A colonel Blotto gladiator game

Yosef Rinott*, Marco Scarsini, Yaming Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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.

Original languageEnglish
Pages (from-to)574-590
Number of pages17
JournalMathematics of Operations Research
Volume37
Issue number4
DOIs
StatePublished - Nov 2012

Keywords

  • Allocation game
  • Gladiator game
  • Nash equilibrium
  • Probability inequalities
  • Sum of exponential random variables
  • Unimodal distribution

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