A Tool for Solving Differential Games with Co-evolutionary Algorithms

Game theory is concerned with optimization problems involving several players with conicting interests. Di erential games are an interesting area inside this eld in which the problem is formulated by means of dynamical systems. In spite that the theoretical solution of di erential games is well known, faced with large-scale, complex systems, analytical or, even, numerical methods are not usually suitable. Genetic algorithms appear to be useful for solving such problems when dealing with nonlinear, large-scale systems. This paper shows how co-evolutionary algorithms can be applied to solve di erential games and presents a computer tool to formulate and solve these problems. The di erential equations which de ne the system under study are written in Vensim, a visual modeling tool. The usefulness of the presented tool is shown by means of two examples.