Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

TL;DR

This paper reviews how temporal fluctuations and spatial correlations affect evolutionary game dynamics, highlighting deviations from traditional replicator equations and their implications for cooperation evolution.

Contribution

It provides a comprehensive analysis of non-mean-field effects in evolutionary games, extending understanding beyond classical replicator dynamics.

Findings

Temporal and spatial effects induce significant deviations from replicator outcomes.

Non-trivial modifications influence the emergence of cooperation.

Linearity assumptions relate to strategy update rules and their effects.

Abstract

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.