Cooperation in alternating interactions with memory constraints

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous. Individuals provide help at one time and receive help at another. Here, we explore such alternating games in which players take turns. We mathematically characterize all Nash equilibria among memory-one strategies. Moreover, we use evolutionary simulations to explore various model extensions, exploring the effect of discounted games, irregular alternation patterns, and higher memory. In all cases, we observe that mutual cooperation still evolves for a wide range of parameter values. However, compared to simultaneous games, alternating games require different strategies to maintain cooperation in noisy environments. Moreover, none of the respective strategies are evolutionarily stable. In many instances of reciprocity, individuals cooperate in turns. Here, the authors analyze the equilibria and the dynamics of such alternating games, and in particular describe all strategies with one-round memory that maintain cooperation.

Automated summary

Researchers in this study analyzed the strategies in alternating games through mathematical characterization and evolutionary simulations, finding that mutual cooperation still evolves under various model extensions and parameter values. However, in noisy environments, alternating games require different strategies to maintain cooperation, and none of the strategies are evolutionarily stable.