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Stochastic Learning Dynamics and Speed of Convergence in Population Games

  • Itai Arieli
  • H Peyton Young

Consider a finite, normal form game G in which each player position is occupied by a population of N individuals, and the payoff to any given individual is the expected payoff from playing against a group drawn at random from the other positions.� Assume that individuals adjust their behavior asynchronously via a stochastic better reply dynamic.� We show that when G is weakly acyclic, convergence occurs with probability one, but the expected waiting time to come close to Nash equilibrium can grow exponentially in N.� Unlike previous results in the literature our results show that Nash convergence can be exponentially slow even in games with very simple payoff structures.� We then show that the introduction of aggregate shocks to players' information and/or payoffs can greatly accelerate the learning process.� In fact, if G is weakly acyclic and the payoffs are generic, the expected waiting time to come e-close to Nash equilibrium is bounded by a function that is polynomial e-1, exponential in the number of strategies, and independent of the population size N.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 570.

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Date of creation: 01 Sep 2011
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Handle: RePEc:oxf:wpaper:570
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Web page: http://www.economics.ox.ac.uk/
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  1. Sandholm, William H. & Hofbauer, Josef, 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
  2. 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.
  3. 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.
  4. Hart, Sergiu & Mansour, Yishay, 2010. "How long to equilibrium? The communication complexity of uncoupled equilibrium procedures," Games and Economic Behavior, Elsevier, vol. 69(1), pages 107-126, May.
  5. Foster, Dean P. & Young, H. Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
  6. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic uncoupled dynamics and Nash equilibrium," Economics Working Papers 783, Department of Economics and Business, Universitat Pompeu Fabra.
  7. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  8. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
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