Nash Equilibrium and Dynamics of Social Learning Agents

Abstract

We study a model for social-learning agents in a restless multiarmed bandit (rMAB). The rMAB has one good arm that changes to a bad one with a certain probability. Each agent seeks the good arm by random search with probability 1-r, or copying information from other agents (social learning) with probability r. Each agent’s fitness is the probability to know the good arm. In this model, we explicitly construct the unique Nash equilibrium state and show that the corresponding strategy for each agent is an evolutionarily stable strategy (ESS) in the sense of Thomas. The ESS Nash equilibrium is a solution to Rogers ’paradox. We also consider the space of mixed strategies and introduce a natural dynamics aiming at increasing each agent’s fitness. It is shown that the dynamics converges to the ESS Nash equilibrium.