Koller, Megiddo and von Stengel showed how to efficiently compute minimax strategies for two-play... more Koller, Megiddo and von Stengel showed how to efficiently compute minimax strategies for two-player extensive-form zero-sum games with imperfect information but perfect recall using linear programming and avoiding conversion to normal form. Their algorithm has been used by AI researchers for constructing prescriptive strategies for concrete, often fairly large games. Koller and Pfeffer pointed out that the strategies obtained by the algorithm are not necessarily sequentially rational and that this deficiency is often problematic for the practical applications. We show how to remove this deficiency by modifying the linear programs constructed by Koller, Megiddo and von Stengel so that pairs of strategies forming a sequential equilibrium are computed. In particular, we show that a sequential equilibrium for a two-player zero-sum game with imperfect information but perfect recall can be found in polynomial time. In addition, the equilibrium we find is normal-form perfect. We also describe an extension of our technique to general-sum games which is likely to be prove practical, even though it is not polynomial-time.
We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a l... more We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game.
Koller, Megiddo and von Stengel showed how to efficiently compute minimax strategies for two-play... more Koller, Megiddo and von Stengel showed how to efficiently compute minimax strategies for two-player extensive-form zero-sum games with imperfect information but perfect recall using linear programming and avoiding conversion to normal form. Their algorithm has been used by AI researchers for constructing prescriptive strategies for concrete, often fairly large games. Koller and Pfeffer pointed out that the strategies obtained by the algorithm are not necessarily sequentially rational and that this deficiency is often problematic for the practical applications. We show how to remove this deficiency by modifying the linear programs constructed by Koller, Megiddo and von Stengel so that pairs of strategies forming a sequential equilibrium are computed. In particular, we show that a sequential equilibrium for a two-player zero-sum game with imperfect information but perfect recall can be found in polynomial time. In addition, the equilibrium we find is normal-form perfect. We also describe an extension of our technique to general-sum games which is likely to be prove practical, even though it is not polynomial-time.
We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a l... more We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game.
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