Multigame Effect in Finite Populations Induces Strategy Linkage Between Two Games

TL;DR

This paper explores how finite populations playing two interconnected games tend to develop specific strategy linkages, revealing finite size effects in evolutionary game dynamics.

Contribution

It introduces the concept of multigame effects in finite populations, showing how strategy linkages emerge between two games, which is a novel insight beyond single-game analyses.

Findings

Finite populations tend to evolve toward specific strategy linkages.

Multigame effects influence evolutionary trajectories in finite populations.

Finite size effects are significant in understanding strategy evolution.

Abstract

Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption that the population size is infinite. However, in reality, population sizes are finite. Recently, stochastic processes in finite populations have been introduced into evolutionary games in order to study finite size effects in evolutionary game dynamics. However, most of these studies focus on populations playing only single games. In this study, we investigate a finite population with two games and show that a finite population playing two games tends to evolve toward a specific direction to form particular linkages between the strategies of the two games.