Affiliations: [a] Institute of Applied Mathematical Research, Karelia Research Centre, Russian Academy of Science, Pushkinskaya ulitsa 11, Petrozavodsk, Karelia, 185910, Russia. takashi.matsuhisa@krc.karelia.ru | [b] Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie Gory, Moscow, 119991 Russia
Correspondence:
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Address for correspondence: Ibaraki Christian University, Ohmika 6-11-1, Hitachi-shi, Ibaraki 319-1295, Japan; Dedicated to Shoji Koizumi for his 90th birthday
Abstract: 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 information with 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.
Keywords: Communication, Conjecture, Message, Nash equilibrium, Protocol, Conjecture, Non-corporative game, Non partition information, S4n-knowledge model
