“…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].…”