Subjective Games and Equilibria
Applying the concepts of Nash, Bayesian or correlated equilibrium to 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 subjective Na.sh and correlated equilibria, replace unavailable objective knowledge by subjective assessments. When playing such a game repeatedly, subjective optimizers will converge to a subjective equilibrium. We apply this approach to some well known examples including a single multi-arm bandit player, multi-person multi-arm bandit games, and repeated Cournot oligopoly games.
The authors wish to acknowledge valuable conversations with Eddie Dekel-Tabak and other seminar participants of the 1993 Summer in Tel Aviv Workshop, the University of California, San Diego, the California Institute of Technology, and the University of Chicago. This research was supported by NSF Economics, Grant Nos. SES-9022305 and SBR-9223156, and by the Division of Humanities and Social Sciences of the California Institute of Technology. This is an extended version of the paper entitled "Bounded Learning Leads to Correlated Equilibrium" (see Kalai and Lehrer (1991)). Published as Kalai, Ehud, and Ehud Lehrer. "Subjective games and equilibria." Games and Economic Behavior 8, no. 1 (1995): 123-163.
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