Evolution of the perception about the opponent in hypergames

This paper studies the evolution of the perceptions of players about the game they are involved in using the framework of hypergame theory. The focus is on developing methods that players can implement to modify their perception about other players´ payoffs by incorporating the lessons learned from observing their actions. We introduce a misperception function that measures the mismatch between a player´s perception and the true payoff structure of the other players. Our first update mechanism, called swap learning method, is guaranteed to decrease the value of the misperception function but in general can lead to inconsistencies in the stability properties of the resulting perception. This motivates the introduction of a second mechanism, called modified swap update method, that is guaranteed to produce a consistent perception. Finally, we identify a class of hypergames for which the modified strategy is also guaranteed to decrease the misperception function.