Titlebook: Algorithmic Game Theory; Third International Spyros Kontogiannis,Elias Koutsoupias,Paul G. Spir Conference proceedings 2010 Springer-Verla

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https://doi.org/10.1007/978-3-662-39685-8e existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a . pure Nash equilibrium in every . implies the weak acyclicity of a game. In contrast, the possible existence of . pure Nash equilibria in every subgame is . for weak acyclicity.

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A Simplex-Like Algorithm for Fisher Markets,this polytope. The convex cost function depends only on the initial endowments of the buyers. This formulation yields an easy simplex-like pivoting algorithm which is provably strongly polynomial for many special cases.

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Computing Stable Outcomes in Hedonic Games,ble outcome and all these problems are in PLS. The different stability requirements correspond to different local search neighbourhoods. For different neighbourhood structures, our findings comprise positive results in the form of polynomial-time algorithms for finding stable outcomes, and negative (PLS-completeness) results.

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The Computational Complexity of Trembling Hand Perfection and Other Equilibrium Refinements,was previously shown to be .-hard by Borgs ., while a . hardness result is given in this paper. The latter proof yields bounds on the algebraic degree of the minmax value of a three-player game that may be of independent interest.

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Pareto Efficiency and Approximate Pareto Efficiency in Routing and Load Balancing Games,erent solutions. The settings we consider include load balancing games on identical, uniformly-related, and unrelated machines, both using pure and mixed strategies, and nonatomic routing in general and some specific networks.

Organization

A Direct Reduction from ,-Player to 2-Player Approximate Nash Equilibrium,r games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, eliminating some of the difficulties involved in following the known indirect reduction.