A Colonel Blotto Gladiator Game

A Colonel Blotto Gladiator Game

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Article ID: iaor20127195
Volume: 37
Issue: 4
Start Page Number: 574
End Page Number: 590
Publication Date: Nov 2012
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: Nash equilibrium, stochastic games
Abstract:

We consider a stochastic version of the well‐known Blotto game, called the gladiator game. In this zero‐sum allocation game two teams of gladiators engage in a sequence of one‐on‐one fights in which the probability of winning is a function of the gladiators' strengths. Each team's strategy is the allocation of its total strength among its gladiators. We find the Nash equilibria and the value of this class of games and show how they depend on the total strength of teams and the number of gladiators in each team. To do this, we study interesting majorization‐type probability inequalities concerning linear combinations of gamma random variables. Similar inequalities have been used in models of telecommunications and research and development.

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