Evolutionary stability of first price auctions
This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial populations. In contrast, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown-von Neumann-Nash dynamics. They suggest that the convergence for the replicator dynamic is slow compared to the Brown-von Neumann-Nash dynamics.
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.
| Length: | |
| Date of creation: | 16 Aug 2011 |
| Handle: | RePEc:bie:wpaper:435 |
| Contact details of provider: | Postal: Postfach 10 01 31, 33501 Bielefeld Phone: +49(0)521-106-4907 Web page: http://www.imw.uni-bielefeld.de/ 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.:
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009.
"Brown-von Neumann-Nash dynamics: The continuous strategy case,"
Games and Economic Behavior,
Elsevier, vol. 65(2), pages 406-429, March.
- Josef Hofbauer & Jörg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Bonn Econ Discussion Papers bgse38_2005, University of Bonn, Germany.
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Sonderforschungsbereich 504 Publications 05-41, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005. "Brown-von Neumann-Nash dynamics : the continuous strategy case," Papers 05-41, Sonderforschungsbreich 504.
- 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.
- Josef Hofbauer & Joerg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Game Theory and Information 0512003, EconWPA.
- Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 65-88, September.
- Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information 9610004, EconWPA, revised 07 Oct 1996.
- Monderer, Dov & Shlomit Hon-Snir & Aner Sela, 1996. "A Learning Approach to Auctions," Discussion Paper Serie B 388, University of Bonn, Germany.
- Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
- Jörg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Bonn Econ Discussion Papers bgse7_2000, University of Bonn, Germany.
- 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.
- Joerg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Game Theory and Information 0004004, EconWPA.
- Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
- Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847.
- Saran Rene & Serrano Roberto, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Rene Saran & Roberto Serrano, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Working Papers 2010-11, Brown University, Department of Economics.
- Rene Saran & Roberto Serrano, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Levine's Working Paper Archive 661465000000000083, David K. Levine.
- Rene Saran & Roberto Serrano, 2010. "Ex-post regret learning in games with fixed and random matching: The case of private values," Working Papers 2010-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
- Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 221-247, June.
- Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
- Karl H. Schlag, "undated". "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
- Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
- Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
- JÃrg Oechssler & Frank Riedel, 2001. "Evolutionary dynamics on infinite strategy spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 141-162.
- Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, EconWPA, revised 12 May 1998.
- Oechssler, Joerg & Frank Riedel, 1999. "Evolutionary Dynamics on Infinite Strategy Spaces," Discussion Paper Serie A 606, University of Bonn, Germany.
- Oechssler, Jörg & Riedel, Frank, 1998. "Evolutionary dynamics on infinite strategy spaces," SFB 373 Discussion Papers 1998,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Ross Cressman & Josef Hofbauer & Frank Riedel, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers bgse12_2005, University of Bonn, Germany.
- Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
- Krishna, Vijay, 2002. "Auction Theory," Elsevier Monographs, Elsevier, edition 1, number 9780124262973.
- Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
- Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
- Louge, Fernando, 2011. "On the stability of CSS under the replicator dynamic," Center for Mathematical Economics Working Papers 436, Center for Mathematical Economics, Bielefeld University. 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:bie:wpaper:435. 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: (Bettina Weingarten)
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.