Contribution of the dynamic programming approach to solving a War game of attrition and attack

Abstract

In this thesis, we focus on applying Ș. Mirică's Dynamic Programming method to solve the Attack and attrition warfare differential game introduced by R. Isaacs. We propose feedback strategies as a new contribution that offers adaptability, efficiency, and simplicity while reducing algorithmic complexity. This approach employs a refined Cauchy characteristics method to handle stratified Hamilton-Jacobi equations while ensuring the existence of the value function. The optimality of the feedback strategies is rigorously validated using the Verification Theorem for value functions of class 𝓒𝟏 and further supported by established numerical tests.