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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.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp419.

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Date of creation: Mar 2006
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Publication status: Published in The 39th ACM Symposium on Theory of Computing (STOC) (2007), 345-353 [extended abstract: "The Communication Complexity of Uncoupled Nash Equilibrium Procedures"] & in Games and Economic Behavior 69 (2010), 1, 107-126
Handle: RePEc:huj:dispap:dp419

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References

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  1. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer, vol. 33(1), pages 21-40, January.
  4. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  6. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
  7. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  8. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
  9. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
  10. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
  11. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  12. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
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Cited by:
  1. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series dp600, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. J. Jordan, 2009. "Communication complexity and stability of equilibria in economies and games," Review of Economic Design, Springer, vol. 13(1), pages 115-135, April.
  3. Levin, Hagay & Schapira, Michael & Zohar, Aviv, 2008. "Interdomain routing and games," MPRA Paper 8476, University Library of Munich, Germany.
  4. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer, vol. 42(1), pages 193-236, January.

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