IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v131y2022icp171-185.html
   My bibliography  Save this article

The absence of attrition in a war of attrition under complete information

Author

Listed:
  • Georgiadis, George
  • Kim, Youngsoo
  • Kwon, H. Dharma

Abstract

We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show that if the players' payoffs whilst in “war” vary stochastically and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This is true irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model. In contrast, when the players' flow payoffs are deterministic or their exit payoffs are homogeneous, the game admits equilibria in pure and mixed strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:131:y:2022:i:c:p:171-185
    DOI: 10.1016/j.geb.2021.11.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825621001445
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2021.11.004?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. David P. Myatt, 2005. "Instant Exit from the Asymmetric War of Attrition," Economics Series Working Papers 160, University of Oxford, Department of Economics.
    2. Bilodeau, Marc & Slivinski, Al, 1996. "Toilet cleaning and department chairing: Volunteering a public service," Journal of Public Economics, Elsevier, vol. 59(2), pages 299-308, February.
    3. Pankaj Ghemawat, 1997. "Games Businesses Play: Cases and Models," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262071827, December.
    4. Kambe, Shinsuke, 1999. "Bargaining with Imperfect Commitment," Games and Economic Behavior, Elsevier, vol. 28(2), pages 217-237, August.
    5. Kornhauser, Lewis & Rubinstein, Ariel & Wilson, Charles, 1989. "Reputation and Patience in the 'War of Attrition.'," Economica, London School of Economics and Political Science, vol. 56(221), pages 15-24, February.
    6. Bliss, Christopher & Nalebuff, Barry, 1984. "Dragon-slaying and ballroom dancing: The private supply of a public good," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 1-12, November.
    7. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    8. Pauli Murto, 2004. "Exit in Duopoly Under Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 111-127, Spring.
    9. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    10. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    11. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    12. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    13. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    14. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    15. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    16. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    17. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    18. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    19. Yuya Takahashi, 2015. "Estimating a War of Attrition: The Case of the US Movie Theater Industry," American Economic Review, American Economic Association, vol. 105(7), pages 2204-2241, July.
    20. Zhongmin Wang, 2009. "(Mixed) Strategy in Oligopoly Pricing: Evidence from Gasoline Price Cycles Before and Under a Timing Regulation," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 987-1030, December.
    21. 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.
    22. Christian Seel & Philipp Strack, 2016. "Continuous Time Contests with Private Information," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1093-1107, August.
    23. 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. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    2. Steg, Jan-Henrik & Thijssen, Jacco J.J., 2023. "Strategic investment with positive externalities," Games and Economic Behavior, Elsevier, vol. 138(C), pages 1-21.
    3. Betto, Maria & Thomas, Matthew W., 2024. "Asymmetric all-pay auctions with spillovers," Theoretical Economics, Econometric Society, vol. 19(1), January.
    4. Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas, 2022. "Mixed-Strategy Equilibria in the War of Attrition under Uncertainty," TSE Working Papers 22-1374, Toulouse School of Economics (TSE), revised 22 Nov 2023.

    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. George Georgiadis & Youngsoo Kim & H. Dharma Kwon, 2021. "The Absence of Attrition in a War of Attrition under Complete Information," Papers 2110.12013, arXiv.org, revised Nov 2021.
    2. David P. Myatt, 2005. "Instant Exit from the Asymmetric War of Attrition," Economics Series Working Papers 160, University of Oxford, Department of Economics.
    3. 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.
    4. 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.
    5. Li, Hongcheng, 2019. "Multi-Player War of Attrition with Asymmetric Incomplete Information," MPRA Paper 109511, University Library of Munich, Germany, revised 31 Aug 2021.
    6. Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas, 2022. "Mixed-Strategy Equilibria in the War of Attrition under Uncertainty," TSE Working Papers 22-1374, Toulouse School of Economics (TSE), revised 22 Nov 2023.
    7. Jan-Henrik Steg, 2015. "Symmetric Equilibria in Stochastic Timing Games," Papers 1507.04797, arXiv.org, revised May 2018.
    8. Johannes Hörner & Nicolas Sahuguet, 2011. "A war of attrition with endogenous effort levels," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 1-27, May.
    9. Hironori Otsubo & Amnon Rapoport, 2008. "Dynamic Volunteer's Dilemmas over a Finite Horizon," Journal of Conflict Resolution, Peace Science Society (International), vol. 52(6), pages 961-984, December.
    10. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    11. Paul Klemperer, 2000. "Why Every Economist Should Learn Some Auction Theory," Microeconomics 0004009, University Library of Munich, Germany.
    12. H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    13. Stenborg, Markku, 2003. "Waiting for F/OSS: Coordinating the Production of Free/Open Source Software," Discussion Papers 884, The Research Institute of the Finnish Economy.
    14. Hannah Hörisch & Oliver Kirchkamp, 2010. "Less fighting than expected," Public Choice, Springer, vol. 144(1), pages 347-367, July.
    15. Asako Yasushi, 2015. "One-Sided Games in a War of Attrition," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(2), pages 313-331, July.
    16. Steg, Jan-Henrik & Thijssen, Jacco, 2015. "Quick or Persistent? Strategic Investment Demanding Versatility," Center for Mathematical Economics Working Papers 541, Center for Mathematical Economics, Bielefeld University.
    17. LaCasse, Chantale & Ponsati, Clara & Barham, Vicky, 2002. "Chores," Games and Economic Behavior, Elsevier, vol. 39(2), pages 237-281, May.
    18. Yixuan Shi, 2022. "Dynamic Volunteer’s Dilemma with Procrastinators," Working Papers tax-mpg-rps-2022-17, Max Planck Institute for Tax Law and Public Finance.
    19. Brünner, Tobias & Reiner, Jochen & Natter, Martin & Skiera, Bernd, 2019. "Prospect theory in a dynamic game: Theory and evidence from online pay-per-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 164(C), pages 215-234.
    20. Chatterjee, Krishnendu & Reiter, Johannes G. & Nowak, Martin A., 2012. "Evolutionary dynamics of biological auctions," Theoretical Population Biology, Elsevier, vol. 81(1), pages 69-80.

    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:gamebe:v:131:y:2022:i:c:p:171-185. 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/inca/622836 .

    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.