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Non-monotoniticies and the all-pay auction tie-breaking rule

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  • Araujo, Aloisio
  • Castro, Luciano I. de
  • Moreira, Humberto

Abstract

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information. We also characterize when special tie-breaking rules are really needed.

Suggested Citation

  • Araujo, Aloisio & Castro, Luciano I. de & Moreira, Humberto, 2006. "Non-monotoniticies and the all-pay auction tie-breaking rule," UC3M Working papers. Economics we065924, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we065924
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    2. Lu, Jingfeng & Parreiras, Sérgio O., 2017. "Monotone equilibrium of two-bidder all-pay auctions Redux," Games and Economic Behavior, Elsevier, vol. 104(C), pages 78-91.
    3. Kotowski, Maciej H. & Li, Fei, 2014. "The war of attrition and the revelation of valuable information," Economics Letters, Elsevier, vol. 124(3), pages 420-423.
    4. Kotowski, Maciej H. & Li, Fei, 2014. "On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints," Games and Economic Behavior, Elsevier, vol. 85(C), pages 84-108.
    5. 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..
    6. Gagan Ghosh, 2015. "Non-existence of equilibria in simultaneous auctions with a common budget-constraint," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 253-274, May.
    7. Subhasish M. Chowdhury, 2017. "The All‐Pay Auction with Nonmonotonic Payoff," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 375-390, October.
    8. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Araujo, Aloisio & de Castro, Luciano I., 2009. "Pure strategy equilibria of single and double auctions with interdependent values," Games and Economic Behavior, Elsevier, vol. 65(1), pages 25-48, January.
    10. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    11. Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 67-85, September.
    12. Elitzur, Ramy & Gavious, Arieh, 2011. "Selection of entrepreneurs in the venture capital industry: An asymptotic analysis," European Journal of Operational Research, Elsevier, vol. 215(3), pages 705-712, December.
    13. Hironori Otsubo, 2015. "Nash Equilibria in a Two-Person Discrete All-Pay Auction with Unfair Tie-Break and Complete Information," Economics Bulletin, AccessEcon, vol. 35(4), pages 245-245.

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    More about this item

    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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