Probability Inequalities for a Gladiator Game
AbstractBased 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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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp571.
Length: 21 pages
Date of creation: 08 Apr 2011
Date of revision:
Allocation game; Colonel Blotto game; David and Goliath; exponential distribution; Nash equilibrium; probability inequalities; unimodal distribution.;
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