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Abstract: We explore the computational complexity of computing pure Nash equilibria fora new class of strategic games called integer programming games with differenceof piecewise linear convex payoffs. Integer programming games are games whereplayers- action sets are integer points inside of polytopes. Using recentresults from the study of short rational generating functions for encoding setsof integer points pioneered by Alexander Barvinok, we present efficientalgorithms for enumerating all pure Nash equilibria, and other computations ofinterest, such as the pure price of anarchy, and pure threat point, when thedimension and number of -convex- linear pieces in the payoff functions arefixed. Sequential games where a leader is followed by competing followers aStackelberg-Nash setting are also considered.



Author: Matthias Köppe, Christopher Thomas Ryan, Maurice Queyranne

Source: https://arxiv.org/







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