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The all-pay auction with non-monotonic payoff

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  • Subhashish Modak Chowdhury

    (University of East Anglia)

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    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.

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    Bibliographic Info

    Paper provided by School of Economics, University of East Anglia, Norwich, UK. in its series Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) with number 09-09.

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    Date of creation: 01 Dec 2009
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    Handle: RePEc:uea:wcbess:09-09

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    Related research

    Keywords: contests; all-pay auction; no-win; non-monotonicity; pure strategy;

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    References

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    1. Baye, M.R. & Kovenock, D. & De Varies, C.G., 1990. "The All-Pay Auction With Complete Information," Papers 9051, Tilburg - Center for Economic Research.
    2. Tullock, Gordon, 1997. " Where Is the Rectangle?," Public Choice, Springer, vol. 91(2), pages 149-59, April.
    3. 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.
    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. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "Rigging The Lobbying Process: An Application Of The All- Pay Auction," Purdue University Economics Working Papers 1002, Purdue University, Department of Economics.
    6. 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.
    7. Yasar Barut & Dan Kovenock & Charles Noussair, 1999. "A Comparison of Multiple-Unit All-Pay and Winner-Pay Auctions Under Incomplete Information," CIG Working Papers FS IV 99-09, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    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. Aloisio Araujo & Luciano I. de Castro & Humberto Moreira, 2006. "Non-Monotoniticies And The All-Pay Auction Tie-Breaking Rule," Economics Working Papers we065924, Universidad Carlos III, Departamento de Economía.
    10. Loury, Glenn C, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, MIT Press, vol. 93(3), pages 395-410, August.
    11. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
    12. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
    13. 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.
    14. Bertoletti, Paolo, 2006. "On the reserve price in all-pay auctions with complete information and lobbying games," MPRA Paper 1083, University Library of Munich, Germany.
    15. Todd Kaplan, 2001. "All-Pay Auctions with Variable Rewards," Discussion Papers 0109, Exeter University, Department of Economics.
    16. Wakelin, Katharine, 2001. "Productivity growth and R&D expenditure in UK manufacturing firms," Research Policy, Elsevier, vol. 30(7), pages 1079-1090, August.
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    Cited by:
    1. Chowdhury, Subhasish & Sheremeta, Roman, 2014. "Strategically Equivalent Contests," MPRA Paper 55450, University Library of Munich, Germany.
    2. 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..
    3. Olivier Bos & Martin Ranger, 2010. "All-Pay Auctions with Endogenous Rewards," Working Paper Series in Economics 46, University of Cologne, Department of Economics.
    4. 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..

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