First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

The Bayesian Foundations of solution concepts of games

We transform a non co-operati ve game into a -Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the pr iors of other players on the choice of other players, the priors over priors and so on.We provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successfulIy eliminate strategies which are not best responses. This paper therefore provides the informational foundations of iteratively unàominated strategies and rationalizable strategic behavior (Bernheim (1984) and Pearce (1984». Moreover, sufficient condi tions are also found for Nash equilibrium behavior. We also provide Aumann's (1985) results on correlated equilibria .

Phase transition of demand explained by the heterogeneity of consumers' intrinsic preferences

In 1991 Gary S. Becker presented A Note on Restaurant Pricing and Other Examples of Social In uences on Price explaining why many successful restaurants, plays, sporting events, and other activities do not raise their prices even with persistent excess demand. The main reason for this is due to the discontinuity of stable demands, which is explained in Becker's (1991) analysis. In the present paper we construct a discrete time stochastic model of socially interacting consumers deciding for one of two establishments. With this model we show that the discontinuity of stable demands, proposed by Gary S. Becker, depends crucially on an additional factor: the dispersion of the consumers' intrinsic preferences for the establishments.