Reciprocity with stochastic loss

Nathan W. Chan; Leonard Wolk

doi:10.1007/s40881-023-00129-3

Reciprocity with stochastic loss

Published online by Cambridge University Press: 17 January 2025

Nathan W. Chan and

Leonard Wolk

Show author details

Nathan W. Chan*: Affiliation:
Stockbridge Hall, 80 Campus Center Way, Resource Economics, University of Massachusetts Amherst, MA 01003 Amherst, USA
Leonard Wolk*: Affiliation:
Department of Finance, Vrije Universiteit Amsterdam, De Boelelaan 1105, NL-1081HV Amsterdam, The Netherlands
*: nchan@umass.edu
e-mail: l.wolk@vu.nl

Article contents

Abstract
Introduction
Experimental design and procedure
Results
Discussion
Declarations
Footnotes
References

Rights & Permissions

Abstract

We introduce stochastic loss into a gift exchange game to study how information on intentions affects reciprocity. In one treatment, the respondent observes the amount received and whether a loss occurred, so both the consequential outcome and the sender’s original intention are known. In the other two treatments, information about whether a loss occurred is hidden, and the respondent is only informed of the amount received (outcome) or the amount initially sent (intention). Using both regression-based approaches and non-parametric tests, we find greater reciprocity in the two treatments that reveal intentions. These differences arise even in a simple one-shot setting without reputational benefits and are economically meaningful; they are similar in magnitude to the difference attributable to a full point reduction in the amount received. Our findings show the impact of the information environment on reciprocity in settings with uncertainty and suggest that transparency is important to reciprocity.

Keywords

Reciprocity Gift exchange Uncertainty Information

JEL classification

C91: Laboratory, Individual Behavior D80: General D91: Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making‡ C72: Noncooperative Games

Information

Type: Original Paper
Information: Journal of the Economic Science Association , Volume 9 , Issue 1 , June 2023 , pp. 51 - 65

DOI: https://doi.org/10.1007/s40881-023-00129-3 [Opens in a new window]
Creative Commons: This is an Open Access article, distributed under the terms of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright: Copyright © The Author(s) 2023

1 Introduction

Reciprocity is central to economic relationships and has particular importance given the prevalence of incomplete contracts (Fehr and Gächter Reference Fehr and Gächter2000). Intentions, or perceived intentions, may affect agents’ decisions, even when observable outcomes are indistinguishable (McCabe et al. Reference McCabe, Rigdon and Smith2003; Dufwenberg and Kirchsteiger Reference Dufwenberg and Kirchsteiger2004; Charness et al. Reference Charness and Levine2007; Stanca et al. Reference Stanca and Corazzini2009; Stanca Reference Stanca2010; Sebald Reference Sebald2010). Yet assessing intentions can be difficult, particularly when they are shrouded by uncertainty.

We ask: how does positive reciprocity unfold when outcomes are determined by both intentions and chance? We posit that transparency of intentions may enhance trust in and of itself. This issue is germane to many settings that involve both trust and chance. For example, consider taxi services. A foreign visitor may be unfamiliar with optimal routes and traffic, making it difficult to ascertain whether a circuitous and lengthy journey resulted from the driver’s intentions or from stochastic factors. Absent such knowledge, the foreign visitor may be hesitant to offer a generous tip, whereas a local passenger will have more cause to trust. In politics, voters may reward or punish politicians based on policy outcomes, even though those outcomes are not entirely under the politician’s control. Transparency from the politician may modulate trust and support at the ballot box, even conditional on the same policies being delivered. Intentions, and observability of intentions, may similarly matter for customers and service providers for car and home repairs. Stochastic factors can affect the success of diagnosis and repair, and the customer’s reciprocity (e.g., online review, willingness to rehire) may depend upon the transparency of the provider’s intentions. In all of these examples, observability of intentions can affect underlying behaviors as well as the welfare of the involved parties.

To study these settings, we modify the classic gift-exchange game by making it possible for the first-mover’s gift to experience a partial loss. In one treatment (Intentions and Outcomes, or I+O), the respondent observes the amount received and whether a loss occurred, making the first-mover’s intention perfectly observable. We contrast this with two treatments where information about the loss is hidden. In the first such treatment (Outcomes), the respondent can only observe the amount received, leaving uncertain the first-mover’s intention. In the other (Intentions), the respondent observes the amount sent but not how much has actually been received.

We find greater reciprocity when intentions are known than when they are not. Differences are economically meaningful: they are roughly the same magnitude as the difference attributable to a full point reduction in the amount received. We find these results in a simple one-shot setting without reputational benefits, suggesting that transparency is a virtue in itself for reciprocity, even while ruling out dynamic strategic considerations. Our experimental setup and results are unique from the extant literature, which has focused primarily on observable intentions and observable outcomes.

In reciprocal relationships, one must assess the kindness (intentions) of a partner’s actions (Rabin Reference Rabin1993; Dufwenberg and Kirchsteiger Reference Dufwenberg and Kirchsteiger2004; Falk and Fischbacher Reference Falk and Fischbacher2006), and chance can furthermore influence perceptions of kindness (Sebald Reference Sebald2010). Several studies incorporate chance in experimental settings with reciprocity. Closely related to our work is that of Charness et al. (Reference Charness and Levine2007). Their gift exchange game includes a random variable that can increase or decrease the first-mover’s gift. Conditional on the same amount received, respondents are more generous when good intentions (and bad luck) give rise to a given result than when good luck augmented an otherwise small gift. Cushman et al. (Reference Cushman, Dreber, Wang and Costa2009) use a different experimental design but likewise allow different choice/chance combinations to reach the same consequential outcomes. These studies demonstrate the importance of both intentions and outcomes, with strong parallels to our I+O treatment. However, our additional Intentions and Outcomes treatments shed unique light on the nature of reciprocity when risk and incomplete information are involved.

Rubin and Sheremeta (Reference Rubin and Sheremeta2016) implement random shocks to effort in a three-stage principal-agent game. First, the principal offers a suggested wage and effort combination; second, the agent chooses effort; and third, the principal observes the outcome and can reward or punish the agent. The authors vary whether a random shock alters the agent’s effort in the second stage, and they also vary whether the principal can observe this random shock (in addition to the realized outcome) in the third stage. Adding random shocks to the effort leads to lower effort by agents and lower payoffs for the principal but, interestingly, not for the agents. In Rubin and Sheremeta (Reference Rubin and Sheremeta2016), the principal can communicate expectations in the first round and use that as a reference point in the third stage; in contrast, our focus is on situations where an individual cannot offer a contract or signal expectations.

Other papers also explore related questions in different settings. Rand et al. (Reference Rand, Fudenberg and Dreber2015) use a repeated prisoner’s dilemma and report that observable intentions lead to more cooperation. However, they study cooperativeness in an infinitely repeated prisoner’s dilemma game, which is distinct from reciprocity in a one-shot game like ours. In spite of the one-shot setting, we continue to find that observability of intentions matters for reciprocity. Falk et al. (Reference Falk, Fehr and Fischbacher2008) implement a sequential game to show that intention-based models are limited and that preferences for fairness remain important for the respondent. Gago (Reference Gago2021) uses a dictator game with punishment opportunities, finding that unkind intentions trigger punishments, even if the realized outcome is not a bad one. His subjects are fully informed about intentions, whereas in our experiment, we directly compare behavior when varying the observability of intentions.

In a closely related paper, Toussaert (Reference Toussaert2017) studies the role of intentions using a noisy binary trust game in which the first-mover’s decision can be replaced by a random decision by a computer with some probability. The second-mover faces uncertainty about the likelihood that this happens and is unaware of the true state they are in.Footnote ¹ The findings show that trust relationships are less likely to occur when the probability of computer involvement is large, suggesting that players are more prosocial when trust intentions can be more credibly signaled. Building on the insights of Toussaert (Reference Toussaert2017), we directly vary the observability of intentions, outcomes, or both in this paper. In our case, the respondent always knows that the intention is at least as kind as the outcome. Furthermore, the action sets for both the first- and second-mover are discrete rather than binary in our study. This has the advantage that the second-mover can adjust their response to match their beliefs more closely than when only having two actions (e.g. trust or don’t trust) at their disposal. This makes our game relevant for questions such as: “When something bad happens in a trust relationship, how much reciprocity will we see? How does the level of reciprocity depend on the information available to the respondent?” A further difference is that Toussaert (Reference Toussaert2017) uses the strategy method; doing so can dampen emotional responses, which may be important for pro-social behavior.

In related work by Friehe and Utikal (Reference Friehe and Utikal2018), a player chooses between a probability distribution that will favor herself or a different distribution that will (in expectation) provide better benefits to her partner. The partner only observes the final outcome, but there is some probability that the first-mover’s choice will be revealed. The authors find that intentions and outcomes both matter, but furthermore, the respondent will punish more strongly if the first-mover attempts to conceal the original choice. Their findings suggest that hiding intentions is viewed as unfair. Unlike (Friehe and Utikal Reference Friehe and Utikal2018), we focus on the (exogenous) observability of intentions rather than (endogenous) concealment of intentions, and we do so in a setting with positive rather than negative reciprocity.

Taken together, our study is unique in identifying the dual roles of uncertainty and the overarching information environment. Our work provides new insights on settings with incomplete or unenforceable contracts by investigating how information—or lack of information—on the realization of uncertainty shapes reciprocal relationships. These findings are relevant for wide classes of problems in the real-world where uncertainty may shroud the link between intentions and outcomes.

2 Experimental design and procedure

2.1 Design

Subjects were randomly assigned to pairs to play an anonymous one-shot game based on the classic gift-exchange game. The game involved two roles—a first-mover (P1, “she”) and a respondent (P2, “he”)—and each subject was randomly assigned to one of these roles.

Each subject was endowed with 5 points. P1 was then asked to allocate some of her endowment to send to the P2, keeping the remainder of her endowment in her private account. The amount sent would be multiplied by 3, and that total would be entered into P2’s account. P2 would then decide how much of his initial endowment (from 0 to 5) to send back to P1. The amount sent would be multiplied by the same factor of 3, and the total would be entered into P1’s account.

We compare three experimental conditions with visibility of Intentions and Outcomes (I+O), Outcomes only (Outcomes), and Intentions only (Intentions). In all treatments, there was a 50% chance that one unit would be lost from the first-mover’s gift before being multiplied by the multiplication factor.Footnote ² For I+O, P2 could observe both the outcome and whether there was a loss. The Outcomes and Intentions treatments were identical to I+O, except P2 could not observe whether a loss occurred or not. In Outcomes, the respondent only observed the amount received; in Intentions, only the amount sent was shown.

2.2 Procedure

We ran the experiment online with participants recruited via Prolific (https://www.prolific.ac/), a platform for online studies.Footnote ³ All participants had to be (1) above the age of eighteen and (2) fluent in English to ensure that they understood the task. We recruited 468 participants for the study, for a total of 234 pairs. The data for I+O and Outcomes were collected across multiple sessions between 2018 and 2020, and the data for Intentions were collected in September and October of 2021. The experimental software was implemented in Python running the oTree server (Chen et al. Reference Chen, Schonger and Wickens2016). We obtained ethical approval from Vrije University’s Research Ethics Review Board at the School of Business and Economics and the Institutional Review Board at the University of Massachusetts Amherst.

Subjects began by providing informed consent. Those giving consent were randomly assigned into pairs for the one-shot game. They proceeded to read instructions that outlined the rules of the game, information about payoffs, and an example scenario. Subjects were then asked to complete two unincentivized quiz questions to check their comprehension. The first control question (true/false) was answered correctly by 420 out of 468 subjects in a single try and the second control question (calculation) was answered correctly by 129 subjects on their first and only try. For the second control question, another 130 subjects gave an answer that was within two points of the correct answer. This error is equivalent to forgetting to deduct the cost of their own contribution from the payoff. After each answer, they received feedback on their responses, including detailed information on how to solve the problems.Footnote ⁴

From there, subjects played the one-shot game. Upon completion, subjects were paid via the Prolific system using a conversion rate of 1 point = $0.30 USD. In general, once a subject entered the experiment on Prolific, it took only a few minutes to complete. Screenshots of the instructions and decisions screens for the I+O treatment are available in Figs. 1, 2, 3 and 4 in Appendix 1.

Fig. 1

Instructions

Fig. 2

First-mover task

Fig. 3

Respondent task

Fig. 4

Result screen

3 Results

3.1 Sample composition

Prolific provides information on participant characteristics, which we can use to assess balance across treatments. In Table 1, we observe only minor differences between I+O and Outcomes; the third treatment, Intentions, however, shows meaningful differences from the others. Due to this, we control for participant characteristics in subsequent analysis.Footnote ⁵ However, as we will show, our results are very similar regardless of whether we use non-parametric tests or regressions that include or exclude controls for these individual characteristics.

Table 1

Participant characteristics by treatment. The Prolific score is a rating of the user’s quality as assessed by Prolific with a maximum of 100

	I+O	Intentions	Outcomes
Age	32.0	25.1	29.94
Female	48.9%	62.4%	45.2%
Student	37.4%	60.1%	45.2%
Prolific score	99.2	99.6	99.1

Table 2 presents summary statistics for each treatment, with averages for the original amount sent by the first-mover (Sent), the amount received by the respondent (Received), the amount the respondent returned to the first-mover (Returned), and a binary variable indicating whether a loss occurred (Loss). There are no significant differences across treatments, except for the amount returned in Outcomes, which is lower than in Intentions and I+O.

Table 2

Summary statistics split by treatment

	I+O	Intentions	Outcomes
Sent	3.37 (1.27)	3.33 (1.16)	3.37 (1.17)
Received	2.84 (1.35)	2.85 (1.36)	2.87 (1.21)
Returned	3.24 (1.31)	3.1 (1.13)	2.67 (1.3)
Loss	0.53 (0.50)	0.48 (0.50)	0.49 (0.50)
$N$	92	79	63

Variable means are shown as the primary entries; standard deviations are in parentheses

In what follows, we will provide a closer investigation of participant behavior. Throughout, the generic regression framework we use is:

(1)

\begin{matrix} y_{i} = α + β t r e a t_{i} + γ c o n t r o l s_{i} + ε_{i}, \end{matrix}

where $y_{i}$ is the outcome of interest (e.g., amount sent or amount returned), $t r e a t_{i}$ is a categorical variable denoting the treatment that player i is assigned to, and $c o n t r o l s_{i}$ is a vector of individual characteristics.

In all, we had 234 pairs, each of which comprises a unique data point. Sample sizes for each treatment are: 92 in I+O, 63 in Outcomes, and 79 in Intentions. The subsequent regressions use these sample sizes, pooling across treatments; in some specifications, the sample sizes are slightly smaller because several participants are missing data for control variables. We included the most participants in the I+O treatment, as this would allow us to examine whether reciprocity is affected by the observation of a loss.

3.2 First-mover behavior

Before examining respondent reciprocity, we first establish whether first-movers’ actions differ across treatments. Because different information will be revealed to the respondent, this may in turn affect first-mover behavior. We regress the amount sent by P1 on treatment categories and present results in Table 3; Outcomes is the omitted reference category.

For both regressions, we find no significant differences in P1 behavior across treatments, and the inclusion/exclusion of participant characteristics does not meaningfully affect between-treatment differences. Moreover, we verify using t-tests and Mann-Whitney U tests that there are no significant differences in the average amount sent by P1 or the amount received by P2 across treatments. Overall, this implies that the amount sent by P1 is not significantly driven by the information that we provide to P2. On this evidence, we feel confident to proceed in analyzing P2’s reciprocity—which is the object of primary interest—using both non-parametric and regression-based tests.

Table 3

Regression for P1 amount sent, with Outcomes as the baseline treatment

	Sent
	(1)	(2)
I+O	0.00	$-$ 0.05
	(0.20)	(0.21)
Intentions	$-$ 0.04	0.06
	(0.20)	(0.21)
Student (=1)		0.08
		(0.19)
Female (=1)		$-$ 0.22
		(0.17)
Prolific score		0.14 $^{* * *}$
		(0.04)
Age (years)		0.01
		(0.01)
Constant	3.37 $^{* * *}$	$-$ 10.80 $^{* *}$
	(0.15)	(4.18)
Observations	234	218
$R^{2}$	0.00	0.04

Robust standard errors in parentheses. *, **, and *** indicate significance at the 0.10, 0.05, and 0.01 levels, respectively. Testing for equality between I+O and Intentions gives p-values of 0.982 and 0.798, respectively

3.3 Reciprocity from the respondent

We find higher reciprocity when respondents can perfectly infer intentions of the first-mover. We present several regressions to support this claim in Table 4.

First, consider the Outcomes and Intentions treatments. Comparing only the amount returned (Column 1 in Table 4) reveals significant differences in respondent behavior: respondents in Intentions return on average 0.43 units more, simply from revealing intentions of the first-mover instead of outcomes. This finding is robust to controlling for respondent characteristics, the amount sent, and the amount received (Columns 2 and 3).Footnote ⁶ In short, columns 1–3 offer the same fundamental insight: return amounts are 0.43 $-$ 0.52 points (16% $-$ 19.5%) higher in Intentions than Outcomes. These findings are all significant at the 5% level and the magnitudes are comparable across specifications.

Table 4

Regression analysis of P2 reciprocity. The reference treatment is denoted with a ‘ $∙$ ’. A ‘−’ indicates that the treatment group was excluded from the regression

	Dependent variable: Returned
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Intentions	0.43 $^{* *}$	0.52 $^{* *}$	0.51 $^{* *}$	−	−	$-$ 0.12	$-$ 0.06	−	$∙$
	(0.21)	(0.22)	(0.22)			(0.17)	(0.20)
Outcomes	$∙$	$∙$	$∙$	$-$ 0.59 $^{* * *}$	$-$ 0.54 $^{* * *}$	−	−	$∙$	−
				(0.19)	(0.19)
I+O	−	−	−	$∙$	$∙$	$∙$	$∙$	0.49 $^{* *}$	0.35
								(0.23)	(0.24)
I+O $\times$ loss								0.09	$-$ 0.50 $^{* *}$
								(0.24)	(0.25)
Sent		0.30 $^{* * *}$				0.40 $^{* * *}$	0.40 $^{* * *}$		0.41 $^{* * *}$
		(0.09)				(0.07)	(0.08)		(0.08)
Received			0.26 $^{* * *}$	0.50 $^{* * *}$	0.49 $^{* * *}$			0.50 $^{* * *}$
			(0.08)	(0.08)	(0.09)			(0.09)
Student (=1)		0.05	0.08		0.11		$-$ 0.23	0.11	$-$ 0.27
		(0.26)	(0.26)		(0.24)		(0.22)	(0.24)	(0.21)
Female (=1)		0.03	$-$ 0.01		0.02		$-$ 0.19	0.02	$-$ 0.23
		(0.20)	(0.21)		(0.19)		(0.18)	(0.19)	(0.18)
Prolific score		$-$ 0.06	$-$ 0.05		$-$ 0.03		$-$ 0.02	$-$ 0.03	$-$ 0.04
		(0.04)	(0.04)		(0.04)		(0.06)	(0.04)	(0.06)
Age (years)		0.01	0.01		0.01		$-$ 0.00	0.01	$-$ 0.01
		(0.01)	(0.01)		(0.01)		(0.01)	(0.01)	(0.01)
Constant	2.67 $^{* * *}$	7.10 $^{*}$	6.38 $^{*}$	1.83 $^{* * *}$	4.66	1.88 $^{* * *}$	4.11	3.94	5.93
	(0.16)	(3.68)	(3.69)	(0.26)	(4.21)	(0.28)	(6.52)	(4.18)	(6.17)
I+O + I+O $\times$ loss = 0 (p-value)								<0.01	0.50
Observations	142	134	134	155	150	171	160	150	160
R-squared	0.03	0.12	0.11	0.28	0.28	0.16	0.17	0.28	0.19

Robust standard errors in parentheses. *, **, and *** indicate significance at the 0.10, 0.05, and 0.01 levels, respectively

However, simply comparing Intentions and Outcomes does not provide a complete picture because they have two degrees of difference: Intentions provides information on intentions but not outcomes, while Outcomes does the reverse. To address this issue, we bring in the I+O treatment, which is only one degree of difference from each. Both I+O and Outcomes reveal outcomes, but I+O also reveals intentions. Similarly, I+O and Intentions both reveal intentions, but I+O additionally reveals outcomes.

I+O features higher reciprocity than Outcomes, as seen in Table 4, Columns 4 and 5. Both regressions condition on the P2 outcome (i.e., amount received, which is observable in both treatments), and the latter also controls for P2 individual characteristics. We find that P2 returns 0.54 $-$ 0.59 points (20%–22%) more in I+O than in Outcomes. The coefficient on amount received is also sensible, indicating that receiving more leads P2 to return more to P1.

Next, we compare I+O and Intentions in Table 4, Columns 6 and 7. Here, both regressions condition on the P1 intentions, and the latter also controls for P2 individual characteristics. We find no significant difference in reciprocity between I+O and Intentions in either specification, while reciprocity tends to increase in the P1 intention (amount sent), as one might expect.

Lastly, let us consider how reciprocity differs in I+O under different loss realizations, relative to Outcomes (Column 8) and Intentions (Column 9). In both cases, we include a treatment dummy for I+O, but we additionally include an interaction term for I+O $\times$ Loss, which indicates how much more or less was returned when a loss was realized in I+O. This variable is sensible to condition on because it is visible to the respondent in the I+O treatment. However, we should note that the interpretation of this variable differs across columns because we condition on amount received in Column 8 (since this is visible in both I+O and Outcomes) and amount sent in Column 9 (since this is visible in both I+O and Intentions).

In Column 8, the coefficient on amount received is positive and significant, indicating that the outcome matters. However, the more interesting observation is that return amounts are higher in I+O, regardless of whether a loss was realized or not. Because I+O and Outcomes differ only on whether the amount sent is knowable, we attribute this difference to the observability of intentions.

In Column 9, the coefficient on amount sent is positive and significant, indicating that intentions matter. More interestingly, the coefficients on I+O and I+O $\times$ Loss have opposite signs and comparable magnitudes. The point estimates suggest that return amounts are slightly higher in I+O when no loss occurs (+0.35), and slightly lower when loss occurs (net effect: 0.35 $-$ 0.50 = $-$ 0.15, p-value: 0.50). Given that we condition on the amount sent, both observations are consistent with the fact that outcomes matter; return amounts are higher when the amount received is higher (i.e., no loss) than when the amount received is lower (i.e., loss). Behavior in Intentions is essentially a convex combination of behavior in I+O across loss states, which is consistent with the respondent acting on expected outcomes when they do not know about losses in Intentions. Thus, we conclude that communicating the intentions, with or without communicating outcomes, leads to similar P2 behavior. Any differences between the two can be attributed to differences in outcomes, with higher returns in I+O without loss and lower returns in I+O with loss.

In sum, all of these findings align with our overarching claim: knowledge of intentions affects reciprocity. I+O and Intentions feature similar behavior, with both providing information about the first-mover’s intentions. Meanwhile, both of these treatments differ from Outcomes, where intentions are unknown. Notably, subjects reciprocate more in I+O than Outcomes, regardless of whether they experienced a loss or not in I+O. Moreover, our regression-based results can be corroborated with non-parametric tests. Comparing return amounts across treatments, we find significantly higher return amounts in I+O than in Outcomes (Mann–Whitney U test p-value: 0.008) and likewise higher return amounts in Intentions than in Outcomes (Mann–Whitney U test p-value: 0.059). We do not find significant differences between I+O and Intentions (Mann–Whitney U test p-value: 0.301).

4 Discussion

Extensive research has investigated the relative import of intentions and outcomes in social interactions. However, the majority of such work has focused on known intentions and known outcomes. We investigate how the overarching information environment—i.e., whether intentions can be gleaned or not—shapes these interactions. To this end, we introduce uncertainty into the classic gift exchange game and vary the availability of information.

We find that reciprocity is higher when intentions are transparent than when they are hidden. Based on our regressions, these discrepancies in generosity between I+O and Outcomes (0.54) and Intentions and Outcomes (0.51) are of comparable or larger in magnitude than the coefficients on amount sent (0.30) or amount received (0.49). Thus, the consequences of having intentions visible or not are at least as large as the impact of increasing or reducing the first-mover’s gift by a full point.

These results speak to the importance of information availability, and they would be difficult to rationalize through other channels. Besides transparency of intentions, what else might explain why Outcomes has uniquely low return amounts? These discrepancies are not explainable through differences in P1’s generosity or differential levels of loss, as the amount sent by P1 and loss rates are comparable across treatments. Moreover, we directly control for amount sent (intentions), amount received (outcomes), and participant demographics across regression specifications, and the sizable gap in P2 reciprocity is robust to such variations.

One potential explanation is motivated reasoning.Footnote ⁷ In Outcomes, if P2 believes (or decides to believe) that no loss occurred, then he can return less to P1. Doing so would improve his own payoffs without harming his self-image or social-image. He can reasonably believe he is reciprocating appropriately given unobservability of P1’s initial intention, and P1 cannot distinguish whether P2 is being unreciprocal or if P2 simply believes that no loss occurred. Such reasoning would not be possible in I+O and Intentions, where P1’s intentions are known.Footnote ⁸

Could weaknesses in the experimental implementation confound our interpretation? Perhaps there are concerns about anchoring and salience. Intentions and Outcomes make different values salient (amount sent and amount received, respectively). Mechanically, the amount sent will be weakly larger than the amount received, so if P2 is thinking uncritically, he may judge P1’s actions to be less generous in the latter case. Along similar lines, it may be possible that P2 anchors to the value presented to him, which is the amount sent in Intentions and the amount received in Outcomes, and P2’s subsequent choice may be affected by this anchoring. Thus, the Intentions vs. Outcomes comparison may be confounded by these behavioral biases. However, our findings from the I+O treatment help rule out both of these possibilities. I+O, like Outcomes, places greater attention and salience on the outcome. In I+O, respondents are informed about how much they received (exactly as in Outcomes) and whether a loss occurred. Hence, if salience or anchoring were driving our results, then we would expect I+O and Outcomes to look similar to one another and Intentions to be unique among the three.Footnote ⁹

Taken together, our experiment yields robust results on the importance of the overarching information environment. Future work may consider whether transparency and knowability of intentions play a similar role in settings with negative reciprocity. It will also be interesting to investigate how our findings change when uncertainty (i.e., the probability of loss) or stakes (i.e., the size of loss) change.

Acknowledgements

We thank the participants at the New England Experimental Economics Workshop at Middlebury College for valuable feedback and we are grateful to Ella Gu for excellent research assistance. We also acknowledge helpful suggestions from our editor and anonymous referees. This study was approved by the Institutional Review Board at the University of Massachusetts Amherst as well as the Research Ethics Review Board of the School of Business and Economics at VU Amsterdam. A pilot study was conducted with funding from a Colby College Social Science Grant and with approval from the Institutional Review Board at Colby College.

Declarations

Conflict of interest

The authors have no competing interests to declare.

Appendix 1: Screenshots

In this section, we show screenshots, including instructions and tasks, for the I+O treatment.

Footnotes

¹ Because of how noise is incorporated, the first-mover’s intentions are never observable or even inferrable by the second mover (except in the edge case with zero noise). She asks: “When actions are noisy signals of trust intentions, how much noise becomes too much noise for the trust-reciprocity outcome to emerge?” (p.141).

² If P1’s gift was initially zero or one, a loss would reduce the gift to zero (i.e., gifts could not be made negative by the loss). This design choice was made for practical reasons, as we did not want to take money for participants.

³ Prolific has reliable data quality and has been used in prior experimental studies. For direct studies of Prolific data quality, see (Palan and Schitter Reference Palan and Schitter2018), Arechar et al. (Reference Arechar, Gächter and Molleman2018), and Peer et al. (Reference Peer, Brandimarte, Samat and Acquisti2017).

⁴ Relatively few participants got the second control question correct, which may raise concerns about whether comprehension affects our experimental findings. We address discuss these concerns in Sect. 4.

⁵ As mentioned in Sect. 2.2, data for Intentions were collected at a later date in which time Prolific’s subject pool may have changed.

⁶ For the comparison between Intentions and Outcomes, controlling for amount sent by P1 or amount received by P2 is not entirely sensible, as P2 cannot observe the amount sent in Outcomes or the amount received in Intentions. We implement the I+O treatment to alleviate any concerns about the comparability between Intentions and Outcomes.

⁷ We thank an anonymous referee for this suggestion.

⁸ Could our results be driven by inequality aversion rather than reciprocity? In our setting, concerns about reciprocity and inequality aversion would both drive P2 to return more when P1 sends more, so we cannot distinguish between these explanations. However, prior work by Engelmann and Strobel (Reference Engelmann and Strobel2010) shows that behavior in games like these is better captured by reciprocity than inequality aversion.

⁹ Another possibility: might differences in comprehension drive differences across treatments? To probe this question, we re-run our analyses on two alternative subsamples: (i) only respondents who were correct on both control questions and (ii) only respondents who were correct on the first question and who have the correct or ‘almost’ correct answer for the second question, as described before. For the second criteria, the significance of results in Table 4 are retained, and many of the point estimates actually grow in magnitude. For the first criteria, the differences between Intentions and Outcomes (columns 1 to 3 in Table 4) become insignificant. Yet, in all such cases, the point estimates grow in magnitude. Crucially, we retain significance in the post-regression test (I+O + I+O × loss = 0) in column 8 for both subsamples (p-values for sub-samples: (i) 0.06 (ii) 0.03). This suggests that our results are not only about P2 repaying kind intentions of P1.

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Fig. 1 Instructions

Fig. 2 First-mover task

Fig. 3 Respondent task

Fig. 4 Result screen

Table 1 Participant characteristics by treatment. The Prolific score is a rating of the user’s quality as assessed by Prolific with a maximum of 100

Table 2 Summary statistics split by treatment

Table 3 Regression for P1 amount sent, with Outcomes as the baseline treatment

Table 4 Regression analysis of P2 reciprocity. The reference treatment is denoted with a ‘∙’. A ‘−’ indicates that the treatment group was excluded from the regression

Article contents

Reciprocity with stochastic loss

Abstract

Keywords

JEL classification

Information

1 Introduction

2 Experimental design and procedure

2.1 Design

2.2 Procedure

3 Results

3.1 Sample composition

3.2 First-mover behavior

3.3 Reciprocity from the respondent

4 Discussion

Acknowledgements

Declarations

Conflict of interest

Appendix 1: Screenshots

Footnotes

References

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