Subjective Games and Equilibria

Applying the concepts of Nash, Bayesian, and correlated equilibria to the analysis of strategic interaction requires that players possess objective knowledge of the game and opponents' strategies. Such knowledge is often not available. The proposed notions of subjective games and of subjective Nash and correlated equilibria replace essential but unavailable objective knowledge by subjective assessments. Whea playing a subjective game repeatedly, subjective optimizers converge to a subjective equilibrium. We apply this approach to some well known examples including single-and multi-person, multi-arm bandit games and repeated Cournot oligopoly games. The concept of Nash (1950) equilibrium and its extensions to Bayesian equilibrium by Harsanyi (1967) and to correlated equilibrium by Aumann (1974) have become the main tools for modeling strategic interaction under uncertainty. In addition to their logical elegance these concepts give researchers the ability to make predictions in uncertain environments. How