A Colonel Blotto Gladiator Game

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.

The Optimal Defense of Networks of Targets

“…Recent work on Blotto‐type games includes extensions such as: asymmetric players (Dziubiński ; Hart ; Macdonell and Mastronardi ; Roberson ; Weinstein ), nonconstant‐sum variations (Hortala‐Vallve and Llorente‐Saguer , ; Kvasov ; Roberson and Kvasov ), alternative definitions of success (Golman and Page ; Rinott, Scarsini, and Yu ; Tang, Shoham, and Lin ), and political economy applications (Laslier ; Laslier and Picard ; Roberson ; Thomas ).…”

The Markov-quantile process attached to a family of marginals

“…This corresponds to the case of α and β with finite support. In this particular case the above mentioned exercise reduces to the so-called 'gladiator game' [27] that is a stochastic version of Borel's Blotto game [42]. so that, due to the Markov property, for every s s and t t, Y s and Y t are independent.…”

Sequential Majoritarian Blotto Games

“…5 Deck and Sheremeta (2012) consider a sequence of all-pay auctions with fixed total resources and an asymmetric objective: One player wins the game if he wins a single auction, while the opponent must win all auctions. Rinott et al (2012) develop a model in which two teams must allocate fixed resources to their members (gladiators) who face each other in pairwise Tullock contests. The winning gladiator of the first battle faces off against the next member of the opposing team, and so on, until one team has lost all gladiators.…”