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The Communication Complexity of Uncoupled Nash Equilibrium Procedures

  • Sergiu Hart
  • Yishay Mansour

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
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
  2. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  3. 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.
  4. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  5. 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.
  6. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  7. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  8. 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.
  9. 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.
  10. 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.
  11. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  12. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer, vol. 33(1), pages 21-40, January.
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