Alladi Ramakrishnan Hall

Nonconvergent outcomes in the evolutionary game theory: A case study of replicator dynamics

Archan Mukhopadhyay

School of Computer Science, University of Birmingham, Edgbaston, Birmingham

The celebrated Folk theorems connect static game theoretic equilibrium concepts (like Nash, ESS) with the dynamical convergent outcomes of evolutionary game dynamics (like fixed, stable fixed points, etc.). However, non-convergence is an omnipresent phenomenon in nature that is enough to compel us to analyze the occurrence of non-convergence in evolutionary models and decipher them from a game-theoretic point of view. In this talk, I try to connect the dots: the occurrence of non-convergence in evolutionary game dynamics and their game-theoretic meaning while taking the replicator map as our prototype model. I will also show how a stochastic Wright-Fisher-like process can be described by having the replicator map as the governing mean-field dynamics. Our work helps us to decipher non-convergence in evolutionary game dynamics from a game theoretic point of view akin to how one interprets fixed-point convergence as the attainment of a rational outcome.