Deciphering chaos in evolutionary games

TL;DR

This paper explores the emergence of chaos in evolutionary game dynamics and constructs a new game-theoretic solution that corresponds to chaotic outcomes, extending understanding beyond fixed points.

Contribution

It introduces a novel game-theoretic solution concept linked to chaotic dynamics in evolutionary games, bridging the gap between chaos and traditional equilibrium solutions.

Findings

Chaotic outcomes can be interpreted as a form of game-theoretic solution.

A new solution concept based on fitness and heterogeneity is proposed.

Chaos in evolutionary dynamics is connected to optimization of population interactions.

Abstract

Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium and the evolutionarily stable strategy. By construction, only the fixed point solutions of the dynamics can possibly be interpreted as the aforementioned game-theoretic solution concepts. Although more complex outcomes like chaos are omnipresent in the nature, it is not known to which game-theoretic solutions they correspond. Here we construct a game-theoretic solution that is realized as the chaotic outcomes in the selection monotone game dynamic. To this end, we invoke the idea that in a population game having two-player--two-strategy one-shot interactions, it is the product of the fitness and the heterogeneity (the probability of finding two individuals playing different strategies in the infinitely large population) that is optimized over the generations of the evolutionary process.