Pairwise-Interaction Games
نویسندگان
چکیده
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 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.
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