Evolutionarily stable strategy in asymmetric games: Dynamical and information-theoretical perspectives.

Area of Science:

• Evolutionary Game Theory
• Dynamical Systems Theory
• Information Theory

Background:

• Evolutionarily stable strategy (ESS) is a core concept in evolutionary game theory.
• Existing ESS definitions for asymmetric games have varied relationships with replicator dynamics.
• Replicator equations model the evolutionary dynamics of strategy frequencies in populations.

Purpose of the Study:

• To review and present key definitions of ESS in asymmetric games.
• To scrutinize these definitions and establish hitherto unreported equivalences.
• To connect ESS definitions to the asymptotic stability of fixed points in replicator dynamics.

Main Methods:

• Coherent presentation and close scrutiny of various ESS definitions for asymmetric games.
• Analysis of the correspondence between ESS definitions and fixed points of the replicator equation.
• Application of relative entropy minimization for information-theoretic insights into ESS.

Main Results:

• Established equivalences between different ESS definitions, some previously unreported.
• Demonstrated connections between ESS definitions and the dynamical stability of replicator dynamics.
• Revealed a threefold connection linking game theory, dynamical systems, and information theory via ESS.

Conclusions:

• The study provides a unified perspective on ESS definitions in asymmetric games.
• It highlights the importance of dynamical stability in defining ESS.
• It establishes a novel link between game theory, dynamical systems, and information theory.