SFB 303 Discussion Paper No. B - 93

Author: Selten, Reinhard
Title: Anticipatory Learning in Two-Person Games
Abstract: A learning process for 2-person games in normal form is introduced. The game is assumed to be played repeatedly by two large populations, one for player 1 and one for player 2. Every individual plays against changing opponents in the other population. Mixed strategies are adapted to experience. The process evolves in discrete time.All individuals in the same population play the same mixed strategy. The mixed strategies played in one period are publicly known in the next period. The payoff matrices of both players are publicly known.In a preliminary version of the model, the individuals increase and decrease probabilities of pure strategies directly in response to payoffs against last period's observed opponent strategy. In this model the stationary points are the equilibrium points, but genuinely mixed equilibrium points fail to be locally stable.On the basis of the preliminary model an anticipatory learning process is defined, where the individuals first anticipate the opponent strategies according to the preliminary model and then react to these anticipated strategies in the same way as to the observed strategies in the preliminary model. This means that primary learning effects on the other side are anticipated, but not the secondary effects due to anticipations in the opponent population.
Creation-Date: 1988
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