Surveys in Combinatorics 2011 2011
DOI: 10.1017/cbo9781139004114.003
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A survey of PPAD-completeness for computing Nash equilibria

Abstract: PPAD refers to a class of computational problems for which solutions are guaranteed to exist due to a specific combinatorial principle. The most wellknown such problem is that of computing a Nash equilibrium of a game. Other examples include the search for market equilibria, and envy-free allocations in the context of cake-cutting. A problem is said to be complete for PPAD if it belongs to PPAD and can be shown to constitute one of the hardest computational challenges within that class.In this paper, I give a … Show more

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Cited by 10 publications
(6 citation statements)
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“…We refer the reader to [Gol11] and to the related work sections of [OPR14,Rub14] for further details.…”
Section: Related Workmentioning
confidence: 99%
“…We refer the reader to [Gol11] and to the related work sections of [OPR14,Rub14] for further details.…”
Section: Related Workmentioning
confidence: 99%
“…Most problems of this form are shown to be complete for some class in "Total-Function NP" 1 , typically for either PPAD or PLS e.g., Fabrikant et al [2004], Daskalakis et al [2009], Chen et al [2006a,b], Skopalik and Vöcking [2008], Kannan and Theobald [2010], Etessami and Yannakakis [2010], Syrgkanis [2010], Mehta [2014]. The class PPAD captures problems with parity arguments like finding fixed-points of functions, Sperner's Lemma, and finding (mixed) Nash equilibria in general games Papadimitriou [1994], Kintali et al [2013], Daskalakis et al [2009], Chen et al [2006a], Goldberg [2011], while PLS (Polynomial Local Search) captures problems with local-search algorithms, like local-max-cut, local-max-SAT, and pure NE in potential games Johnson et al [1988], Schäffer and Yannakakis [1991], Fabrikant et al [2004], Skopalik and Vöcking [2008], Cai and Daskalakis [2011].…”
Section: Introductionmentioning
confidence: 99%
“…As we explain in Section 2, this is very much necessary: there are examples where the equilibrium is irrational, and therefore cannot be computed exactly in many standard models of computation. As a ma er of fact, this is a common theme in most papers in equilibrium computation; see, e.g., [Daskalakis et al, 2009;Chen et al, 2009] or the survey of Goldberg [2011] for a related discussion.…”
Section: Discussion and Further Resultsmentioning
confidence: 93%