A Simple P-Matrix Linear Complementarity Problem for Discounted Games

Authors:
Marcin Jurdziński;Rahul Savani
Affiliations:
Department of Computer Science, University of Warwick, UK;Department of Computer Science, University of Warwick, UK
Venue:
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Year:
2008

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Abstract

The values of a two-player zero-sum binary discounted game are characterized by a P-matrix linear complementarity problem (LCP). Simple formulas are given to describe the data of the LCP in terms of the game graph, discount factor, and rewards. Hence it is shown that the unique sink orientation (USO) associated with this LCP coincides with the strategy valuation USO associated with the discounted game. As an application of this fact, it is shown that Murty's least-index method for P-matrix LCPs corresponds to both known and new variants of strategy improvement algorithms for discounted games.