Frustration and anger in the Ultimatum Game: An experiment

Abstract

In social dilemmas, choices may depend on belief-dependent motivations enhancing the credibility of promises or threats at odds with personal gain maximization. We address this issue theoretically and experimentally in the context of the Ultimatum Minigame, assuming that the choice of accepting or rejecting a greedy proposal is affected by a combination of frustration, due to unfulfilled expectations, and inequity aversion. We increase the responder's payoff from the default allocation (the proposer's outside option) with the purpose of increasing the responder's frustration due to the greedy proposal, and thus his willingness to reject it. In addition, we manipulate the method of play, with the purpose of switching on (direct response method) and off (strategy method) the responder's experience of anger. Our behavioral predictions across and within treatments are derived from the theoretical model complemented by explicit auxiliary assumptions, without relying on equilibrium analysis.

Introduction

In this paper we test experimentally the theory of frustration and anger by Battigalli, Dufwenberg, and Smith (2019)—henceforth BDS—in the strategic context of the Ultimatum Minigame. In this social dilemma, a proposer can decide to make a fair offer that is automatically accepted, the “default allocation”, or a greedy offer that the responder can either accept or reject. Experimental results about behavior in this and in similar negotiation scenarios (e.g., Ultimatum Game) systematically deviate from the predictions of traditional economic theory, reporting a positive frequency of both default allocations and rejections of greedy offers.¹ We ask whether rejections of the greedy offer can be explained by belief-dependent preferences in line with BDS theory of anger from blaming behavior. Upon observing the greedy offer, the responder may experience frustration, which is measured by the gap between his initially expected payoff and the payoff obtained accepting the greedy offer. Frustration triggers anger that may result in a rejection, depending on the responder's sensitivity to this emotion.

In the experiment, subjects play one-shot and anonymously an Ultimatum Minigame (henceforth UMG). Our experimental manipulation is twofold, affecting both the payoff structure and the method of play in a 2×2 design. We manipulate the responder's monetary payoff from the default allocation to increase his initial expectations and thus his frustration in case of a greedy offer. In addition, we manipulate the method of play, i.e., direct response versus strategy method, to determine whether responders actually observe the greedy offer before making their choice and can thus experience frustration. Indeed, when the game is played with the strategy method, responders have to decide whether to accept or reject the greedy offer without observing whether it was actually made. According to BDS theory, anger can only be triggered by the observation of an event that was initially unexpected. Thus, anger should not affect the responder's choice with the strategy method.

Subjects are assigned to one of four treatments, characterized by the method of play and the responder's (Player B) monetary payoff from the default allocation, which is either $m_{\mathrm{b}}^1$ (baseline payoff treatment) or $m_{\mathrm{b}}^2>m_{\mathrm{b}}^1$ (high payoff treatment). In every treatment, prior to choices in the experimental game, they face a prediction task through which we elicit beliefs about the behavior of subjects playing in the opponent's role. Since frustration is rooted in unfulfilled expectations, our behavioral predictions across payoff treatments in the experimental game crucially depend on the responder's initial belief about the default allocation, which is endogenous and may vary with the treatment.

Given that only the responder can be affected by frustration and anger, our theoretical analysis mostly focuses on the psychological motivations that drive his decision given his initial belief about the proposer's behavior. We derive predictions about responders assuming that they have belief-dependent preferences, given by a combination of anger and inequity aversion. Predictions about the proposers are instead derived from the simplifying assumption that they maximize their expected monetary payoff.

Our theoretical analysis takes into account that the anonymous interaction of experimental subjects necessarily features incomplete information about co-players' relevant traits. In addition, the textbook equilibrium hypothesis that players have correct conjectures about the co-players' decision rules is unjustified in this context. Therefore, we just assume that (i) both players choose best replies given their personal traits and beliefs, (ii) proposers take this into account, and (iii) some mild across-treatment restrictions on beliefs hold. Assumption (i) is a subjective rationality condition. In the case of responders, it involves addressing a trade-off between increasing one's own payoff and decreasing the payoff of the proposer conditional on the greedy offer. Frustration and anger make this trade-off belief-dependent: the higher the initially expected payoff, the higher the incentive to reject the greedy offer. For what regards beliefs, across-payoff treatments assumptions matter only for the direct response method, as the belief-dependent motive of anger matters only in this condition. Specifically, we assume that responders in the high payoff treatment $m_{\mathrm{b}}^2$ are not less optimistic than responders in the baseline treatment $m_{\mathrm{b}}^1$. We also assume that the relation between the distributions of the proposer's second-order beliefs in $m_{\mathrm{b}}^1$ and $m_{\mathrm{b}}^2$ reflects the relation between the distributions of the responder's first-order beliefs in these two treatments.

Given our experimental design, the theoretical analysis delivers comparative behavioral predictions across treatments. We predict a higher rejection rate with the direct response method than with the strategy method, because the frustration motive is assumed to be relevant only in the former. Focusing on the direct response method, our auxiliary comparative assumption about the responder's beliefs implies that his initially expected payoff is higher in the high payoff treatment $m_{\mathrm{b}}^2$ than in the baseline treatment $m_{\mathrm{b}}^1$. With this, the frustration motive implies a higher frequency of rejections in the high payoff treatment $m_{\mathrm{b}}^2$ than in the baseline treatment $m_{\mathrm{b}}^1$. Instead, the distribution of responders' choices is expected to be constant across payoff treatments with the strategy method, where rejections can only be caused by inequity aversion.

Again focusing on the direct response method, proposers are assumed to understand that the probability of rejection is increasing in the responder's initially expected payoff. With this, our auxiliary assumption about the distributions of the proposers' second-order beliefs across payoff treatments implies that they deem rejections more likely in the high payoff treatment $m_{\mathrm{b}}^2$ than in the baseline treatment $m_{\mathrm{b}}^1$. Therefore, we predict a higher frequency of the default allocation in the high payoff treatment with the direct response method. With the strategy method, instead, proposers' beliefs about conditional rejection and their choices in the game should be constant across payoff treatments because they expect the frustration motive to be absent. For the same reason, we predict more greedy offers with the strategy than with the direct response method.

Importantly, the behavioral predictions of our model hinge on whether the responder can actually experience frustration upon observing the greedy offer, which is not the case with the strategy method. As we discuss in Section 7, by adopting a broader definition of frustration—different from the one proposed in BDS—and admitting that responders can to some extent imagine the feeling of frustration and react accordingly, we can in principle allow for a positive effect of the payoff increase on rejections with the strategy method. However, it is rather implausible that imagining oneself being frustrated could produce the same angry response as actually feeling frustrated.² Thus, anger should at least be significantly attenuated with the strategy method compared to the direct response method.

The simplifying assumption that proposers merely maximize their expected payoff affects the predictions about their behavior. If proposers are inequity averse, an increase in the default-allocation payoff of the responder (only) may make them more prone to make the greedy offer. Since we measure proposers' beliefs, such counterbalancing effect may be revealed by the data. We discuss in Section 7 the implications of a generalized model that allows proposers to be inequity averse. Note, however, that the aforementioned predictions about responders are unaffected, because they do not rely on strategic reasoning of the responder about the proposer.

In line with the theory of frustration and anger, we find that, with the direct response method, responders' tendency to reject is positively correlated with the elicited initial expectation of the default allocation, and that the rejection rate is higher with the direct response method than with the strategy method. Also, the payoff treatment does not significantly affect behavior with the strategy method; yet, contrary to our prediction, neither it does with the direct response method.