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

  • Constantinos Daskalakis
  • Alex Fabrikant
  • Christos H. Papadimitriou
Conference paper

DOI: 10.1007/11786986_45

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)
Cite this paper as:
Daskalakis C., Fabrikant A., Papadimitriou C.H. (2006) The Game World Is Flat: The Complexity of Nash Equilibria in Succinct Games. In: Bugliesi M., Preneel B., Sassone V., Wegener I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Constantinos Daskalakis
    • 1
  • Alex Fabrikant
    • 1
  • Christos H. Papadimitriou
    • 1
  1. 1.Computer Science DivisionUC Berkeley 

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