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.

A Colonel Blotto gladiator game / Rinott, Joseph; Scarsini, Marco; Yu, Y.. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 37:4(2012), pp. 574-590. [10.1287/moor.1120.0550]

A Colonel Blotto gladiator game

RINOTT, JOSEPH;SCARSINI, MARCO;
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-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.
allocation game; gladiator game; sum of exponential random variables; Nash equilibrium; probability inequalities; unimodal distribution
A Colonel Blotto gladiator game / Rinott, Joseph; Scarsini, Marco; Yu, Y.. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 37:4(2012), pp. 574-590. [10.1287/moor.1120.0550]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/40094
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