Pairwise-Interaction Games

  • Martin Dyer
  • Velumailum Mohanaraj
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)


We study the complexity of computing Nash equilibria in games where players arranged as the vertices of a graph play a symmetric 2-player game against their neighbours. We call this a pairwise-interaction game. We analyse this game for n players with a fixed number of actions and show that (1) a mixed Nash equilibrium can be computed in constant time for any game, (2) a pure Nash equilibrium can be computed through Nash dynamics in polynomial time for games with a symmetrisable payoff matrix, (3) determining whether a pure Nash equilibrium exists for zero-sum games is NP-complete, and (4) counting pure Nash equilibria is #P-complete even for 2-strategy games. In proving (3), we define a new defective graph colouring problem called Nash colouring, which is of independent interest, and prove that its decision version is NP-complete. Finally, we show that pairwise-interaction games form a proper subclass of the usual graphical games.


Nash equilibrium graphical game computational complexity pairwise interaction 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Dyer
    • 1
  • Velumailum Mohanaraj
    • 1
  1. 1.School of ComputingUniversity of LeedsLeedsUnited Kingdom

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