Dynamic Stability in Population Games derived from Social Decision Problems

Abstract

As shown in a companion paper (Balter et al., Solving Maxmin Optimization Problems via Population Games, SSRN 4264811), solutions of a certain class of maxmin optimization problems can be found from symmetric Nash equilibria of related population games. In this paper we give sufficient conditions for such equilibria to arise as locally stable fixed points of the exponential form of the multiplicative weights algorithm, which is a time-discretized version of the standard replicator dynamics.

Keywords: Maxmin optimization, population games, collective decision, Nash equilibrium, local stability

JEL Classification: C61, C73, D70, D81, G11