Evolution of direct reciprocity in complex environments
Direct reciprocity is a fundamental mechanism for cooperation among non-kin. It is based on the idea that individuals are more cooperative when they interact in stable groups in which retaliation is possible. To model the evolution of reciprocity, researchers have used the framework of repeated games. Traditionally, these models rest on two assumptions. First, players are symmetric: they coincide in their strategic options, in their incentives to cooperate, and how they discount future payoffs. Second, the players' environment is fixed: players face the same game, with the same payoffs, in every round. Both assumptions are crucial, as they promote conditionally cooperative strategies like Tit-for-Tat.  Yet in most natural applications, individuals are heterogeneous, and the games they play change over time.   To address these two critical model limitations, we need to expand the theory of reciprocity. We focus on the following objectives: 1) Develop a theory of reciprocity in heterogeneous groups. Based on mathematical models and simulations, we study how different dimensions of heterogeneity affect the evolution of reciprocity. 2) Develop a theory of reciprocity in changing environments. Here, we explore the evolution of cooperation when the players' environment (and hence their feasible payoffs and strategies) can change from one round to the next. We ask which environmental feedback is most favorable to cooperation. 3) Explore the dynamics of asymmetric games with changing environments. Here, we analyze the intricacies that arise when both previous sources of complexity are present. 4) Verify the theory using behavioral experiments with human subjects. The success of the project will establish a novel framework and new tools to study the evolution of strategic behavior in non-constant environments. It will significantly enhance our ability to predict when reciprocity emerges under natural conditions.