A Colonel Blotto Gladiator Game

• 成果类型: Article
• 署名作者: Rinott, Yosef; Scarsini, Marco; Yu, Yaming
• 署名单位: Hebrew University of Jerusalem; Hebrew University of Jerusalem; Luiss Guido Carli University; University of California System; University of California Irvine
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1120.0550
• 发表日期: 2012
• 页码: 574-590
• 关键词: integral-equations; probabilities; inequalities; models; borel

摘要

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.