On the Communication Complexity of Approximate Nash Equilibria

  • Paul W. Goldberg
  • Arnoud Pastink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)


We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. We are interested in algorithms where the communication is substantially less than the contents of a payoff matrix, for example logarithmic in the size of the matrix. At one extreme is the case where the players do not communicate at all; for this case (with 2 players having n×n matrices) ε-Nash equilibria can be computed for ε = 3/4, while there is a lower bound of slightly more than 1/2 on the lowest ε achievable. When the communication is polylogarithmic in n, we show how to obtain ε = 0.438. For one-way communication we show that ε = 1/2 is the exact answer.


Nash Equilibrium Mixed Strategy Pure Strategy Communication Complexity Nash Equilibrium Strategy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paul W. Goldberg
    • 1
  • Arnoud Pastink
    • 2
  1. 1.Department of Computer ScienceUniversity of LiverpoolU.K.
  2. 2.Department of Information and Computing ScienceUtrecht UniversityUtrechtThe Netherlands

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