Cooperation and competition between pair and multi-player social games in spatial populations

TL;DR

This paper explores how individuals in spatial populations choose between pairwise and group interactions in social games, revealing complex dynamics and counterintuitive outcomes driven by multi-player interactions and pattern formation.

Contribution

It introduces a model allowing players to switch attitudes between pair and multi-player games, demonstrating how these choices affect evolutionary outcomes and pattern formation.

Findings

Both attitudes can be advantageous at specific parameters.

Increasing public goods multiplication can lead to full defection.

Pattern formation is driven by multi-player interactions and microscopic states.

Abstract

The conflict between individual and collective interests is in the heart of every social dilemmas established by evolutionary game theory. We cannot avoid these conflicts but sometimes we may choose which interaction framework to use as a battlefield. For instance some people like to be part of a larger group while other persons prefer to interact in a more personalized, individual way. Both attitudes can be formulated via appropriately chosen traditional games. In particular, the prisoner's dilemma game is based on pair interaction while the public goods game represents multi-point interactions of group members. To reveal the possible advantage of a certain attitude we extend these models by allowing players not simply to change their strategies but also let them to vary their attitudes for a higher individual income. We show that both attitudes could be the winner at a specific parameter value. Interestingly, however, the subtle interplay between different states may result in a counterintuitive evolutionary outcome where the increase of the multiplication factor of public goods game drives the population to a fully defector state. We point out that the accompanying pattern formation can only be understood via the multipoint or multi-player interactions of different microscopic states where the vicinity of a particular state may influence the relation of two other competitors.