Expectations in the Ultimatum Game: Distinct Effects of Mean and Variance of Expected Offers

Abstract

Being treated fairly by others is an important need in everyday life. Experimentally, fairness can be studied using the Ultimatum Game, where the decision to reject a low, but non-zero offer is seen as a way to punish the other player for an unacceptable offer. The canonical explanation of such behavior is inequity aversion: people prefer equal outcomes over personal gains. However, there is abundant evidence that people's decision to reject a low offer can be changed by contextual factors and their emotional state, which cannot be explained by the inequity aversion model. Here, we expand a recent alternative explanation: rejections are driven by deviations from expectations: the larger the difference between the actual offer and the expected offer, the more likely one is to reject the offer. Specifically, we provided participants with explicit information on what kind of offers to expect using histograms depicting distribution of offers given in a previous experiment by the same proposers. Crucially, we showed four different distributions, manipulating both the mean and the variance of these expected sets of offers. We found that 50% of our participants clearly and systematically changed their behavior as a function of their expectations (11% followed the standard-economic model of pure self-interest and 39% where not distinguishable from the inequity-aversion model). Using a logistic mixed-model analysis, we found that the mean and variance differently affect the decision to reject an offer. Specifically, the mean expected offer affected the threshold of what offers are acceptable, while the expected variance of offers changed how strict participants were about this threshold. Together, these results suggest that social expectations have a more complex nature as current theories propose.

Victim Sensitivity and Proposal Size Modulate the Ingroup Favoritism During Fairness Norm Enforcement

“…Moreover, the regression analyses found that the higher high victim sensitive allocation expectation of persons, the lower the acceptance possibility of offer 8:2 during intergroup interaction. Both behavioral and neuroimaging research found that expectations of people of what they will receive was negatively associated with acceptance responses (Vavra et al, 2018 ), and participants might adopt the group conformity norm toward ingroup, and the expectations norm to outgroup (Wang et al, 2017 ). This pattern supports and extends the findings of the previous studies.…”

Direct feedback and social conformity promote behavioral change via mechanisms indexed by centroparietal positivity: Electrophysiological evidence from a role‐swapping ultimatum game

“…Splitting at the median maximizes statistical power relative to other splits. Psychologically, offers of $5 and $4 are also similar in that they are both overwhelmingly accepted (Vavra et al, 2018), and both reflect what subjects themselves tend to propose most frequently (Oosterbeek et al, 2004).…”

Social and Non-social Mechanisms of Inequity Aversion in Non-human Animals

“…By consequence, reward rejections or refusals of task performance could also be caused by failed expectations and negative reward prediction errors, and, hence, cannot with certainty be attributed to IA. A recent human study provided further evidence for the importance of expectations (Vavra et al, 2018). Participants in an ultimatum game were provided with explicit information on what kind of offers to expect by a certain proposer.…”

“…The authors showed four different distributions, manipulating both the mean and the variance of these expected sets of offers. They found that 50% of the participants systematically changed their behavior as a function of their reward expectations (Vavra et al, 2018). As only the offer expectations differed between conditions, social processes alone cannot explain the changes in behavior corresponding to these offer expectations.…”