The evolution of conventions under incomplete information

We formulate an evolutionary learning process in the spirit of Young (1993a) for games of incomplete information. The process involves trembles. For many games, if the amount of trembling is small, play will be in accordance with the games' (semi- strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Further, often play will most of the time be in accordance with exactly one Bayesian equilibrium. This gives a selection among the Bayesian equilibria. For two specific games of economic interest we characterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as Chicken. The second is an incomplete information bilateral monopoly, which is also an extension to incomplete information of Nash's demand game, or a simple version of the so-called sealed bid double auction. For both games selection by evolutionary learning is in favor of Bayesian equilibria where some types of players fail to coordinate, such that the outcome is inefficient.