Communication Leading to Subgroup Nash Equilibrium for Generalized Information

• Autorzy: Matsuhisa T.

Identyfikatory

DOI

10.3233/FI-2016-1363

• Języki publikacji: EN

Abstrakty

EN

This paper treats subgroup Nash equilibriums which concept is given as an extension of Nash equilibrium of a strategic game with non-partitional information, and addresses the problem how to reach the equilibrium by communication through messages according to network among players. A subgroup Nash equilibrium of a strategic game consists of (1) a subset S of players, (2) independent mixed strategies for each member of S together with (3) the conjecture of the actions for the other players outside S provided that each member of S maximizes his/her expected payoff according to the product of all mixed strategies for S and the conjecture about other players' actions. Suppose that the players have a reflexive and transitive informationwith a common prior distribution, and that each player in a subgroup S predicts the other players' actions as the posterior of the others' actions given his/her information. He/she communicates privately his/her belief about the other players' actions through messages to the recipient in S according to the communication network in S.We show that in the pre-play communication according to the revision process of their predictions about the other players' actions, their future predictions converges to a subgroup Nash equilibrium of the game in the long run.

Słowa kluczowe

EN

communication; conjecture; message; Nash equilibrium; protocol; noncorporative game; non partition information; S4n-knowledge model

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 145, nr 3
• Strony: 323--340
• Opis fizyczny: Bibliogr. 17 poz., tab.

Twórcy

autor

Matsuhisa T.

• Institute of Applied Mathematical Research Karelia Research Centre, Russian Academy of Science, Pushkinskaya ulitsa 11, Petrozavodsk, Karelia, 185910, Russia
• Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie Gory, Moscow, 119991 Russia

Bibliografia

• [1] Matsuhisa T. Communication Leading to Subgroup Nash Equilibrium I – S5n-Knowledge Case. Preprint; 2015.
• [2] Bacharach M. Some extensions of a claim of Aumann in an axiomatic model of knowledge. Journal of Economic Theory. 1985; 37:167–190. doi: 10.1016/0022-0531(85)90035-3.
• [3] Binmore K. Fun and Games. Lexington, Massachusetts USA, D. C. Heath and Company; 1992. ISBN-10:0669246034, 13: 978-0669246032.
• [4] Aumann RJ, Brandenburger A. Epistemic conditions for mixed strategy Nash equilibrium. Econometrica. 1995; 63:1161–1180. doi: DOI: 10.2307/2171725.
• [5] Parikh R, Krasucki P.Journal of Economic Theory. 1990; 52:178–189. doi: 10.1016/0022-0531(90)90073-S.
• [6] Matsuhisa T. Communication leading to mixed strategy Nash equilibriumI, T.Maruyama (eds)Mathematical Economics, Suri-Kaiseki-Kenkyusyo Kokyuroku. 2000; 1165:245–256.
• [7] Matsuhisa T, Kamiyama K. Lattice structure of knowledge and agreeing to disagree. Journal of Mathematical Economics Vol. 27. 1997. p. 389–410. doi: 10.1016/S0304-4068(97)00785-4.
• [8] Kalai E, Lehrer E. Rational learning to mixed strategy Nash equilibrium. Econometrica. 1993; 61:1019–1045. Available from: http://www.jstor.org/stable/2951492.
• [9] Jordan JS. Bayesian learning in normal form games. Games and Economic Behavior. 1991; 3:60–81.
• [10] Myerson RB. Acceptable and predominant correlated equilibria. International Journal of Game Theory. 1986; 15:133–154.
• [11] Nash JF. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America. 1950; 36:48–49. doi: 10.1073/pnas.36.1.48.
• [12] Aumann RJ. Agreeing to disagree. Annals of Statistics. 1976; 4:1236–1239.
• [13] Matsuhisa T. Communication leading to a Nash equilibrium without acyclic condition (S4-knowledge case). M. Bubak et al (eds) International Conference on Computer Science, Springer Lecture Notes in Computer Science. 2004; 3039:884–891. doi: 10.1007/978-3-540-25944-2 114.
• [14] Matsuhisa T. Bayesian communication under rough sets information. C. J. Butz et al (eds) 2006 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, WI-ITA 2006Workshop Proceedings. IEEE Computer Society; 2006. p. 378–381. doi: 10.1109/WI-IATW.2006.50.
• [15] Matsuhisa T. and Strokan, P. Bayesian belief communication leading to a Nash equilibrium in belief. Deng, X. and Ye, Y. (eds) Internet and Network Economics, Springer Lecture Notes in Computer Science. 2005; 3828:299–306. doi: 10.1007/11600930 29.
• [16] Monderer D, Samet D. Approximating common knowledge with common beliefs, Games and Economic Behaviors. 1989; 1:170–190.
• [17] Kuhn H. Extensive games and the problem of information. Contributions to the Theory of Games. 1953; 2(28):193–216.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).