Computing Stackelberg Equilibria of Large General-Sum Games

09/07/2019 ∙ by Avrim Blum, et al. ∙ 0

We study the computational complexity of finding Stackelberg Equilibria in general-sum games, where the set of pure strategies of the leader and the followers are exponentially large in a natrual representation of the problem. In zero-sum games, the notion of a Stackelberg equilibrium coincides with the notion of a Nash Equilibrium <cit.>. Finding these equilibrium concepts in zero-sum games can be efficiently done when the players have polynomially many pure strategies or when (in additional to some structural properties) a best-response oracle is available <cit.>. Despite such advancements in the case of zero-sum games, little is known for general-sum games. In light of the above, we examine the computational complexity of computing a Stackelberg equilibrium in large general-sum games. We show that while there are natural large general-sum games where the Stackelberg Equilibria can be computed efficiently if the Nash equilibrium in its zero-sum form could be computed efficiently, in general, structural properties that allow for efficient computation of Nash equilibrium in zero-sum games are not sufficient for computing Stackelberg equilibria in general-sum games.

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