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

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 subgame, G, of O for which a certain condition holds. We also show that such a subgame 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. Finally, 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.

• Type: Conference
• Year: 2006
• Where: ATAL
• Authors: Vincent Conitzer, Tuomas Sandholm
• Keywords: ATAL 2006, Horn Satisfiability Problem, Intelligent Agents, Nash Equilibrium, Smaller Normal-form Game