Differential Game Theory Applied to a Model of the Arms Race

The arms race model of L. F. Richardson is considered within a differential game theoretic context. Five different approaches to the game are considered and the results compared. The particular model considered is a three nation arms race model which becomes a three player differential game. The five approaches to the game are the minimax, Nash, and Pareto approaches as well as two coalition approaches: C.P.O. (Coalitive Pareto Optimality) and N.C.O. (Nash Coalitive Optimality). Some suggestions are made for future research and some possible economic, social, and political implications of this work are considered.