Correlated equilibria in nonzero-sum differential games.

*(English)*Zbl 0792.90099The author extends his previous investigations [J. Math. Anal. Appl. 163, No. 1, 104-112 (1992; Zbl 0778.90102)] concerning so-called correlated equilibria in nonzero-sum differential games with nonlinear dynamics. The idea of correlated mixed strategies for static games was stated by R. J. Aumann in 1974. Its sense is that the use of probability distributions on the set of collections of pure actions often makes it possible to increase payoffs of the players compared with the case when one uses products of probability distributions of the players’ pure actions. An existence theorem for the correlated \(\varepsilon\)-equilibrium is proved. Ky Fan’s minimax theorem is used in the proof. The problem of physical realization of these equilibrium strategies in the course of the game is not discussed in the paper.

Reviewer’s remark. The existence theorem for equilibrium coalitional mixed strategies in positional differential games with nonlinear dynamics was proved in a paper of the reviewer [Probl. Control Inf. Theory 11, 85- 95 (1982; Zbl 0488.90091)]. In the same paper the question concerning the physical realization of these strategies is discussed also. Detailed investigation of all these questions can be found in the Russian monograph by the reviewer “Nonantagonistic positional differential games”, Nauka Publishers (Ekaterinburg 1993).

Reviewer’s remark. The existence theorem for equilibrium coalitional mixed strategies in positional differential games with nonlinear dynamics was proved in a paper of the reviewer [Probl. Control Inf. Theory 11, 85- 95 (1982; Zbl 0488.90091)]. In the same paper the question concerning the physical realization of these strategies is discussed also. Detailed investigation of all these questions can be found in the Russian monograph by the reviewer “Nonantagonistic positional differential games”, Nauka Publishers (Ekaterinburg 1993).

Reviewer: A.Klejmenov (Sverdlovsk)