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Allocation Games with Caps: From Captain Lotto to All-Pay Auctions

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  • Sergiu Hart

Abstract

A Lotto game is a two-person zero-sum game where each player chooses a distribution on nonnegative real numbers with given expectation, so as to maximize the probability that his realized choice is higher than his opponent's. These games arise in various competitive allocation setups (e.g., contests, research and development races, political campaigns, Colonel Blotto games). A Captain Lotto game is a Lotto game with caps, which are upper bounds on the numbers that may be chosen. First, we solve the Captain Lotto games. Second, we show how to reduce all-pay auctions to simpler games—expenditure games—using the solution of the corresponding Lotto games. As a particular application we solve all-pay auctions with unequal caps, which yield a significant increase in the seller's revenue (or, the players' efforts).

Suggested Citation

  • Sergiu Hart, 2014. "Allocation Games with Caps: From Captain Lotto to All-Pay Auctions," Discussion Paper Series dp670, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp670
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    Cited by:

    1. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    2. Boyer, Pierre C. & Konrad, Kai A. & Roberson, Brian, 2017. "Targeted campaign competition, loyal voters, and supermajorities," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 49-62.
    3. Llorente-Saguer, Aniol & Sheremeta, Roman M. & Szech, Nora, 2023. "Designing contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions," European Economic Review, Elsevier, vol. 154(C).
    4. Aner Sela, 2018. "Reverse Contests," Working Papers 1804, Ben-Gurion University of the Negev, Department of Economics.
    5. Cohen, Chen & Levi, Ofer & Sela, Aner, 2019. "All-pay auctions with asymmetric effort constraints," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 18-23.
    6. Llorente-Saguer, Aniol & Sheremeta, Roman & Szech, Nora, 2016. "Designing Contests Between Heterogeneous Contestants: An Experimental Study of Tie-Breaks and Bid-Caps in All-Pay Auctions," MPRA Paper 71202, University Library of Munich, Germany.
    7. Dan Kovenock & Brian Roberson, 2021. "Generalizations of the General Lotto and Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 997-1032, April.
    8. Nadav Amir, 2015. "Uniqueness of optimal strategies in captain lotto games," Discussion Paper Series dp687, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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