A technique for reducing normal-form games to compute a Nash equilibrium

  • Authors:

  • Vincent Conitzer;Tuomas Sandholm

  • Affiliations:

  • Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

We present a technique for reducing a normal-form (aka. (bi)matrix) game, O, to a smaller normal-form game, R, for the purpose of computing a Nash equilibrium. This is done by computing a Nash equilibrium for a subcomponent, G, of O for which a certain condition holds. We also show that such a subcomponent G on which to apply the technique can be found in polynomial time (if it exists), by showing that the condition that G needs to satisfy can be modeled as a Horn satisfiability problem. We show that the technique does not extend to computing Pareto-optimal or welfare-maximizing equilibria. We present a class of games, which we call ALAGIU (Any Lower Action Gives Identical Utility) games, for which recursive application of (special cases of) the technique is sufficient for finding a Nash equilibrium in linear time. Finally, we discuss using the technique to compute approximate Nash equilibria.