Nash equilibrium in multi-player games with the choice of time instants and integral cost functionals
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We consider the multi-player game in which each of the players chooses a positive number meaning a time instant. The cost functions involve improper integrals with infinite upper limit. The authors obtain necessary conditions for the strategy of a player to be the best response to the strategies of other players and also sufficient conditions for the existence of the best response. Using these results, the authors formulate conditions for a tuple of strategies to be a Nash equilibrium. The result on the reduction of the initial game to a game in which each of the players has finitely many strategies is presented. For a game with certain symmetry properties, the authors give a complete description of the set of Nash equilibrium points. Algorithms for finding best responses and Nash equilibria in the initial game are presented. The algorithms consist of a finite number of item-by-item examinations.
KeywordsNash Equilibrium NASH Time Instant Nash Equilibrium Point Symmetric Game
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- 1.S. A. Brykalov, “The choice of the temination instant in a certain differential game,” Izv. Ross. Akad. Nauk Teor. Sistemy Upravlen., 1, 105–108 (1997).Google Scholar
- 3.A. F. Kleimenov, Nonantagonistic Positional Differential Games [in Russian], Nauka, Ekaterinburg (1993).Google Scholar
- 4.A. N. Krasovskii and N. N. Krasovskii, Control under Lack of Information, Birkhäuser, Boston (1995).Google Scholar
- 5.N. N. Krasovskii, Control of a Dynamical System [in Russian], Nauka, Moscow (1985).Google Scholar
- 6.N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).Google Scholar
- 8.G. Owen, Game Theory [Russian translation], Mir, Moscow (1971).Google Scholar
- 9.H. Robbins, D. Siegmund, and Y. Chow, The Theory of Optimal Stopping [Russian translation], Nauka, Moscow (1977).Google Scholar
- 11.A. I. Subbotin and A. G. Chentsov, Optimization of Guarantees in Control Problems [in Russian], Nauka, Moscow (1981).Google Scholar
- 12.N. N. Vorob’ev, Game Theory, Lectures for Economists [in Russian], LGU, Leningrad (1974).Google Scholar
- 13.V. I. Zhukovskii and A. A. Chikrii, Linear-Quadratic Differential Games [in Russian], Naukova Dumka, Kiev (1994).Google Scholar