Evolutionary games on graphs

TL;DR

This paper reviews how the structure of social networks influences the evolution of strategic interactions in game theory, highlighting key models and the impact of graph topology on long-term behaviors.

Contribution

It provides a comprehensive tutorial on evolutionary game theory on graphs, emphasizing the effects of network structure on dynamic outcomes and behavioral patterns.

Findings

Network topology significantly alters evolutionary stable strategies.

Graph structures can promote cooperation or competition depending on the model.

Dynamic behaviors vary with different game classes and network configurations.

Abstract

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.