How to Maximize the Total Strength of Survivors in a Battle and Tournament in Gladiator Game Models

In 1984, Kaminsky, Luks, and Nelson formulated the gladiator game model of two teams with given strengths. Suppose that a team wants to maximize its expected strength at the end of a battle. We consider an optimization problem: how to distribute the team’s strength among its gladiators. In the above we suppose that the teams distribute their strengths at the beginning of a battle. We also consider Nash equilibria when the teams may change gladiators’ strengths before every fight. We consider two cases. In both, the first team wants to maximize its strength. The second team wants to maximize its strength too in the first case or wants to minimize the first team’s strength in the second case.