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Linear Complementarity Algorithms for Infinite Games

John Fearnley, Marcin Jurdziński, Rahul Savani
Arxiv ID: 0909.5653Last updated: 1/16/2020
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have not been previously studied in the context of infinite games, and they offer alternatives to the classical strategy-improvement algorithms. The two algorithms are described purely in terms of discounted games, thus bypassing the reduction from the games to LCPs, and hence facilitating a better understanding of the algorithms when applied to games. A family of parity games is given, on which both algorithms run in exponential time, indicating that in the worst case they perform no better for parity, average-reward, or discounted games than they do for general P-matrix LCPs.

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