Abstract

We study the evolution of cooperation in a structured population, combining insights from evolutionary game theory and the study of interaction networks. In earlier studies it has been shown that cooperation is difficult to achieve in homogeneous networks, but that cooperation can get established relatively easily when individuals differ largely concerning the number of their interaction partners, such as in scale-free networks. Most of these studies do, however, assume that individuals change their behaviour in response to information they receive on the payoffs of their interaction partners. In real-world situations, subjects do not only learn from their interaction partners, but also from other individuals (e.g. teachers, parents, or friends). Here we investigate the implications of such incongruences between the ‘interaction network’ and the ‘learning network’ for the evolution of cooperation in two paradigm examples, the Prisoner's Dilemma game (PDG) and the Snowdrift game (SDG). Individual-based simulations and an analysis based on pair approximation both reveal that cooperation will be severely inhibited if the learning network is very different from the interaction network. If the two networks overlap, however, cooperation can get established even in case of considerable incongruence between the networks. The simulations confirm that cooperation gets established much more easily if the interaction network is scale-free rather than random-regular. The structure of the learning network has a similar but much weaker effect. Overall we conclude that the distinction between interaction and learning networks deserves more attention since incongruences between these networks can strongly affect both the course and outcome of the evolution of cooperation.

Highlights

  • Cooperation is common in humans, but difficult to explain

  • Payoffs We focus on two paradigm examples for the evolution of cooperation, the Prisoner’s Dilemma Game (PDG) and the Snowdrift Game (SDG)

  • Since it is useful to complement individual-based simulations with a mathematical analysis, we will extend the pair approximation method, which has successfully been applied in the special case where the learning network is identical with the interaction network

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Summary

Introduction

Cooperation is common in humans, but difficult to explain. The reason is that defectors have an intrinsic advantage over cooperators since they can reap the benefits of cooperation without contributing to the costs of cooperation [1,2]. There is a huge literature on this topic, both in the biological and human sciences [3,4,5]. Two main mechanisms can help to resolve the paradox of cooperation. The first is based on the idea that cooperation is conditional and only directed to individuals that (for whatever reason) have a high tendency to cooperate as well. The second is based on non-random interactions: if the population is structured in such a way that cooperators tend to interact with cooperators while defectors tend to interact with defectors, defection will in a short-term perspective not be a successful strategy

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