On the dynamics of word of mouth learningwith and without anticipations

Abstract

We analyze the learning behavior of two populations engaged in playing a “battle of thesexes” game. The boundedly rational players change their strategy with some positive probabilityif they learn, via direct communication with other players, about a strategy whichcurrently has a higher payoff than their own. In games with no risk‐dominant equilibrium,this learning rule leads to convergence towards one of the pure strategies' coordinationequilibria if the initial population distributions are asymmetric. For symmetric initialpopulation distributions, depending on the players' propensity to adopt new strategies, convergencetowards the mixed strategies' equilibrium or periodic and complex behavior mightoccur. The introduction of anticipations leads to the emergence of stable fixed points of thelearning process, which are no Nash equilibria, via a fold and a transcritical bifurcation. Ifone equilibrium is risk dominant, this equilibrium has a larger basin of attraction than theother coordination state for both the dynamics with and without anticipations. However, theintroduction of anticipations increases the basin of attraction of the risk‐dominated equilibrium.