Evolutionary multiplayer games on graphs with edge diversity

TL;DR

This paper introduces a framework for evolutionary multiplayer games on graphs with diverse social ties, accounting for different types of edges that influence payoffs and interaction outcomes, advancing understanding of cooperation and social structure effects.

Contribution

It develops a general formula for predicting behavior success in complex social networks with diverse ties and applies it to novel scenarios like labor division and relationship-dependent games.

Findings

Labor division promotes cooperation by splitting large games into smaller ones.

Relationship-dependent interactions can be approximated by a transformed unified game.

The framework captures effects of social ties like genetic similarity and proximity on evolution.

Abstract

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division facilitates collective cooperation by decomposing a many-player game into several games of smaller sizes. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.