ON A CLASS OF NASH EQUILIBRIA WITH MEMORY STRATEGIES FOR NONZERO-SUM DIFFERENTIAL GAMES

Jean Michel Coulomb and Vladimir Gaitsgory
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Jean Michel Coulomb: School of Mathematics, University of South Australia, The Levels, Pooraka, SA, 5095, Australia
Vladimir Gaitsgory: School of Mathematics, University of South Australia, The Levels, Pooraka, SA, 5095, Australia

International Game Theory Review (IGTR), 2000, vol. 02, issue 02n03, 173-192

Abstract: A two-player nonzero-sum differential game is considered. Given a pair of threat payoff functions, we characterise a set of pairs of acceptable feedback controls. Any such pair induces a history-dependent Nash δ-equilibrium as follows: the players agree to use the acceptable controls unless one of them deviates. If this happens, a feedback control punishment is implemented. The problem of finding a pair of "acceptable" controls is significantly simpler than the problem of finding a feedback control Nash equilibrium. Moreover, the former may have a solution in case the latter does not. In addition, if there is a feedback control Nash equilibrium, then our technique gives a subgame perfect Nash δ-equilibrium that might improve the payoff function for at least one player.

JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S021919890000010X

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