Cooperation in alternating interactions with memory constraints

Peter S Park,Martin A Nowak,Christian Hilbe

doi:10.1038/s41467-022-28336-2

Peter S Park, Martin A Nowak + Show 1 more

Open Access

https://doi.org/10.1038/s41467-022-28336-2

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Abstract

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.

Highlights

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation
The respective strategies in the alternating game are Nash equilibria, we show that none of them is evolutionarily stable
There is a discrete number of rounds

Summary

Introduction

Individuals often employ reciprocal strategies to maintain cooperation. For many natural manifestations of reciprocity, simultaneous cooperative exchanges are unlikely or even impossible, such as when people ask for favors[22], vampire bats donate blood to their conspecifics[20], sticklebacks engage in predator inspection[23], or ibis take turns when leading their flock[24]. Such interactions are better captured by alternating games, in which players consecutively decide whether to cooperate[25,26,27,28].

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