This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Generalized projection dynamics in evolutionary game theory

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Reinoud Joosten
Berend Roorda
Abstract

We introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global ray-projection dynamics we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point. We also show that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ several projections on a wider set of functions derived from the payoff structure. This yields an interesting class of so-called generalized projection dynamics which contains best-response, logit, replicator, and Brown-Von-Neumann dynamics among others.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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: ftp://papers.econ.mpg.de/evo/discussionpapers/2008-11.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Max Planck Institute of Economics, Evolutionary Economics Group in its series Papers on Economics and Evolution with number 2008-11.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length:
Date of creation: Oct 2008
Date of revision:
Handle: RePEc:esi:evopap:2008-11

Contact details of provider:
Postal: Kahlaische Strasse 10, D-07745 Jena
Phone: +49-3641-68 65
Fax: +49-3641-68 69 90
Web page: http://www.econ.mpg.de/
More information through EDIRC

Order Information:
Email:
Web: http://www.econ.mpg.de/english/research/EVO/discuss.php

For technical questions regarding this item, or to correct its listing, contact: (Inken Poßner).

Related research
Keywords: evolutionary game theory; projection dynamics; orthogonal projection; ray projection; asymptotical and evolutionary stability Length 27 pages;

Find related papers by JEL classification:
A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

This paper has been announced in the following NEP Reports:

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.:
  1. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May. [Downloadable!] (restricted)
  2. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
  3. Tsakas, Elias & Voorneveld, Mark, 2007. "The target projection dynamic," Working Paper Series in Economics and Finance 670, Stockholm School of Economics, revised 13 Aug 2007. [Downloadable!]
  4. Mark Voorneveld, 2006. "Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions," International Journal of Game Theory, Springer, vol. 34(1), pages 105-121, April. [Downloadable!] (restricted)
    Other versions:
  5. Reinoud Joosten, 1996. "Deterministic evolutionary dynamics: a unifying approach," Journal of Evolutionary Economics, Springer, vol. 6(3), pages 313-324.
  6. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May. [Downloadable!] (restricted)
  7. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March. [Downloadable!] (restricted)
  8. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July. [Downloadable!] (restricted)
    Other versions:
  9. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November. [Downloadable!] (restricted)
    Other versions:
  10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March. [Downloadable!] (restricted)
  11. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  12. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November. [Downloadable!] (restricted)
  13. Sethi, Rajiv, 1998. "Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics," Games and Economic Behavior, Elsevier, vol. 23(2), pages 284-304, May. [Downloadable!] (restricted)
  14. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  15. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November. [Downloadable!] (restricted)
  16. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August. [Downloadable!] (restricted)
    Other versions:
  17. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October. [Downloadable!] (restricted)
  18. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October. [Downloadable!] (restricted)
  19. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October. [Downloadable!] (restricted)
    Other versions:
Full references

Statistics
Access and download statistics

Did you know? A tutorial is available.

This page was last updated on 2009-11-30.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.