Underweighting of rare events in strategic games

Research on individual decisions from experience reveals a robust tendency to behave as if rare events are underweighted. Experimental studies of strategic interactions often exclude probabilistic outcomes, thus neglecting the potential extension of this tendency to strategic games. Our study addresses this gap by examining how players in games adjust their strategies when confronted with low-probability, high-impact outcomes. We introduce two finitely repeated, asymmetric games with lottery-based payoffs. These games, when simplified by replacing lotteries with their expected values, yield straightforward equilibrium predictions based on dominant strategies. However, results from three experiments reveal players strongly deviate from these predictions, instead behaving consistently with underweighting of rare events. The results additionally indicate that social preferences also play a role in shaping behavior. To explain these observations, we propose the simplistic Reciprocal Altruistic Sampler (REALS) model. This model posits that players' decisions are a result of the interplay between reliance on small samples of past experiences, altruistic tendencies, and strategic considerations. We experimentally compare behavior in variants of the games that disentangle the behavior to these three components, and show that the REALS model, despite its simplicity, effectively captures their complex interactions. Our results additionally demonstrate that players can often choose strictly dominated strategies in a sophisticated effort to react to underweighting of rare events by other players. Overall, this study enhances our understanding of strategic decision making by highlighting the crucial impact of rare events and the interplay of different uncertainties in influencing players' choices.