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The Communication Complexity of Uncoupled Nash Equilibrium Procedures

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  • Sergiu Hart

  • Yishay Mansour

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 number of bits that need to be transmitted in order to reach a Nash equilibrium, 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. Finally, we show that some very simple and naive procedures lead to similar exponential upper bounds.

Suggested Citation

  • Sergiu Hart & Yishay Mansour, 2006. "The Communication Complexity of Uncoupled Nash Equilibrium Procedures," Discussion Paper Series dp419, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp419
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    Cited by:

    1. Levin, Hagay & Schapira, Michael & Zohar, Aviv, 2008. "Interdomain routing and games," MPRA Paper 8476, University Library of Munich, Germany.
    2. J. Jordan, 2009. "Communication complexity and stability of equilibria in economies and games," Review of Economic Design, Springer;Society for Economic Design, vol. 13(1), pages 115-135, April.
    3. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series dp600, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 193-236, January.

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