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

Gradient dynamics in population games: Some basic results

  • Friedman, Daniel
  • Ostrov, Daniel N.

When each player in a population game continuously adjusts her action to move up the payoff gradient, then the state variable (the action distribution) obeys a nonlinear partial differential equation. We find conditions that render gradient adjustment myopically optimal and analyze two broad classes of population games. For one class, we use known results to establish the existence and uniqueness of solutions to the PDE. In some cases, these solutions exhibit shock waves or rarefaction waves. For a second class, we use a local form of Nash equilibrium to characterize the steady state solutions of the PDE and find sufficient conditions for asymptotic convergence.

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.sciencedirect.com/science/article/B6VBY-50RVNSW-2/2/a7e7498aa0de208de48a08d156593d66
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 5 (September)
Pages: 691-707

as
in new window

Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:691-707
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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. Josef Hofbauer & Jörg Oechssler, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Working Papers 0424, University of Heidelberg, Department of Economics, revised Dec 2005.
  2. Oechssler, Jörg & Riedel, Frank, 2000. "On the dynamic foundation of evolutionary stability in continuous models," SFB 373 Discussion Papers 2000,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series dp309, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Apr 2003.
  4. Veblen, Thorstein, 1899. "The Theory of the Leisure Class," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number veblen1899.
  5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  6. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
  8. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  9. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  10. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
  11. Sonnenschein, Hugo, 1982. "Price Dynamics Based on the Adjustment of Firms," American Economic Review, American Economic Association, vol. 72(5), pages 1088-96, December.
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:eee:mateco:v:46:y:2010:i:5:p:691-707. 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: (Zhang, Lei)

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.