Abstract
In this paper we apply the concept of a mixed Berge equilibrium to finite n-person games in extensive form. We study the mixed Berge equilibrium in both perfect and imperfect information finite games. In addition, we define the notion of a subgame perfect mixed Berge equilibrium and show that for a 2-person game, there always exists a subgame perfect Berge equilibrium. Thus there exists a mixed Berge equilibrium for any 2-person game in extensive form. For games with 3 or more players, however, a mixed Berge equilibrium and a subgame perfect mixed Berge equilibrium may not exist. In summary, this paper extends extensive form games to include players acting altruistically.
Highlights
The Berge equilibrium (BE) is a solution concept in game theory introduced in [1] and formally defined in [2]
We extend the concept of the subgame perfect Nash equilibrium (SPNE) to a subgame perfect MBE (SPMBE)
We applied the concept of an MBE to finite n-person games in extensive form
Summary
The Berge equilibrium (BE) is a solution concept in game theory introduced in [1] and formally defined in [2]. The Berge equilibrium represents a strategy that is mutually cooperative. At a Berge equilibrium player i cannot gain a better payoff if any other player changes his strategy unilaterally. An MBE represents the situation where every n −1 players choose the best joint mixed strategy for the remaining player. We apply the concept of an MBE to finite extensive form games, where players make decisions sequentially. We consider here finite n-person extensive form games both with complete information and incomplete information. In a complete information game, each player is aware of the actions. Players are not aware of the actions that other players choose.
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