IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v81y2012i1p69-80.html
   My bibliography  Save this article

Evolutionary dynamics of biological auctions

Author

Listed:
  • Chatterjee, Krishnendu
  • Reiter, Johannes G.
  • Nowak, Martin A.

Abstract

Many scenarios in the living world, where individual organisms compete for winning positions (or resources), have properties of auctions. Here we study the evolution of bids in biological auctions. For each auction, n individuals are drawn at random from a population of size N. Each individual makes a bid which entails a cost. The winner obtains a benefit of a certain value. Costs and benefits are translated into reproductive success (fitness). Therefore, successful bidding strategies spread in the population. We compare two types of auctions. In “biological all-pay auctions†, the costs are the bid for every participating individual. In “biological second price all-pay auctions†, the cost for everyone other than the winner is the bid, but the cost for the winner is the second highest bid. Second price all-pay auctions are generalizations of the “war of attrition†introduced by Maynard Smith. We study evolutionary dynamics in both types of auctions. We calculate pairwise invasion plots and evolutionarily stable distributions over the continuous strategy space. We find that the average bid in second price all-pay auctions is higher than in all-pay auctions, but the average cost for the winner is similar in both auctions. In both cases, the average bid is a declining function of the number of participants, n. The more individuals participate in an auction the smaller is the chance of winning, and thus expensive bids must be avoided.

Suggested Citation

  • Chatterjee, Krishnendu & Reiter, Johannes G. & Nowak, Martin A., 2012. "Evolutionary dynamics of biological auctions," Theoretical Population Biology, Elsevier, vol. 81(1), pages 69-80.
    • Handle: RePEc:eee:thpobi:v:81:y:2012:i:1:p:69-80
    DOI: 10.1016/j.tpb.2011.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580911000992
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2011.11.003?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. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    2. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2008. "Rigging the lobbying process: An application of the all-pay auction," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 331-336, Springer.
    3. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 225-250, Springer.
    4. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    5. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    6. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    7. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    8. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    9. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    10. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    11. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
    12. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    13. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    14. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    15. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    16. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, April.
    17. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    18. Gary S. Becker, 1983. "A Theory of Competition Among Pressure Groups for Political Influence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(3), pages 371-400.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel G. Stephenson & Alexander L. Brown, 2021. "Playing the field in all-pay auctions," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 489-514, June.
    2. Alexandros Rigos & Heinrich H. Nax, 2015. "Assortativity evolving from social dilemmas," Discussion Papers in Economics 15/19, Division of Economics, School of Business, University of Leicester.
    3. Buiter, Willem & Rahbari, Ebrahim, 2013. "Why do governments default, and why don't they default more often?," CEPR Discussion Papers 9492, C.E.P.R. Discussion Papers.
    4. Bettina Klose & Dan Kovenock, 2015. "The all-pay auction with complete information and identity-dependent externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 1-19, May.

    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. David P. Myatt, 2005. "Instant Exit from the Asymmetric War of Attrition," Economics Series Working Papers 160, University of Oxford, Department of Economics.
    2. 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.
    3. 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.
    4. Ødegaard, Fredrik & Anderson, Chris K., 2014. "All-pay auctions with pre- and post-bidding options," European Journal of Operational Research, Elsevier, vol. 239(2), pages 579-592.
    5. Kwiek, Maksymilian & Marreiros, Helia & Vlassopoulos, Michael, 2019. "Voting as a war of attrition," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 104-121.
    6. Morath, Florian & Münster, Johannes, 2008. "Private versus complete information in auctions," Economics Letters, Elsevier, vol. 101(3), pages 214-216, December.
    7. Noussair, Charles & Silver, Jonathon, 2006. "Behavior in all-pay auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 55(1), pages 189-206, April.
    8. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 99-129, September.
    9. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    10. Noussair, C.N. & Silver, J., 2006. "Behavior in all-pay auctions under incomplete information," Other publications TiSEM 9833c8a8-7aa4-4529-a617-8, Tilburg University, School of Economics and Management.
    11. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    12. Segev, Ella & Sela, Aner, 2014. "Multi-stage sequential all-pay auctions," European Economic Review, Elsevier, vol. 70(C), pages 371-382.
    13. Soumyakanti Chakraborty & Anup K. Sen & Amitava Bagchi, 2015. "Addressing the valuation problem in multi-round combinatorial auctions," Information Systems Frontiers, Springer, vol. 17(5), pages 1145-1160, October.
    14. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    15. Hiroki Saitoh & Shigehiro Serizawa, 2008. "Vickrey allocation rule with income effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 391-401, May.
    16. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    17. Didier Laussel & Michel Le Breton, 2005. ""Favors" for Sale: Strategic Analysis of a Simple Menu Auction with Adverse Selection," Annals of Economics and Finance, Society for AEF, vol. 6(1), pages 53-73, May.
    18. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    19. Papakonstantinou, A. & Bogetoft, P., 2013. "Crowd-sourcing with uncertain quality - an auction approach," MPRA Paper 44236, University Library of Munich, Germany.
    20. repec:cte:werepe:we081207 is not listed on IDEAS
    21. Baik, Kyung Hwan, 1998. "Difference-form contest success functions and effort levels in contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 685-701, November.

    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:thpobi:v:81:y:2012:i:1:p:69-80. 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: https://www.journals.elsevier.com/intelligence .

    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.