IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.economics.ox.ac.uk/materials/papers/5259/young5702.pdf
Download Restriction: no

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

as
in new window

Length:
Date of creation: 01 Sep 2011
Date of revision:
Handle: RePEc:oxf:wpaper:570
Contact details of provider: Postal: Manor Rd. Building, Oxford, OX1 3UQ
Web page: http://www.economics.ox.ac.uk/
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Working Papers 174, Barcelona Graduate School of Economics.
  2. 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.
  3. 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.
  4. Hofbauer,J. & Sandholm,W.H., 2003. "Evolution in games with randomly disturbed payoffs," Working papers 20, Wisconsin Madison - Social Systems.
  5. 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.
  6. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249 World Scientific Publishing Co. Pte. Ltd..
  7. 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.
  8. Sandholm, William H. & Hofbauer, Josef, 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:oxf:wpaper:570. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Caroline Wise)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.