Doubtful Deviations and Farsighted Play
Nash equilibrium is based on the idea that a strategy profile is stable if no player can benefit from a unilateral deviation. We observe that some locally rational deviations in a strategic form game may not be profitable anymore if one takes into account the possibility of further deviations by the other players. As a solution, we propose the concept of farsighted pre-equilibrium, which takes into account only deviations that do not lead to a decrease of the player’s outcome even if some other deviations follow. While Nash equilibria are taken to include plays that are certainly rational, our pre-equilibrium is supposed to rule out plays that are certainly irrational. We prove that positional strategies are sufficient to define the concept, study its computational complexity, and show that pre-equilibria correspond to subgame-perfect Nash equilibria in a meta-game obtained by using the original payoff matrix as arena and the deviations as moves.
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- 1.Osborne, M., Rubinstein, A.: A Course in Game Theory. MIT Press (1994)Google Scholar
- 6.Nakanishi, N.: Purely noncooperative farsighted stable set in an n-player Prisoners Dilemma. Technical Report 707, Kobe University (2007)Google Scholar
- 7.Mailath, G., Samuelson, L.: Repeated Games and Reputations: Long-Run Relationships. Oxford University Press (2006)Google Scholar
- 8.Greenberg, J.: The theory of social situations: an alternative game-theoretic approach. Cambridge University Press (1990)Google Scholar
- 10.Halpern, J.Y., Rong, N.: Cooperative equilibrium. In: International Conference on Autonomous Agents and Multi Agent Systems, pp. 1465–1466 (2010)Google Scholar