Paper No . 9805 Learning with Forward Looking Players

Experiments show different plays among identical players and change of reaction rules (how plays are adjusted after an observation) over time. These phenomena are not easily incorporated in adaptive learning models. We model a sophisticated learning model, where players hold “theories” which map information to beliefs using the knowledge of the game and rationality. For example, a player can think that the opponents will choose the same actions as last period, which is a Cournot type theory, but he/she could be one step forward looking and thinks that the opponents have such theory. Both theories use the same information rationally, and yet can give different best responses. As a consequence, when identical players hold diverse theories, they can play differently. Players may also rationally revise theories based on their performance, which results in changes in reaction rules over time. We show various convergence results based on a model where players are allowed to hold diverse theories as explained above. When each player holds the same theory over time, we get (a) global convergence to the Nash equilibrium in dominance solvable games, (b) a large set of initial states leading to a pure Nash equilibrium in coordination games, and (c) non-Nash limit patterns in matching pennies. If players change theories in reaction to performance in sufficiently diverse ways the dynamics exhibit enough entropy for global convergence to pure Nash equilibria in coordination games. JEL classification number: C 73