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How long to equilibrium? The communication complexity of uncoupled equilibrium procedures

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  • Hart, Sergiu
  • Mansour, Yishay

Abstract

We study the question of how long it takes players to reach a Nash equilibrium in uncoupled setups, where each player initially knows only his own payoff function. We derive lower bounds on the communication complexity of reaching a Nash equilibrium, i.e., on the number of bits that need to be transmitted, and thus also on the required number of steps. Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. We then show that, in contrast, the communication complexity of reaching a correlated equilibrium is polynomial in the number of players.

Suggested Citation

  • Hart, Sergiu & Mansour, Yishay, 2010. "How long to equilibrium? The communication complexity of uncoupled equilibrium procedures," Games and Economic Behavior, Elsevier, vol. 69(1), pages 107-126, May.
  • Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:107-126
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    Citations

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    Cited by:

    1. Sergiu Hart & Noam Nisan, 2013. "The Query Complexity of Correlated Equilibria," Discussion Paper Series dp647, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    3. Pradelski, Bary S.R. & Young, H. Peyton, 2012. "Learning efficient Nash equilibria in distributed systems," Games and Economic Behavior, Elsevier, vol. 75(2), pages 882-897.
    4. Yakov Babichenko, 2014. "How long to Pareto efficiency?," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 13-24, February.
    5. Babichenko, Yakov, 2013. "Best-reply dynamics in large binary-choice anonymous games," Games and Economic Behavior, Elsevier, vol. 81(C), pages 130-144.
    6. Goldberg, Paul W. & Pastink, Arnoud, 2014. "On the communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 85(C), pages 19-31.
    7. Babaioff, Moshe & Blumrosen, Liad & Schapira, Michael, 2013. "The communication burden of payment determination," Games and Economic Behavior, Elsevier, vol. 77(1), pages 153-167.
    8. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
    9. Itai Arieli & H Peyton Young, 2011. "Stochastic Learning Dynamics and Speed of Convergence in Population Games," Economics Series Working Papers 570, University of Oxford, Department of Economics.
    10. Jiang, Albert Xin & Leyton-Brown, Kevin, 2015. "Polynomial-time computation of exact correlated equilibrium in compact games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 347-359.

    More about this item

    Keywords

    Uncoupled dynamics Nash equilibrium Communication complexity Correlated equilibrium Speed of convergence;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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