Price competition and limited attention
In this article, I examine a model of oligopolistic competition in which consumers search for prices but have no knowledge of the underlying price distribution. The consumers' behaviour satisfies four consistency requirements and, as a result, their beliefs about the underlying distribution maximise Shannon entropy. I derive the optimal stopping rule and equilibrium price distribution of the model. Unlike in Stahl (1989), the expected price is decreasing in the number of firms. Moreover, consumers can benefit from being uninformed, if the number of firms is sufficiently large.
We examine an equilibrium concept for 2-person non-cooperative games with boundedly rational agents which we call Nash-2 equilibrium. It is weaker than Nash equilibrium and equilibrium in secure strategies: a player takes into account not only current strategies but also all profitable next-stage responses of the partners to her deviation from the current profile that reduces her relevant choice set. We provide a condition for Nash-2 existence in finite games and complete characterization of Nash-2 equilibrium in strictly competitive games. Nash-2 equilibria in Hotelling price-setting game are found and interpreted in terms of tacit collusion.
We consider a model of location-price competition between two firms, located on the circle. Nash equilibrium, equilibrium in secure strategies, and Nash-2 equilibrium are compared. We demonstrate that Nash-2 equilibrium exists for any locations of firms. The set of Nash-2 equilibria is treated as tacit collusion.