Communication Leading to Subgroup Nash Equilibrium for Generalized Information
What is it about?
In the analysis of game theoretical situations, the concept of Nash equilibrium plays central role. This paper proposes an extended notion of the Nash equilibrium for a strategic game with non-partitional information, called `subgroup Nash equilibriums', and addresses the problem how to reach the equilibrium by communication through messages according to network among players.
Why is it important?
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. In fact. 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.