𝑦𝑑𝐹 (𝑥) = 𝐸(𝑌 ). In other words, a risk-neutral participant would answer
with the expected value.
13

12

A. Sent amount

35

25
20
15

p = 0.735[p = 0.995]
p = 0.006[p = 0.001]

p = 0.003[p < 0.001]

12.29

10

11.80
7.98

5
0

p < 0.001[p < 0.001]

30
Sample average (tokens)

Sample average (tokens)

30

B. Received amount35

25

p < 0.001[p < 0.001]

20

15.35

15
10
5

Enforcement

Hidden Action
Treatments

0

Promisep = 0.024[p = 0.199]

2.37
Enforcement

Hidden Action
Treatments

4.48
PromiseFigure 2: Average Sent Amount and Received Amount for Each Treatment Group. Note:
Error bars represent standard errors of mean. The p-value is the result of a difference-inmeans test between two treatment groups. The p-value in a square bracket is the result ofMann-Whitney U test.
There were 14 rounds per session for the promise treatment. Thus, the total number ofobservations for the promise treatment group was 420. The balance test between sessions
is presented in Table 5 in Appendix A. As a result, because of a slight variation in students’
academic fields across sessions, we controlled for round dummies and variables related to
students’ academic fields in the regression analysis.

4

Results

4.1

Sent Amount and Received AmountFigure 2 showed the average amount sent by the dictator (left panel) and the average
payoff of the receiver (right panel) in each treatment group. First, we examined theconsequences of moral hazard in the charity market. Compared to the enforcement treatmentgroup, the hidden action treatment decreases the average amount sent by 4.31 tokens, 35%
reduction (7.98 tokens in the hidden action treatment group versus 12.29 tokens in theenforcement treatment group). Additionally, the hidden action treatment decreases thereceiver’s average payoffs by about 12.98 tokens, 85% reduction (2.37 tokens in the13hidden action treatment group versus 15.35 tokens in the enforcement treatment group).16
These differences are statistically significant and robust to controlling covariates andstatistical inference with session-level clustered standard errors (see Table 6 in Appendix
A). Furthermore, nonparametric tests such as the Mann-Whitney U test (Figure 2) andtwo-sample Kolmogorov-Smirnov test (Figure 5 in Appendix A) yield similar results.
Result 1: Hidden action environment discourages donation behavior and reduces recipients’
welfare. The decrease in recipients’ welfare exceeds the reduction in donations.
Next, we examined the effect of non-binding promises by the deliverer under asymmetric information. Compared to the hidden action treatment group, the promise treatment
increases the average amount sent by about 3.82 tokens, 48% increase (7.98 tokens in
the hidden action treatment group versus 11.8 tokens in the promise treatment group),
which is statistically significant. Consequently, the average amount sent in the promise
treatment group no longer exhibits a statistically significant difference compared withthe enforcement treatment group. Compared with the enforcement treatment group, thepromise treatment only reduces the average amount sent by 0.49 tokens (4% reduction).
These results are robust to controlling covariates, using session-level clustered standard
errors (Table 6 in Appendix A), and nonparametric tests (Figure 2 and Figure 5 in Appendix
A). Thus, under asymmetric information conditions, introducing non-binding promises
by the deliverer induces donation behavior comparable to situations without asymmetric
information.
However, such promises do not sufficiently improve recipients’ welfare. Comparedwith the hidden action treatment group, the promise treatment increases the receiver’s
average payoff by about 2.11 tokens, 89% increase (2.37 tokens in the hidden action
treatment group versus 4.48 tokens in the promise treatment group), which is statisticallysignificant by a simple 𝑡-test. However, this result is not robust to controlling covariates,
using session-level clustered standard errors (Table 6 in Appendix A), and nonparametrictests (Figure 2 and Figure 5 in Appendix A). Compared with the enforcement treatmentgroup, the promise treatment still reduces the receiver’s average payoff by 10.87 tokens,
16

Recent meta-analysis indicates that the average contribution of dictators (average payoff to receivers)in dictator games is 20% of the dictator’s initial endowment (Umer et al., 2022). Since the enforcement
treatment involves dictators deciding (𝑥, 𝑠), there is no asymmetric information. In this case, receiver’s
average payoff is 15% of the dictator’s initial endowment, which is slightly lower than in dictator games.

14

125
Sample average (tokens)

120
115
110

p < 0.001[p < 0.001]
p < 0.001[p < 0.001]

105.65105
100

p = 0.155[p = 0.024]
107.36

96.96

95
90

Enforcement

Hidden Action
Treatments

PromiseFigure 3: Average Deliverer’s Payoff for Each Treatment Group. Note: Error bars represent
standard errors of mean. The p-value is the result of a difference-in-means test between
two treatments. The p-value in a square bracket is the result of Mann-Whitney U test.
comprising a decrease of 71%, which is statistically significant and robust. Therefore,
the deliverer’s non-binding promises do not sufficiently offset the negative effect on thewelfare of the receiver in the hidden action environment.
Result 2: In a hidden action environment, non-binding promises by the deliverer can offset
the negative effect of information asymmetry on the average amount sent. However, suchpromises do not sufficiently offset the negative effect on the receiver’s average payoff.
Result 1 and 2 suggest that, regardless of the introduction of promises, hidden action
environment provides opportunities for the deliverer to increase their payoffs. Figure 3
illustrates the average payoffs of the deliverer for each treatment group. Compared withto the enforcement treatment group, the hidden action treatment increases the average
payoff by 9.69 tokens, 10% increase (105.65 tokens in the hidden action treatment groupversus 96.96 tokens in the enforcement treatment group). Moreover, in comparison to theenforcement treatment group, the promise treatment increases the average payoff by 10.4
tokens, 11% increase (107.36 tokens in the promise treatment group versus 96.96 tokens in

15

Table 1: Response of Amount Sent

(Intercept)
Allocation ratio (percent)
1 = Positive allocation ratio (percent)

Treatment: E(1)(2)
10.155∗∗∗3.745(2.999)(2.451)0.019-0.041∗(0.011)(0.023)16.975∗∗∗(4.872)First-order belief (percent)

Treatment: HA and P(3)(4)
6.266∗∗∗
2.597∗∗∗(0.644)(0.623)0.110∗∗∗(0.024)

1 = Positive first-order belief (percent)Observations
Adjusted 𝑅2

245
0.003

245
0.064

665
0.111

0.044
(0.030)10.459∗∗∗(2.015)665
0.170

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clustered by sessions are in parentheses. Outcome variable is the amount sent by the dictator (unit: token). In columns (1)and (2), the sample assigned to the enforcement treatment is used. In columns (3) and (4),the sample assigned the hidden action or promise treatment is used.

the enforcement treatment group). These differences are statistically significant and robust
to controlling covariates, using clustered standard errors (see Table 7 in Appendix A), andnonparametric tests (see Figure 6 in Appendix A for two-sample KS test). Therefore, thedeliverers can leverage asymmetric information to enhance their own payoffs.

4.2

Why Does the Hidden Action Treatment Reduce Sent Amount?

Hidden action environments decrease the average amount sent by dictators, but the introduction of promises offsets this negative effect. In order to examine this result in detail,we first investigate the relationship between the amount sent and allocation ratio, using
samples from the enforcement treatment group where dictators decide both these values.
Columns (1) and (2) of Table 1 present the estimated results. Column (1) suggests nocorrelation between the amount sent and the allocation ratio. However, column (2) implies
that the lack of correlation is a result of the two conflicting effects. First, when dictators
decide to send their own contribution to the receiver (𝑠 > 0), they significantly increase
the amount sent. If dictators care about the deliverer’s payoff, the coefficient of the dummy
variable, indicating a positive allocation ratio, should be negative. This reveals that dictators prioritize the receiver’s payoff over the that of the deliverer’s. Second, while thestatistical significance is marginal, when dictators decide to send a large portion of their16

own contribution to the receiver (large 𝑠), they may simultaneously decrease the amount
sent.
Similar behavioral responses are observed even in hidden action environments.
Columns (3) and (4) of Table 1 present the estimated results using samples from thehidden action treatment group and the promise treatment group. Notably, regardless ofthe presence of promises, dictators cannot observe the allocation ratio determining thedeliverer’s and receiver’s payoffs in hidden action environments. Therefore, we use thedictator’s expectations about the allocation ratio (first-order belief) as explanatory variables
for the same . Column (3) indicates a positive correlation between the amount sent and thefirst-order belief. In particular, this correlation is due to whether dictators expect a positive
allocation ratio. By column (4), dictators significantly increase the amount sent when
dictators expect some of their own transfers to contribute to the receiver’s payoff. The
motives behind such behavioral responses are discussed in Section 5.1.
Next, based on the dictator’s behavioral responses, we explain the reason behind thehidden action treatment reducing the average amount sent. Again, dictators significantly
increase the amount sent when they decide (expect) that some of their contribution will
go to the receiver. In the enforcement treatment group, 78% of dictators choose positive
allocation ratio (𝑠 > 0). In the hidden action treatment group, 48% of dictators expectthat some of their contribution will be allocated to the receiver’s payoff (𝐸𝐷 (𝑠) > 0).17
Therefore, information asymmetry reduces the proportion of dictators who anticipate
that some of their contributions will benefit the receiver at the decision-making stage,
resulting in the negative effect of the hidden action treatment. The effect of the hidden
action treatment via this mechanism is −8.22(= 10.459 × 0.48 − 16.975 × 0.78) tokens,which is greater than the overall effect (−4.31 tokens). This is because the impact of thesubstitutability between 𝑥 and 𝑠 in the enforcement treatment group is not considered.18
Taking this into account, the effect of the hidden action treatment becomes −3.55 tokens,which is closer to the overall effect.
17

The difference between the proportion of 𝑠 > 0 in the enforcement treatment group and the proportionof 𝐸𝐷 (𝑠) > 0 in the hidden action treatment group is statistically significant (𝑡-test and Mann-Whitney U
test: 𝑝 < 0.001).
18
The average allocation ratio in the enforcement treatment is 114%. Due to the substitutability between
𝑥 and 𝑠, the amount sent in the enforcement treatment decreased by 4.67 tokens.

17

Table 2: Decompose of Average Payoff of Player 𝑅

Enforcement
Hidden action
Promise𝐶𝑜𝑣(𝑥, 𝑠)
1.38
-0.76
-0.95

𝐸(𝑥)𝐸(𝑠)
13.98
3.13
5.43

Average payoff of receivers
15.35
2.37
4.48

In the promise treatment group, 66% of dictators expect some of their contribution tobenefit the receiver’s payoff.19 Therefore, under the information asymmetry, the introduction of promises enhances such expectations, leading to a higher average contribution in thepromise treatment group compared with the hidden action treatment group. The effect ofthe promise treatment via this expectation formation is 1.883(= 10.459 × (0.66 − 0.48))
tokens, representing half of the overall effect (3.82 tokens).

4.3

Why Does Not Promise Improve Recipient’s Welfare?

As stated in Result 2, despite offsetting the decrease in average amount sent because of
information asymmetry, non-binding promises do not sufficiently improve the receiver’s
payoff. To examine the underlying cause of this result, we decompose the receiver’s average
payoff using the covariance formula into two parts: 𝐸(𝜋𝑅 ) = Cov(𝑥, 𝑠) + 𝐸(𝑥)𝐸(𝑠).
The results are presented in Table 2. The first component is the covariance between theamount sent and allocation ratio. This reflects the increase in the marginal effect of theamount sent on the recipient’s payoff, as the allocation ratio increases. While the covariancein the enforcement treatment group is positive, the covariance is negative in the hidden
action and promise treatment groups. Through this component, the promise treatment
reduces the recipient’s average payoff by about 2.33(= −0.95 − 1.38) tokens comparedto the enforcement treatment (21% of the overall negative effect of the promise treatment).
The positive covariance in the enforcement treatment group arises from the significant
increase in contributions by dictators who choose a positive allocation ratio (as observedin column (2) of Table 1). In fact, restricting samples where dictators who choose apositive allocation ratio yields a negative covariance (−1.9) in the enforcement treatmentgroup. However, as shown later, behavioral responses in the hidden action and promise
19

The proportion of 𝐸𝐷 (𝑠) > 0 differs significantly between the hidden action treatment and the promise
treatment groups (𝑡-test and Mann-Whitney U test: 𝑝 < 0.001).

18

200
Sample average (tokens)

175
150
125

p < 0.001[p < 0.001]
p < 0.001[p < 0.001]
113.74p = 0.193[p = 0.178]

100
75
50

39.19

46.01

Hidden Action
Treatments

Promise25
0

Enforcement

Figure 4: Average Allocation Ratio for Each Treatment Group. Note: Error bars represent
standard errors of mean. The p-value is the result of a difference-in-means test between
two treatments. The p-value in a square bracket is the result of Mann-Whitney U test.
treatment groups do not involve a significant increase in the allocation ratio due to positive
amounts sent. Instead, a strong behavioral response is observed, in which the allocation
ratio decreases as the amounts sent increases. Consequently, the covariances in the hidden
action and promise treatment groups are negative.20
The second element is the product of the average amount sent and the average allocation
ratio. This simply reflects that increases in both the average amount sent and average
allocation ratio increase the receiver’s average payoff. The average allocation ratios foreach treatment group are shown in Figure 4. As a result, compared with the enforcement
treatment group, the average allocation ratio in the hidden action treatment group is 74.55
percentage points lower, and in the promise treatment group, it is 67.73 percentage points
lower. However, there is no statistically significant difference in the average allocation
ratio between the promise and hidden action treatment groups. These differences are
statistically significant and robust to controlling covariates and dictator’s contributions,20

Figure 8 in Appendix A shows joint distribution of amount sent and allocation ratio for each treatment.

19

Table 3: Response of Allocation Ratio(Intercept)
Amount sent (token)
Second-order belief (percent)

Hidden action treatment(1)
26.226∗∗∗(4.383)-0.483∗∗∗(0.136)0.427∗∗∗(0.028)

Promise of allocation ratio (percent)Observations
Adjusted 𝑅2

245
0.129

Promise treatment(2)(3)
35.090∗∗∗27.884∗∗∗(5.481)(5.538)-0.463∗∗-0.696∗∗∗(0.230)(0.257)0.616∗∗∗(0.104)0.238∗∗∗
0.024(0.071)(0.033)
420
420
0.049
0.232

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clustered by sessions are in parentheses. Outcome variable is allocation ratio (unit: percent). In column (1), we use thesample from the hidden action treatment. In columns (2) and (3), we use the sample fromthe promise treatment.

cluster standard errors, and nonparametric tests.21 Therefore, non-binding promises failto sufficiently increase the allocation ratio, leading to no improvement in the receiver’s
average payoff. As a result, the promise treatment reduces the receiver’s average payoffby −8.5(= 4.48 − 15.35) tokens, accounting for 79% of the overall negative effect ofthe promise treatment group.
The reason for the higher allocation ratio in the enforcement treatment group lies in the
differences in decision-makers regarding the allocation ratio. In the enforcement treatmentgroup, dictators determine the allocation ratio. Since the allocation ratio does not affectdictators’ payoffs at all, altruistic dictators have an incentive to maximize the allocation
ratio as much as possible. On the other hand, in the hidden action and promise treatmentgroups, the deliverer determines the allocation ratio. Altruistic deliverers face a trade-off
between the decrease in their payoff (𝜋𝐸 ) and the increase in the receiver’s payoff (𝜋𝑅 ).
As a result, the average allocation ratio in the enforcement treatment group is higher thanthat in the hidden action and promise treatment groups.
Next, we estimate the deliverer’s behavioral response to examine why no difference isobserved in the average allocation ratio between the hidden action and promise treatmentgroups. The estimation results of the response of the allocation ratio to the amount sent
and the second-order belief (deliverer’s expectation regarding the dictator’s expectation
21

Regression results are presented in Table 8 in Appendix A. Additionally, Figure 7 in Appendix A shows
the distribution of allocation ratios and the results of the two-sample Kolmogorov-Smirnov test.

20

about the allocation ratio) are presented in Table 3. Columns (1) and (3) indicate that as
dictators increase their contributions, deliverers decrease the allocation ratio. Through thismechanism, the promise treatment decreases the allocation ratio by 4.36(= −0.696 ×11.80 − (−0.483) × 7.98) percentage points.
The higher the second-order belief, the more deliverers increase the allocation ratio.
The promise treatment does not increase the average second-order belief (40.06% in thepromise treatment group versus 39.36% in the hidden action treatment group). However,the coefficient value for the second-order belief may differ between the two treatments(𝑧-score: 1.755, 𝑝-value: 0.079). This suggests that the promise treatment may exhibit amore sensitive response to the second-order belief. Through this mechanism, the promise
treatment increases the allocation ratio by 7.87(= 0.616 × 0.4006 − 0.427 × 0.3936)
percentage points.
Column (2) shows that the increase in the allocation ratio at the promise stage increases
the allocation ratio actually chosen. From columns (3) we note that once the secondorder belief is controlled for, this correlation disappears, suggesting that the effect of theallocation ratio at the promise stage only influences the allocation ratio chosen through thesecond-order belief.
In summary, the promise treatment has both a negative effect from the substitution
with the amount sent and a positive effect from the sensitive response to the second-orderbelief. The motives behind such behavioral responses are discussed in Section 5.2. The
cancellation of these conflicting effects results in no difference in the average allocation
ratio between the two treatment groups.22

4.4

Welfare Loss for Recepients by Breaking Promises

As promises are non-binding, the deliverer can choose a lower allocation ratio than that
proposed during the promise stage and break the promise. 56% of deliverer actually breaktheir promises. Table 4 estimates the propensity of deliverer to break promises. The higher
the proposed distribution ratio in the promise stage, the more likely the deliverer is to break22

The sum of these conflicting effects is 3.514% percentage points, accounting for half of the overall
effect.

21

Table 4: Regressions of Response of Deliverer(Intercept)
Allocation ratio in the promise stage (percent)Second-order belief (percent)Amount sent (token)
Observations
Adjusted 𝑅2

1 = Breaking promises(1)
0.497∗∗∗(0.025)0.004∗∗∗(0.001)-0.004∗∗∗(0.001)0.003∗∗(0.001)256
0.196

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clustered by sessions are in parentheses. We use sample with 𝑥 > 0 in the promise treatment. For interpretation purposes, the explanatory variable “Amountsent” is adjusted so that the smallest positive contribution (one token) is
zero.

their promise. Those who keep their promises propose an average distribution ratio of

48.3% in the promise stage and actually choose an average distribution ratio of 88.5%.
In contrast, deliverers who break their promises propose an average distribution ratio of

85.1% in the promise stage and actually choose an average distribution ratio of 12.6%.
Moreover, the deliverer is more likely to break their promises when the dictator allocates alarger amount, or when second-order beliefs are higher. This corresponds to the deliverers’
behavioral responses seen in Table 3.
If deliverers were to actually choose the allocation ratio proposed in the promise stage,receiver’s average payoff would increase from 4.48 tokens to 9.59 tokens (a 114% increase).
Therefore, breaking promises by deliverer results in a reduction of receiver’s payoff toless than half. By the 𝑡-tests, the counterfactual average payoff of receiver if all promises
were kept is statistically significantly higher than the average payoff in the hidden action
treatment group (𝑝 < 0.001), and statistically significantly lower than the average payoffin the enforcement treatment group (𝑝 = 0.001). This suggests that even if everyone
were to keep their promises, the introduction of promises cannot cover the welfare loss ofreceiver due to information asymmetry.

22

5Discussion

5.1

Dictator’s Motivation

As we demonstrate in Section 4.2, dictators significantly increase the amount sent when they
anticipate (or decide) that a portion of their contribution will improve the receiver’s payoff.
This finding is consistent with that of Ashraf et al. (2006), where trustors are more likely
to exhibit trust behavior when the expected return in trust games is high. The dictator’s
contributions stem from altruistic motives to enhance the receiver’s payoff. This motive canbe explained by various models, including the pure altruism model (Andreoni and Miller,
2002), impact philanthropy model considering the social impact of donations (Duncan,
2004), and social preference models incorporating the maximin criterion, considering theplayer with the lowest payoff (Charness and Rabin, 2002).23 Therefore, dictators are more
likely to exhibit trust behavior towards the deliverer, significantly increasing the amountsent, when they anticipate that the deliverer will engage in altruistic behavior, i.e., when
dictators expect high altruistic utility.

5.2

Deliverer’s Motivation

5.2.1

Guilt Aversion

As shown in Section 4.3, the deliverer increases the allocation ratio proportionally tothe second-order belief. This is akin to the findings of Dufwenberg and Gneezy (2000),
wherein the trustee is more likely to exhibit trustworthy behavior, as they believe that thetrustor expects them to act trustworthily in trust games. Dufwenberg and Gneezy (2000)
interprets this result as the trustee’s motivation of guilt aversion, where they do not want toreturn a payoff that falls below the trustor’s expectations, as formalized by Charness andDufwenberg (2006). However, interpreting the deliverer’s behavioral response in terms of
the original guilt aversion is challenging since the payoff of the dictator, who is the trustor,
23

The inequality aversion model (Fehr and Schmidt, 1999) is another representative example of outcomebased social preference models. According to this model, dictators are motivated to reduce inequality between
themselves and the receiver (inequality advantageous to the dictator) without widening inequality between
the dictator and the deliverer (inequality disadvantageous to the dictator). Details on the theoretical model
are provided in the Appendix B.

23

does not depend on the deliverer’s actions.
As mentioned earlier, the dictator sends funds to the deliverer not because they expect anincrease in their own payoff, but because they anticipate an improvement in the receiver’s
payoff. Therefore, if the deliverer perceives the dictator’s motivation in this way, theywould feel guilty about taking actions that fall below the dictator’s expectations regarding
the receiver’s payoff. In our game, the deliverer’s guilt aversion entails avoiding choosing
allocation ratios that fall below the dictator’s expected altruistic utilities. This type of
guilt aversion suggests a positive correlation between the allocation ratio and second-orderbelief. Moreover, the positive correlation in the promise treatment group may be stronger
than in the hidden action treatment group. This could imply that even in the absence ofbinding forces, promises may evoke guilt.24
5.2.2

Altruistic Preferences

A substitution relationship is observed between the dictator’s transfer amount and deliverer’s allocation ratio. This is suggestive of the deliverer’s altruistic motive to increase thereceiver’s payoff, while also avoiding guilt. Here, consider a CES-type pure altruism model.
Andreoni and Miller (2002) shows that this utility function best explains the outcomes of𝜌𝜌the dictator game. This model can be expressed as 𝑈𝐸 = ((1 − 𝛽)𝜋𝐸 + 𝛽𝜋𝑅 )1/𝜌 . The
parameter 𝛽 represents altruism, and the parameter 𝜌 indicates substitutability. A deliverer
with this utility function determines the optimal share ratio of the pie 𝑝 = 𝜋𝑅 /(1 + 𝑥)
based only on 𝛽 and 𝜌.25 An increase in the transfer amount by the dictator increases theshare ratio 𝑝 of the pie.26 Therefore, the deliverer reduces the allocation ratio to maintainthe optimal share ratio of the pie.
24

It is important to note the sources of guilt aversion. There are two types of guilt aversion induced
by promises. First, individuals feel guilt due to deviations from the trustee’s expectations of the trustor’sbeliefs (second-order belief). Charness and Dufwenberg (2006) demonstrates that promises induce guilt
by increasing second-order belief. Second, individuals feel guilty due to deviations from the obligation of“what one should do.” Vanberg (2008) shows that promises themselves entail such obligations and evoke
guilt. The positive correlation between the allocation ratio and second-order belief is consistent with the firstsource. However, unlike Charness and Dufwenberg (2006), our experimental results do not show that thepromise treatment increases second-order belief. The result that the promise treatment is more sensitive tosecond-order belief might relate to the second source.
25
When the dictator makes a constant contribution, the deliverer divides the pie 1 + 𝑥, which is the sumof their initial endowment and the dictator’s contribution, with the receiver. The share ratio 𝑝 of the pie
indicates the receiver’s percentage. See C for detailed derivation.
26
𝜕𝑝/𝜕𝑥 = 𝑠/(1 + 𝑥)2 > 0

24

The substitutability between the dictator’s transfers and the deliverer’s allocation ratio isalso justified in other outcome-based social preference models. Fehr and Schmidt (1999)’s
inequality aversion model suggests that the optimal allocation ratio is one where 𝜋𝑅 = 𝜋𝐸 .
Similarly, Charness and Rabin (2002)’s social preference model proposes that the optimal
allocation ratio is one where 𝜋𝑅 = 𝜋𝐷 . These optimal allocation ratios are decreasing
functions of 𝑥.27 However, few deliverers behave consistently with these models. Table 9
in Appendix A categorizes the motives of deliverers based on outcomes. In both the hidden
action and promise treatment groups, in around 8% of cases, deliverers achieve equal
outcomes such as 𝜋𝑅 = 𝜋𝐸 or 𝜋𝑅 = 𝜋𝐷 by choosing 𝑠 ∈ (0, 2). In such cases, around23-25% of altruistic deliverers exhibit inequality aversion or care for the maximin criterion(2/8 in the hidden action treatment group; 5/16 in the promise treatment group).28

5.3

Implications to Charity Market

Deliverers face a trade-off, according to which increasing the allocation ratio to enhance
the receiver’s payoff may diminish their own potential payoff. In other words, a conflict ofinterest exists between the dictator and the deliverer. Despite motivations to avoid guilty
and to enhance the receiver’s payoff, the hidden action environment provides deliverers
with a strong incentive to act selfishly. Dictators anticipate this and hesitate to contributein such environments. In a market structure where donors cannot observe and verify thesocial impact of their donations, donors may perceive their contributions as having a weak
impact on society. As a result, the hidden action environment significantly decreases thewelfare of the receiver more than the attenuation of donation behavior. Considering theinherent purpose of donations to improve society, this result suggests that the moral hazard
issue in the donation market is more severe than anticipated.
To encourage donation behavior in hidden action environment, interventions that upwardly revise beliefs about social impact are effective. For instance, information provision
27
The allocation ratio that satisfies 𝜋𝑅 = 𝜋𝐸 is 𝑠∗ = (1 + 𝑥)/2𝑥, and 𝑑𝑠∗ /𝑑𝑥 = −1/2𝑥2 < 0.
Similarly, the allocation ratio that satisfies 𝜋𝑅 = 𝜋𝐷 is 𝑠∗ = (1 − 𝑥)/𝑥, and 𝑑𝑠∗ /𝑑𝑥 = −1/𝑥2 < 0.
See Appendix C for detailed derivation.
28
Although we provide calculator in the experiment, it is quite challenging for deliverers to find theallocation ratio that achieves equal outcomes. Considering this cognitive limitation, the proportion ofdeliverers inferred from observational data to exhibit inequality aversion or care for the maximin criterion
should be interpreted as a lower bound.

25

regarding social impact, as examined in Karlan and Wood (2017), is one such intervention.
Additionally, institutional mechanisms where charitable organizations outline their activities in advance (such as non-binding promises by deliverers in our experiment) constituteanother approach. In our experiment, such promises significantly improved donors’ expectations regarding social impact and effectively encouraged donation behavior, even in ahidden action environment. However, non-binding promises did not increase deliverers’
allocation ratios, or sufficiently improve the receiver’s welfare.
The greatest improvement in the welfare of the receiver takes place when the dictator
is able to determine the allocation ratio. This is similar to specific donation systems, where
donors can specify the use of their donations while determining the amount. Such systems
are commonly utilized in universities and research institutes. However, this involves
several considerations. First, there remains a risk of charitable organizations misusing
specific funds. Nevertheless, compared to general donations, specific donation systems
undoubtedly reduce the hidden actions of charitable organizations. Moreover, this system
may make it easier for donors to observe and verify the social impact of their donations.
Our experiment ensures that deliverers adhere to the allocation ratios specified by donors,leaving no room for hidden actions.
Second, the productivity of uses specified by donors may be lower than those determinedby charitable organizations. Generally, charitable organizations are expected to understandthe support needed better than donors. In such cases, donors should delegate the use of
donations to charitable organizations. Our experiment provides common knowledge about
the receiver’s environment and impact of deliverer’s behavior on the receiver’s payoff.
Therefore, in terms of information advantage, delegating the handling of contributions tocharitable organizations is not necessarily appropriate in our experiment.
Two limitations regarding our experiment have been identified. The first pertains tothe structure of the receiver’s payoff. Altruistic deliverers determine the allocation ratio as
inversely proportional to dictator’s contributions. This is because the receiver’s payoff isdetermined by the product of the dictator’s contribution and deliverer’s allocation ratio.
Therefore, this payoff structure might significantly decrease the receiver’s payoff. As such,reexamining the structure of the receiver’s payoff to ensure that the altruistic behavior of26

deliverers does not substitute for that of the dictator is necessary. The conclusion regarding
the decrease in the receiver’s payoff might be conservative.
The second limitation is with regard to the deliverer’s motives. Since we incentivize
their earnings in the game, deliverers face the trade-off mentioned earlier. While criminals
attempting charity fraud or for-profit organizations operating charities (as discussed by
Rose-Ackerman (1996)) may have selfish motives, it is unlikely that most nonprofit
organizations dominating the donation market harbor such strong selfish motives. Nonprofit
organizations produce public goods that are not provided by governments or markets, andsupport those left behind by government aid or market mechanisms. Therefore, to bring theexperiment closer to real markets, economic incentives of the deliverers must be tied to the
payoffs of the receivers. Nonetheless, the hidden action environment suggests opportunities
for profit-seeking organizations or criminals to act more selfishly. In particular, the resultthat half of the deliverers break promises and engage in selfish behavior suggests that thehidden action environment breeds charity fraud.

6

Conclusions

This study created a game incorporating the principal-agent relationship into the dictator
game, in order to examine the consequences of moral hazard in the donation market. The
hidden action environment in the donation market not only hampers donors’ donation
behavior, but also potentially further harms the recipient’s welfare. Introducing nonbinding promises in such an environment promotes donation behavior. However, exploiting
this, fundraising organizations have the opportunity to enhance their own payoffs, withlittle improvement in recipient welfare. As future tasks, it is necessary to examine theeffectiveness of monitoring systems and institutions in which charities specify and adhere
to their operational policies in advance (binding commitments).

27

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31

Appendix
A

Figures and Tables
Table 5: Balance Test

HA & Enforcement Promise F-test, p-value
1 = Male
0.39
0.41
0.85
1 = Foreigner
0.04
0.04
0.90
Age
20.83
20.70
0.56
Academic year
2.86
2.74
0.40
1 = Social science
0.59
0.69
0.02
1 = Economics
0.21
0.16
0.45
1 = Humanities
0.22
0.23
0.86
1 = Natural science
0.19
0.08
0.11
1 = Experience with lab experiments
0.88
0.90
0.71
Note: Average of session-level average of participant’s characteristics. The HA &Enforcement column contains the sessions that are assigned the hidden action treatment
and the enforcement treatment. The Promise column contains sessions that are assigned
the promise treatment. F-test examines the null hypothesis HA & Enforcement =Promise.
Table 6: Regressions of Sent Amount and Received Amount

Hidden action
PromiseControl average
F-test, p-value
Hidden action = Promise
Covariates
Observations
Adjusted 𝑅2

Sent amount(1)(2)-4.310∗∗∗-4.249∗∗∗(1.444)(0.869)-0.485-0.383(2.255)(2.021)
12.29012.290
0.030

0.033
X
910
0.036

910
0.009

Received amount(3)(4)-12.978∗∗∗-12.908∗∗∗(2.783)(1.806)-10.870∗∗∗-10.625∗∗∗(3.214)(2.725)15.34915.349
0.207
910
0.100

0.151
X
910
0.115

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clustered by sessions
are in parentheses. Covariates are round fixed effects, patron’s and dictator’s
academic fields (social science dummy, economics dummy, and natural sciencedummy).

32

A. Sent amount
KS test, p-value
F vs H: 0.007
H vs P: <0.001
F vs P: 0.079

0.07
0.06
0.05

KS test, p-value
F vs H: <0.001
H vs P: 0.179
F vs P: <0.001

0.08
0.06
DensityDensity

B. Received amount

0.04
0.03
0.02

0.04
0.02

0.01
0.00

0

20

40

60

80

Token
Enforcement (F)

100

0.00

0

Hidden action (H)

20

40

60
Token
Promise (P)

80

100

Figure 5: Distribution of Amount Sent by Treatment Group. Note: We show the p-valueof the two-sample Kolmogorov–Smirnov test in the upper right corner of each panel.

Table 7: Regressions of Dictator’s Payoff

Hidden action
PromiseControl average
F-test, p-value
Hidden action = Promise
Covariates
Observations
Adjusted 𝑅2

Payoff of Deliverer (unit: token)(1)(2)
8.690∗∗∗
8.680∗∗∗(1.643)(1.340)10.403∗∗∗10.255∗∗∗(1.495)(1.189)96.95996.959
0.048
910
0.076

0.025
X
910
0.079

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clustered by sessions are in parentheses. Covariates are roundfixed effects, patron’s and dictator’s academic fields (social science dummy, economics dummy, and natural sciencedummy).

33

Enforcement (F)Hidden action (H)Promise (P)0.05

Density

0.04

KS test, p-value
F vs H: <0.001
H vs P: 0.003
F vs P: <0.001

0.03
0.02
0.01
0.00

60

80

100

120
140
Payoff of Deliverer (token)

160

180

200

Figure 6: Distribution of Payoff of Deliverer. Note: We show the p-value of the two-sample
Kolmogorov–Smirnov test in the upper right corner.

Table 8: Regressions of Allocation Ratio

Hidden action
PromiseAmount sent
Control average
F-test, p-value
Hidden action = Promise
Covariates
Observations
Adjusted 𝑅2

Allocation ratio (percent)
(1)
(2)
(3)
-74.551∗∗∗-74.960∗∗∗-74.494∗∗∗(12.393)(12.958)(7.572)-67.731∗∗∗-67.777∗∗∗-65.719∗∗∗(16.750)(16.934)(13.589)-0.095-0.070(0.179)(0.172)113.743
113.743
113.743
0.328

0.291

910
0.160

910
0.160

0.233
X
910
0.167

Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Standard errors clusteredby sessions are in parentheses. Covariates are round fixed effects,
patron’s and dictator’s academic fields (social science dummy,
economics dummy, and natural science dummy).

34

KS test, p-value
F vs H: <0.001
H vs P: 0.355
F vs P: <0.001

0.030

Density

0.025

Enforcement (F)Hidden action (H)Promise (P)

0.020
0.015
0.010
0.005
0.000

0

25

50

75
100
125
Distribution ratio (percent)

150

175

200

Figure 7: Distribution of Allocation Ratio. Note: We show the p-value of the two-sample
Kolmogorov–Smirnov test in the upper right corner.

35

Allocation ratio (percent)

A. Enforcement

200
175
150
125
100
75
50
25
0

Allocation ratio (percent)

0

40
60
80
Amount sent (token)

100

40
60
80
Amount sent (token)

100

40
60
80
Amount sent (token)

100

B. Hidden action

200
175
150
125
100
75
50
25
0
0

Allocation ratio (percent)

20

20

C. Promise

200
175
150
125
100
75
50
25
0
0

20

Figure 8: Joint Distribution of Sent Amount and Distribution Ratio by Each Treatment
Group. Note: The bubble size is the sample36
size.

Table 9: Classification of Deliverer’s Motivation
Hidden action

PromiseNo transaction
121
164
Equitable outcomes can be realized
18
34
Feasible: Selfish
8
13
Feasible: Inequality aversion
02
Feasible: Maximin criterion
2
3Feasible: Other altruistic type8
16
Equitable outcomes cannot be realized
106
222
Infeasible: Selfish
38
99
Infeasible: Possible inequality aversion or maximin criterion
7
17
Infeasible: Other altruistic type61
106
Note: When 𝑥 = 0, there are no transactions. We consider a deliverer who chooses
𝑠 = 0 to be selfish. When 𝑥 > 1/3, the deliverer can achieve an equal outcome at aninterior point. When 𝑥 ≤ 1/3, the deliverer cannot achieve an equal outcome. In thiscase, a deliverer concerned with inequality aversion or the maximin criterion may choose𝑠 = 2 to minimize inequality as much as possible. We consider a deliverer who chooses𝑠 = 2 under 𝑥 ≤ 1/3 to be concerned with inequality aversion or the maximin criterion.
Among deliverers who choose 𝑠 > 0, we consider those who cannot be explained byinequality aversion or the maximin criterion to be other altruistic type.

37

B

Theory of Dictator’s Altruistic Behavior

Here, we theoretically demonstrate the possibility that altruistic dictators, who consider
the payoff of the receiver, have an incentive to send transfers to the deliverer under 𝑠 > 0.
Therefore, we discuss disregarding the equilibrium of the game and dictator’s expectations
regarding 𝑠.
Pure altruism model and impact philanthropy model. The pure altruism model canbe written as 𝑈𝐷 (𝜋𝐷 , 𝜋𝑅 ) for the dictator’s utility function. In our experiments, the impact
philanthropy model has a same utility function. This model explicitly incorporates the
production function of public goods, treating donations as inputs. In our experiment, theproduction output of donations is the receiver’s payoff, and the production function is linear,i.e., 𝑍(𝑥) = 𝑠 ⋅ 𝑥. This model suggests that dictators care about the increase in output due
to contributions (impact philanthropist), proposing a utility function 𝑈𝐷 (1 − 𝑥, 𝛿), where𝛿 = 𝑍(𝑥) − 𝑍(0). This also aligns with the pure altruism model: 𝑈𝐷 (1 − 𝑥, 𝑠𝑥).
Here, consider CES-type pure altruism model:𝜌𝜌 (1/𝜌)𝑈𝐷 (𝜋𝐷 , 𝜋𝑅 ) = [(1 − 𝛽)𝜋𝐷
+ 𝛽𝜋𝑅
]
,

(1)

where 𝛽 ∈ (0, 1) is the altruistic parameter, and 𝜌 ∈ [−1, +∞) {0} is the substitutability
parameter. Then, the marginal utility of contribution is:𝜕𝑈𝐷(1−𝜌)/𝜌𝜌−1
𝜌−1= [−(1 − 𝛽)𝜋𝐷
+ 𝑠𝛽𝜋𝑅
]𝑈𝐷
.
𝜕𝑥

(2)

When 𝑠 = 0, the marginal utility of 𝑥 is always negative, so there is no incentive to choose𝑥 > 0. When 𝑠 > 0, the marginal utility of 𝑥 may be positive, so an incentive to choose𝑥 > 0 arises.
Inequality aversion. In this model, dictators make decisions according to the following
utility function:⎧{𝜋𝐷 − 𝛼2 [(𝜋𝐸 − 𝜋𝐷 ) + (𝜋𝑅 − 𝜋𝐷 )] if 𝑥(1 + 𝑠) > 1
𝑈𝐷 = ⎨.
{𝜋𝐷 − 𝛼2 (𝜋𝐸 − 𝜋𝐷 ) − 𝛽2 (𝜋𝐷 − 𝜋𝑅 ) if 𝑥(1 + 𝑠) ≤ 1
⎩

38

(3)

Here, 𝛽 represents the degree to which dictators dislike advantageous inequality, with𝛽 ∈ [0, 1). Additionally, 𝛼 represents the degree to which dictators dislike disadvantageous
inequality, satisfying 𝛽 ≤ 𝛼. For any 𝑥 and 𝑠, 𝜋𝐸 − 𝜋𝐷 = (2 − 𝑠)𝑥 ≥ 0. However, if𝑥(1 + 𝑠) ≤ 1, then 𝜋𝑅 − 𝜋𝐷 = (𝑠 + 1)𝑥 − 1 ≤ 0.
When 𝑠 = 0, 𝜋𝐸 − 𝜋𝐷 = 2𝑥 and 𝜋𝐷 − 𝜋𝑅 = 1 − 𝑥. Thus, the increase incontributions widens the inequality between dictators and deliverers (disadvantageous
inequality for dictators) while reducing the inequality between dictators and receivers(advantageous inequality for dictators). The negative marginal utility from the former
inequality enlargement outweighs the positive marginal utility from the latter inequality
reduction, so there is no incentive to choose 𝑥 > 0 under 𝑠 = 0. As the allocation ratio
increases, the enlargement of inequality between dictators and deliverers due to increased
contributions is mitigated (reduction in negative marginal utility), while the reduction of
inequality between dictators and receivers is accelerated (increase in positive marginalutility). Therefore, an incentive to choose 𝑥 > 0 arises under 𝑠 > 0.
Social welfare. Consider the Charness-Rabin type of social preference model asfollows:⎧{(1 − 𝜆)𝜋𝐷 + 𝜆[𝛿𝜋𝐷 + (1 − 𝛿) ⋅ 2] if 𝑠(1 + 𝑥) > 1
𝑈𝐸 =.
⎨{(1 − 𝜆)𝜋𝐷 + 𝜆[𝛿𝜋𝑅 + (1 − 𝛿) ⋅ 2] if 𝑠(1 + 𝑥) ≤ 1⎩(4)Here, 𝜆 ∈ [0, 1] represents the degree of importance given to social welfare, and 𝛿 ∈ (0, 1)
represents the degree of importance given to the worst-off individual (maximin criterion).
When dictators choose or anticipate 𝑠 = 0, 𝜋𝑅 = 0. Therefore, there is no incentive tochoose 𝑥 > 0. Under positive allocation ratios, in the region 𝑠(1 + 𝑥) ≤ 1, an increasein contributions contributes to an increase in 𝜋𝑅 , giving dictators an incentive to choose𝑥 > 0.

C

Theory of Deliverer’s Altruistic Behavior

The higher the amount sent by the dictator, the lower the allocation ratio the delivererchooses. Here, we theoretically justify this result using several social preference models.
39

Let 𝑠∗ ∈ [0, 2] be optimal when 𝑥 = 0, as the allocation ratio 𝑠 does not affect player
payoffs. Hence, we focus on the case where 𝑥 > 0.
CES utility function. Assume 𝑈𝐸 (𝜋𝑅 ) follows a CES-type utility function:𝜌 (1/𝜌)𝑈𝐸 (𝜋𝑅 ) = [(1 − 𝛽)(1 + 𝑥 − 𝜋𝑅 )𝜌 + 𝛽𝜋𝑅
]
,

(5)

where 𝜋𝐸 = 1 + 𝑥 − 𝜋𝑅 . Here, 𝛽 ∈ (0, 1) is the altruistic parameter, and 𝜌 ∈ [−1, +∞){0} is the substitutability parameter. Given 𝑥, the optimal first-order condition for 𝑠 is:𝜕𝑈𝐸(1−𝜌)/𝜌𝜌−1= [−(1 − 𝛽)(1 + 𝑥 − 𝜋𝑅 )𝜌−1 + 𝛽𝜋𝑅
]𝑈𝐸
= 0.
𝜕𝜋𝑅

(6)

Thus, the optimal pie share ratio (ratio of pie 1 + 𝑥 sent to the receiver) 𝑝 = 𝜋𝑅 /(1 + 𝑥)is:−1

−1/(1−𝜌)𝛽∗𝑝 = [1 + (
)
]
1−𝛽

,

(7)

1+𝑥
.
𝑥

(8)

or the optimal allocation ratio 𝑠∗ is−1−1/(1−𝜌)𝛽𝑠∗ = [1 + ()]
1−𝛽The optimal allocation ratio is a decreasing function of the dictator’s transfer amount 𝑥:𝑑𝑠∗𝛼= − 2 < 0,
𝑑𝑥
𝑥

(9)

where 𝛼 = (1 + (𝛽/(1 − 𝛽))−1/(1−𝜌) )−1 > 0.
Inequality aversion. Consider the Fehr-Schmidt type of inequality aversion model asfollows:⎧𝛽{𝜋𝐸 − 𝛼2 (𝜋𝑅 − 𝜋𝐸 ) − 2 (𝜋𝐸 − 𝜋𝐷 ) if 𝑠 > 1+𝑥
2𝑥
𝑈𝐸 =
.
⎨
{𝜋𝐸 − 𝛽2 [(𝜋𝐸 − 𝜋𝐷 ) + (𝜋𝐸 − 𝜋𝑅 )] if 𝑠 ≤ 1+𝑥
2𝑥
⎩

(10)

Here, 𝛽 represents the degree to which the deliverer dislikes advantageous inequality andsatisfies 𝛽 ∈ [0, 1). The parameter 𝛼 indicates the degree to which the deliverer dislikes

40disadvantageous inequality and satisfies 𝛽 ≤ 𝛼. Given 𝑥, the marginal utility of 𝑠 is:⎧ 𝛽
1+𝑥𝜕𝑈𝐸 {𝑥 ( 2 − 1 − 𝛼) < 0 if 𝑠 > 2𝑥
=⎨
.
𝜕𝑠
1+𝑥
{𝑥 ( 32 𝛽 − 1)
if 𝑠 ≤ 2𝑥⎩(11)

Therefore, if 2/3 < 𝛽, the optimal allocation ratio is 𝑠∗ = (1 + 𝑥)/2𝑥, which is adecreasing function of 𝑥 (𝑑𝑠∗ /𝑑𝑥 = −1/2𝑥2 < 0). If 𝛽 ≤ 2/3, the optimal allocation
ratio is 𝑠∗ = 0.
Social welfare. Consider the Charness-Rabin type of social preference model asfollows:⎧{(1 − 𝜆)𝜋𝐸 + 𝜆[𝛿𝜋𝐷 + (1 − 𝛿) ⋅ 2] if 𝑠 > 1−𝑥
𝑥
𝑈𝐸 =
.
⎨
{(1 − 𝜆)𝜋𝐸 + 𝜆[𝛿𝜋𝑅 + (1 − 𝛿) ⋅ 2] if 𝑠 ≤ 1−𝑥
𝑥
⎩

(12)

Here, 𝜆 ∈ [0, 1] represents the degree of importance given to social welfare, and 𝛿 ∈ (0, 1)
represents the degree of importance given to the worst-off individual (maximin criterion).
Given 𝑥, the marginal utility of 𝑠 is:⎧1−𝑥𝜕𝑈𝐸 {−𝑥(1 − 𝜆) < 0 if 𝑠 > 𝑥
=
.
⎨
𝜕𝑠
1−𝑥
{𝑥(𝜆𝛿 − (1 − 𝜆)) if 𝑠 ≤ 𝑥⎩(13)Therefore, if (1 − 𝜆)/𝜆 < 𝛿, the optimal allocation ratio is 𝑠∗ = (1 − 𝑥)/𝑥, which isa decreasing function of 𝑥 (𝑑𝑠∗ /𝑑𝑥 = −1/𝑥2 < 0). If 𝛿 ≤ (1 − 𝜆)/𝜆, the optimal
allocation ratio is 𝑠∗ = 0.

41