On the dynamics of word of mouth learning with and without anticipations

We analyze the learning behavior of two populations engaged in playing a ‘battle of the sexes’ game. The boundedly rational players change their strategy with some positive probability if they learn, via direct communication with other players, about a strategy which currently 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' coordination equilibria if the initial population distributions are asymmetric. For symmetric initial population distributions, depending on the players' propensity to adopt new strategies, convergence towards the mixed strategies' equilibrium or periodic and complex behavior might occur. The introduction of anticipations leads to the emergence of stable fixed points of the learning process, which are no Nash equilibria, via a fold and a transcritical bifurcation. If one equilibrium is risk dominant, this equilibrium has a larger basin of attraction than the other coordination state for both the dynamics with and without anticipations. However, the introduction of anticipations increases the basin of attraction of the risk-dominated equilibrium.