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Computing Stackelberg Equilibria of Large General-Sum Games

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Part of the Lecture Notes in Computer Science book series (LNISA,volume 11801)

Abstract

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 natural representation of the problem.

In zero-sum games, the notion of a Stackelberg equilibrium coincides with the notion of a Nash Equilibrium (Korzhyk et al. 2011b). 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 (Ahmadinejad et al. 2016; Dudík et al. 2017; Kalai and Vempala 2005). 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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Fig. 1.

Notes

  1. 1.

    The sparsity requirement is such that the leader can communicate its strategy to the follower efficiently.

  2. 2.

    Interestingly, it is not hard to show that player best-response can also be computed efficiently in the games used by Letchford and Conitzer (2010), Li et al. (2016), although this was not central to their results.

  3. 3.

    The sparsity requirement is such that the leader can communicate its strategy to the follower efficiently.

  4. 4.

    An example of a game where this linear program can be solved efficiently is the shortest path game in Example 1.

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Correspondence to Saeed Seddighin .

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Blum, A., Haghtalab, N., Hajiaghayi, M., Seddighin, S. (2019). Computing Stackelberg Equilibria of Large General-Sum Games. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_12

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  • DOI: https://doi.org/10.1007/978-3-030-30473-7_12

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