Doubtful Deviations and Farsighted Play

  • Wojciech Jamroga
  • Matthijs Melissen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7026)


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.


Nash Equilibrium Deviation Strategy Rational Deviation Solution Concept Noncooperative Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wojciech Jamroga
    • 1
  • Matthijs Melissen
    • 1
  1. 1.University of LuxembourgLuxembourg

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