On asymptotic strategies in the stochastic Colonel Blotto game

We consider a stochastic modification of the Colonel Blotto game, also called the gladiator game. Each of two players has a given amount of resources (strengths), which can be arbitrarily distributed between a given number of gladiators. Once the strengths are distributed, the teams begin a battle consisting of individual fights of gladiators. In each fight, the winning probability of a gladiator is proportional to its strength (the amount of resources). Each player tries to distribute resources in order to maximize the winning probability. We consider the games in which a stronger team has a sufficiently large number of gladiators. For such games, we describe the Nash equilibria, present formulas for evaluation of boundaries between optimal strategy profiles, and investigate the asymptotic behavior of the boundaries.