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


Journal Article

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. Copyright 2006 ACM.

Full Text

Duke Authors

Cited Authors

  • Conitzer, V; Sandholm, T

Published Date

  • December 1, 2006

Published In

  • Proceedings of the International Conference on Autonomous Agents

Volume / Issue

  • 2006 /

Start / End Page

  • 537 - 544

Digital Object Identifier (DOI)

  • 10.1145/1160633.1160731

Citation Source

  • Scopus