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Resource Allocations in Multi-Stage Contests

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  • Sela, Aner
Abstract
We study best-of-k contests (k=2,3) between two players. The players have heterogeneous resource budgets that decrease within the stages proportionally to the resource allocated in the previous stages such that for each resource unit that a player allocates, he loses α (the fatigue parameter) units of resources from his budget. We show that in both contest forms, independent of the values of the fatigue parameters, each player allocates his smallest resource in the last stage. In the best-of three contest where there are different fatigue parameters for each of the two first stages, a sufficient condition that the resource allocation in the first stage is larger than in the second one is that the value of the fatigue parameter of the first stage is smaller than or equal to the value of the fatigue parameter of the second stage. We also show that in the best-of-three contest, if the fatigue parameters are sufficiently large (approaches one), both players allocate almost all their resource budgets in the first two stages such that they have no resources left for the last stage in which the winner might be decided.

Suggested Citation

  • Sela, Aner, 2021. "Resource Allocations in Multi-Stage Contests," CEPR Discussion Papers 16505, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:16505
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    References listed on IDEAS

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    1. Sela, Aner, 2011. "Best-of-three all-pay auctions," Economics Letters, Elsevier, vol. 112(1), pages 67-70, July.
    2. Dan Kovenock & Brian Roberson, 2009. "Is the 50-State Strategy Optimal?," Journal of Theoretical Politics, , vol. 21(2), pages 213-236, April.
    3. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    4. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    5. David Malueg & Andrew Yates, 2006. "Equilibria in rent-seeking contests with homogeneous success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 719-727, April.
    6. Dmitry Ryvkin, 2011. "Fatigue in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(4), pages 1011-1041, December.
    7. Rick Harbaugh & Tilman Klumpp, 2005. "Early Round Upsets and Championship Blowouts," Economic Inquiry, Western Economic Association International, vol. 43(2), pages 316-329, April.
    8. Kai A. Konrad, 2004. "Bidding in hierarchies," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 547-554, Springer.
    9. Aner Sela & Oz Tsahi, 2020. "On the optimal allocation of prizes in best-of-three all-pay auctions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 255-273, August.
    10. Amegashie, J. Atsu & Cadsby, C. Bram & Song, Yang, 2007. "Competitive burnout: Theory and experimental evidence," Games and Economic Behavior, Elsevier, vol. 59(2), pages 213-239, May.
    11. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    12. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    13. Mago, Shakun D. & Sheremeta, Roman M. & Yates, Andrew, 2013. "Best-of-three contest experiments: Strategic versus psychological momentum," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 287-296.
    14. Christopher Ferrall & Anthony A. Smith, 1999. "A Sequential Game Model Of Sports Championship Series: Theory And Estimation," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 704-719, November.
    15. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 193-209.
    16. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    17. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    18. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
    19. David A. Malueg & Andrew J. Yates, 2010. "Testing Contest Theory: Evidence from Best-of-Three Tennis Matches," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 689-692, August.
    20. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    21. Alex Krumer, 2015. "The Order of Games in a Best-of-Three Contest," Journal of Sports Economics, , vol. 16(2), pages 185-200, February.
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    More about this item

    Keywords

    Best-of-three contests; Best-of two contests; Resource budget;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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