A Colonel Blotto Gladiator Game
Mathematics of Operations Research, Vol. 37, No. 4, 574-590, November 2012
Posted: 3 Apr 2012 Last revised: 14 Jul 2013
Date Written: March 25, 2012
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-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 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.
Keywords: Allocation game, gladiator game, sum of exponential random variables, Nash equilibrium, probability inequalities, unimodal distribution
JEL Classification: C72
Suggested Citation: Suggested Citation