Cooperation in Networks Where the Learning Environment Differs from the Interaction Environment

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.