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.
This survey analyzes central ideas and the current state of the economic theory of learning in games. In game theory learning can be thought of as both an alternative to equilibria and as a way to better understand the nature of equilibria. Outside of game theory, theory of learning shows economic theory (for example, the classic Cournot oligopoly) in a new light, provides interesting theoretical problems, is nontrivial from econometric perspective, and can be studied with experimental methods. It also links economics with unexpected scientific disciplines: biology, philosophy of rationality and computer science. However, existing surveys are not particularly accessible to beginners and are not accessible at all in Russian. This survey intends to fill these gaps. It can serve both as an introduction and as a short reference. We analyze issues of classification as well as the models themselves. Theoretical descriptions are illustrated with concrete examples. Special attention is devoted to the empirical and experimental work. We also draw conclusions and hypothesize on perspectives of the field and its future role in economic theory.
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.