Efficient Computation of Equilibria for Extensive Two-Person Games (1996)by D. Koller, N. Megiddo, and B. von Stengel
Abstract:
The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, the game must first be converted to a strategic description such as the normal form. The classical normal form, however, is often exponentially large in the size of the game tree. If the game has perfect recall, a linear-sized strategic description is the sequence form. For the resulting small LCP, we show that an equilibrium is found efficiently by Lemke's algorithm, a generalization of the Lemke-Howson method.
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D. Koller, N. Megiddo, and B. von Stengel (1996). "Efficient Computation of Equilibria for Extensive Two-Person Games." Games and Economic Behavior, 14(2).
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Bibtex citation
@article{Koller+al:GEB96,
author = "D. Koller and N. Megiddo and B. {von Stengel}",
title = "Efficient Computation of Equilibria for Extensive
Two-Person Games",
journal = "Games and Economic Behavior",
volume = "14",
number = 2,
year = "1996",
}
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