IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v50y2014icp160-166.html
   My bibliography  Save this article

Invader strategies in the war of attrition with private information

Author

Listed:
  • Metzger, Lars Peter

Abstract

Second price all-pay auctions (wars of attritions) have an evolutionarily stable equilibrium in pure strategies if valuations are private information. I show that for any level of uncertainty there exists a pure deviation strategy arbitrarily close to the equilibrium strategy such that for some valuations the equilibrium strategy has a selective disadvantage against the deviation if the population mainly plays the deviation strategy. I show that agents with those valuations would prefer to deviate even farther from the equilibrium strategy, if the population collectively uses the deviation strategy. I argue that in the Bayesian game studied here, a mass deviation can be caused by the entry of a small group of agents. The results provided in this paper imply that the equilibrium strategy is indeed unstable if one considers rare and independent mutations on the space of valuations. Numeric calculations indicate that the closer the deviation strategy to the equilibrium strategy, the more valuations are destabilizing.

Suggested Citation

  • Metzger, Lars Peter, 2014. "Invader strategies in the war of attrition with private information," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 160-166.
  • Handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:160-166
    DOI: 10.1016/j.jmateco.2013.11.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440681300116X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmateco.2013.11.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    3. Hehenkamp, B. & Leininger, W. & Possajennikov, A., 2004. "Evolutionary equilibrium in Tullock contests: spite and overdissipation," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1045-1057, November.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    5. 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.
    6. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    7. Damianov, Damian S. & Oechssler, Jörg & Becker, Johannes Gerd, 2010. "Uniform vs. discriminatory auctions with variable supply - experimental evidence," Games and Economic Behavior, Elsevier, vol. 68(1), pages 60-76, January.
    8. 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.
    9. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    10. Konrad, Kai A., 2006. "Silent interests and all-pay auctions," International Journal of Industrial Organization, Elsevier, vol. 24(4), pages 701-713, July.
    11. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bingchao Huangfu & Gagan Ghosh & Heng Liu, 2023. "Resource inequality in the war of attrition," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 33-61, March.
    2. Maxime Menuet & Petros G. Sekeris, 2022. "Engaging in Wars of Attrition," Annals of Economics and Statistics, GENES, issue 147, pages 79-100.
    3. David P. Myatt, 2005. "Instant Exit from the Asymmetric War of Attrition," Economics Series Working Papers 160, University of Oxford, Department of Economics.
    4. Maxime Menuet & Petros G. Sekeris, 2021. "Overconfidence and conflict," Economic Inquiry, Western Economic Association International, vol. 59(4), pages 1483-1499, October.
    5. Segev, Ella & Sela, Aner, 2014. "Sequential all-pay auctions with noisy outputs," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 251-261.
    6. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    7. Deng, Shanglyu & Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2024. "Contests with sequential entry and incomplete information," Theoretical Economics, Econometric Society, vol. 19(2), May.
    8. Peter Helgesson & Bernt Wennberg, 2015. "The N-Player War of Attrition in the Limit of Infinitely Many Players," Dynamic Games and Applications, Springer, vol. 5(1), pages 65-93, March.
    9. Mezzetti, Claudio & Tsetlin, Ilia, 2009. "Auctions in which losers set the price," Games and Economic Behavior, Elsevier, vol. 66(2), pages 855-864, July.
    10. Aner Sela, 2018. "Reverse Contests," Working Papers 1804, Ben-Gurion University of the Negev, Department of Economics.
    11. Florian Morath, 2013. "Volunteering and the strategic value of ignorance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 99-131, June.
    12. Nicola Dimitri, 2021. "The “Italian Football Federation Auction” for Co-ownership Resolution," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(2), pages 275-285, March.
    13. Thomas Giebe & Paul Schweinzer, 2014. "All-pay-all aspects of political decision making," Public Choice, Springer, vol. 161(1), pages 73-90, October.
    14. Emiel Maasland & Sander Onderstal, 2006. "Going, Going, Gone! A Swift Tour of Auction Theory and its Applications," De Economist, Springer, vol. 154(2), pages 197-249, June.
    15. Ella Segev & Aner Sela, 2014. "Sequential all-pay auctions with head starts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 893-923, December.
    16. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.
    17. Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2020. "On superiority and weak stability of population states in evolutionary games," Annals of Operations Research, Springer, vol. 287(2), pages 751-760, April.
    18. Jung, Kyu-Chul & Kim, Kyoo H., 2005. "Revenue and optimality in unequal-sized share auctions," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 177-190.
    19. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    20. Georgiadis, George & Kim, Youngsoo & Kwon, H. Dharma, 2022. "The absence of attrition in a war of attrition under complete information," Games and Economic Behavior, Elsevier, vol. 131(C), pages 171-185.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:160-166. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.