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The all-pay auction with non-monotonic payoff

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  • Subhashish Modak Chowdhury

    (University of East Anglia)

Abstract

We analyze an endogenous prize all-pay auction under complete information where it is possible that none of the bidders wins and the winning payoff becomes non-monotonic in own bid. We derive the conditions for the existence of pure strategy equilibria and fully characterize the unique mixed strategy equilibrium when pure strategy equilibria do not exist. The high-valuation bidder places two distinct mass points in his equilibrium mixed strategy and the equilibrium support of the low-valuation bidder is not continuous. Under common valuation, in the equilibrium mixed strategy both bidders place mass points at the same point of the support. Possible applications are discussed.

Suggested Citation

  • Subhashish Modak Chowdhury, 2009. "The all-pay auction with non-monotonic payoff," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-09, School of Economics, University of East Anglia, Norwich, UK..
    • Handle: RePEc:uea:wcbess:09-09
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    1. repec:bla:jindec:v:50:y:2002:i:4:p:417-30 is not listed on IDEAS
    2. Amegashie, J Atsu, 1999. "The Number of Rent-Seekers and Aggregate Rent-Seeking Expenditures: An Unpleasant Result," Public Choice, Springer, vol. 99(1-2), pages 57-62, April.
    3. Nti, Kofi O, 1997. "Comparative Statics of Contests and Rent-Seeking Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 43-59, February.
    4. Arora, Ashish & Ceccagnoli, Marco & Cohen, Wesley M., 2008. "R&D and the patent premium," International Journal of Industrial Organization, Elsevier, vol. 26(5), pages 1153-1179, September.
    5. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    6. 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.
    7. 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.
    8. Amegashie, J. Atsu, 2001. "An all-pay auction with a pure-strategy equilibrium," Economics Letters, Elsevier, vol. 70(1), pages 79-82, January.
    9. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    10. Jacques Mairesse & Mohamed Sassenou, 1991. "R&D Productivity: A Survey of Econometric Studies at the Firm Level," NBER Working Papers 3666, National Bureau of Economic Research, Inc.
    11. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    12. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    13. Tullock, Gordon, 1997. "Where Is the Rectangle?," Public Choice, Springer, vol. 91(2), pages 149-159, April.
    14. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    15. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 395-410.
    16. Wakelin, Katharine, 2001. "Productivity growth and R&D expenditure in UK manufacturing firms," Research Policy, Elsevier, vol. 30(7), pages 1079-1090, August.
    17. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    18. Yasar Barut & Dan Kovenock & Charles N. Noussair, 2002. "A Comparison of Multiple-Unit All-Pay and Winner-Pay Auctions Under Incomplete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(3), pages 675-708, August.
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    Cited by:

    1. Subhasish M. Chowdhury & Dongryul Lee & Iryna Topolyan, 2013. "The Max-Min Group Contest," University of East Anglia Applied and Financial Economics Working Paper Series 050, School of Economics, University of East Anglia, Norwich, UK..
    2. Kennedy, Matthew & Basu, Biswajit, 2014. "An analysis of the climate change architecture," Renewable and Sustainable Energy Reviews, Elsevier, vol. 34(C), pages 185-193.
    3. BOS, Olivier & RANGER, Martin, 2009. "All-pay auctions with endogenous rewards," LIDAM Discussion Papers CORE 2009059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Subhasish Chowdhury & Roman Sheremeta, 2015. "Strategically equivalent contests," Theory and Decision, Springer, vol. 78(4), pages 587-601, April.
    5. Olivier Bos & Martin Ranger, 2014. "All-Pay Auctions with Polynomial Rewards," Annals of Economics and Statistics, GENES, issue 115-116, pages 361-377.
    6. Cary Deck & Erik O. Kimbrough, 2017. "Experimenting with Contests for Experimentation," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 391-406, October.
    7. Subhashish Modak Chowdhury & Roman M. Sheremeta, 2009. "The equivalence of contests," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-06, School of Economics, University of East Anglia, Norwich, UK..

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    More about this item

    Keywords

    contests; all-pay auction; no-win; non-monotonicity; pure strategy;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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