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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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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000001299.

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Date of creation: 03 Apr 2006
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Handle: RePEc:cla:levrem:122247000000001299

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References

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  1. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, Elsevier, vol. 59(1), pages 187-208, April.
  2. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  3. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  4. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  6. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 373, Department of Economics and Business, Universitat Pompeu Fabra.
  7. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer, Springer, vol. 33(1), pages 21-40, January.
  8. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, American Economic Association, vol. 93(5), pages 1830-1836, December.
  9. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 21(1-2), pages 40-55, October.
  10. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, Elsevier, vol. 60(1), pages 135-154, July.
  11. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  12. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 73-96, October.
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Cited by:
  1. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp600, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer, Springer, vol. 42(1), pages 193-236, January.
  3. J. Jordan, 2009. "Communication complexity and stability of equilibria in economies and games," Review of Economic Design, Springer, Springer, vol. 13(1), pages 115-135, April.
  4. Levin, Hagay & Schapira, Michael & Zohar, Aviv, 2008. "Interdomain routing and games," MPRA Paper 8476, University Library of Munich, Germany.

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