### Working paper

## 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.

The paper is devoted to the economic analysis of rationality in the tradition of Harvey Leibenstein: the authors perceive rationality as “calculatedness” when making decisions, while the degree of this “calculatedness” is interpreted as a variable. Thus, this approach does not correspond to the generally accepted neoclassical interpretation of rationality, according to which rationality is both full and constant. The authors believe that such a neoclassical approach makes too stringent requirements for the abilities of people. In real life, people do not behave like calculating machines. The paper discusses various factors limiting the degree of rationality of individuals. One group of factors is associated with external information constraints such as the complexity and extensiveness of information, as well as the uncertainty of the future. Another group of factors is related to informal institutions. In particular, the paper states that the system of planned socialism contributes to less rationality than the system of market capitalism. Thus, in the post-socialist countries, including contemporary Russia, one should not expect a high degree of rationality of the behavior of economic entities. The paper mentions, in particular, the factors of rationality caused by informal institutions, such as the propensity to calculate, the propensity to be independent when making decisions and the propensity to set goals. The authors also believe that people who live on their own are usually more rational than people who share a common household with someone else. This assumption is verified econometrically based on data on young urban residents collected by the authors. It turned out that the behavior of people included in this database, in general, corresponds to what the authors believed.

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.