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Probability Inequalities for a Gladiator Game


  • Yosef Rinott
  • Marco Scarsini
  • Yaming Yu


Based on a model introduced by Kaminsky, Luks, and Nelson (1984), we consider a zero-sum allocation game called the Gladiator Game, where two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's strategy consist the allocation of its total strength among its gladiators. We find the Nash equilibria of the game and compute its value. To do this, we study interesting majorization-type probability inequalities concerning linear combinations of Gamma random variables.

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  • Yosef Rinott & Marco Scarsini & Yaming Yu, 2011. "Probability Inequalities for a Gladiator Game," Discussion Paper Series dp571, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp571

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    References listed on IDEAS

    1. Sergiu Hart, 2004. "A comparison of non-transferable utility values," Theory and Decision, Springer, vol. 56(2_2), pages 35-46, February.
    2. Sergiu Hart & Andreu Mas-Colell, 2010. "Bargaining and Cooperation in Strategic Form Games," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 7-33, March.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
    5. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
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    More about this item


    Allocation game; Colonel Blotto game; David and Goliath; exponential distribution; Nash equilibrium; probability inequalities; unimodal distribution.;

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