New fictitious play procedure for solving Blotto games

Abstract

In this thesis, a new fictitious play (FP) procedure is presented to solve two-person zero-sum (TPZS) Blotto games. The FP solution procedure solves TPZS games by assuming that the two players take turns selecting optimal responses to the opponent's strategy observed so far. It is known that FP converges to an optimal solution, and it may be the only realistic approach to solve large games. The algorithm uses dynamic programming (DP) to solve FP subproblems. Efficiency is obtained by limiting the growth of the DP state space. Blotto games are frequently used to solve simple missile defense problems. While it may be unlikely that the models presented in this paper can be used directly to solve realistic offense and defense problems, it is hoped that they will provide insight into the basic structure of optimal and near-optimal solutions to these important, large games, and provide a foundation for solution of more realistic, and more complex, problems.