Towards a Theory of Subjective Games

The repeated situation of two-person symmetric games with random matching is considered, where an individual does not know the objective payoff function, and therefore, formulates the subjective payoff function in every period according to a learning rule defined by Matsushima (1998). We assume that the objective game satisfies a property of strategic coordination, which implies that the opponents' choosing the same action as the individual is beneficial to the latter. It is shown that, in the long run, the individual comes to misperceive that there exists no strategic conflict with the opponents with respect to fairness as well as efficiency, i.e., formulate the subjective game which has the unique efficient action vector, and succeeds to implement it as the strictly dominant action vector.