Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective

TL;DR

This paper introduces the concept of information stable orbit in discrete-time evolutionary game dynamics, providing a game-theoretic interpretation of periodic orbits using information theory, and generalizing the evolutionarily stable strategy.

Contribution

It proposes the novel concept of information stable orbit, extending the evolutionarily stable strategy to periodic orbits in evolutionary game dynamics.

Findings

Defines information stable orbit as a generalization of ESS

Links information stable orbit to dynamical stability of periodic orbits

Provides a game-theoretic interpretation of non-convergent evolution

Abstract

Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of evolutionary game theory. As a proof-of-concept, we tap into the information-theoretic concept of relative entropy in order to construct a game-theoretic interpretation for periodic orbits in a wide class of deterministic discrete-time evolutionary game dynamics, primarily investigating the two-player two-strategy case. Effectively, we present a consistent generalization of the evolutionarily stable strategy -- the cornerstone of the evolutionary game theory -- and aptly term the generalized concept: information stable orbit. The information stable orbit captures the essence of the evolutionarily stable strategy in that it compares the total payoff obtained against an evolving mutant with the total payoff that the mutant gets while playing against itself. Furthermore, we discuss the connection of the information stable orbit with the dynamical stability of the corresponding periodic orbit.