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The Communication Complexity of Uncoupled Nash Equilibrium Procedures

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Author Info
Sergiu Hart ()
Yishay Mansour ()

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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 Center for Rationality and Interactive Decision Theory, 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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Handle: RePEc:huj:dispap:dp419

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  1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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  3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  4. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09. [Downloadable!] (restricted)
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  5. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  6. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May. [Downloadable!] (restricted)
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  7. Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer, vol. 33(1), pages 21-40, January. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  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. [Downloadable!]
  10. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
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  11. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine. [Downloadable!]
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  1. 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. [Downloadable!] (restricted)
  2. Levin, Hagay & Schapira, Michael & Zohar, Aviv, 2008. "Interdomain routing and games," MPRA Paper 8476, University Library of Munich, Germany. [Downloadable!]
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This page was last updated on 2009-11-29.

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