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Sad-Loser contests

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  • Matros, Alexander

Abstract

We consider asymmetric winner-reimbursed contests. It turns out that such contests (Sad-Loser) have multiple internal pure-strategy equilibria (where at least two players are active). We describe all equilibria and discuss their properties. In particular, we find (1) that an active player is indifferent among all her non-negative choices and her expected payoff is zero in any internal equilibrium, (2) that a higher-value (stronger) player always spends less than a lower-value (weaker) player and therefore always has a lower chance to win a Sad-Loser contest in any internal equilibrium, and (3) a sufficient condition for a net total spending to be higher in a Sad-Loser contest than in the corresponding asymmetric contest.

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  • Matros, Alexander, 2012. "Sad-Loser contests," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 155-162.
    • Handle: RePEc:eee:mateco:v:48:y:2012:i:3:p:155-162
    DOI: 10.1016/j.jmateco.2012.03.001
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    Cited by:

    1. Chowdhury, Subhasish M. & Sheremeta, Roman M., 2011. "Multiple equilibria in Tullock contests," Economics Letters, Elsevier, vol. 112(2), pages 216-219, August.
    2. Yizhaq Minchuk & Aner Sela, 2020. "Contests with insurance," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 1-22, June.
    3. Alexander Matros & Daniel Armanios, 2007. "Tullock," Working Paper 328, Department of Economics, University of Pittsburgh, revised Sep 2008.
    4. Minchuk, Yizhaq, 2018. "Effect of reimbursement on all-pay auction," Economics Letters, Elsevier, vol. 172(C), pages 28-30.
    5. Liu, Yong & Liu, Shulin, 2019. "Effects of risk aversion on all-pay auction with reimbursement," Economics Letters, Elsevier, vol. 185(C).
    6. Subhashish Modak Chowdhury & Roman M. Sheremeta, 2009. "A generalized Tullock contest and the existence of multiple equilibria," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 09-08, School of Economics, University of East Anglia, Norwich, UK..

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