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Automata, Languages and Programming

Volume 4051 of the series Lecture Notes in Computer Science pp 513-524

The Game World Is Flat: The Complexity of Nash Equilibria in Succinct Games

  • Constantinos DaskalakisAffiliated withCarnegie Mellon UniversityComputer Science Division, UC Berkeley
  • , Alex FabrikantAffiliated withCarnegie Mellon UniversityComputer Science Division, UC Berkeley
  • , Christos H. PapadimitriouAffiliated withCarnegie Mellon UniversityComputer Science Division, UC Berkeley

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Abstract

A recent sequence of results established that computing Nash equilibria in normal form games is a PPAD-complete problem even in the case of two players [11,6,4]. By extending these techniques we prove a general theorem, showing that, for a far more general class of families of succinctly representable multiplayer games, the Nash equilibrium problem can also be reduced to the two-player case. In view of empirically successful algorithms available for this problem, this is in essence a positive result — even though, due to the complexity of the reductions, it is of no immediate practical significance. We further extend this conclusion to extensive form games and network congestion games, two classes which do not fall into the same succinct representation framework, and for which no positive algorithmic result had been known.