Abstract
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.
An extended version of this paper with full proofs is available as arXiv:0909.5653.
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Fearnley, J., Jurdziński, M., Savani, R. (2010). Linear Complementarity Algorithms for Infinite Games. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_32
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