The Theory and Application of Differential Games

The ~irst international con~erence on differential games was held at Amherst, Massachusetts, in September 1969. A second meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new theoretical results and applications, especially in economic problems, were presented. The present volume consists o~ the lectures presented at a N.A.T.O. Advanced Study Institute on the "Theory and Applications of Differential Games" held at the University of Warwick, Coventry, England, from 27th August to 6th September, 1974. The main contributions during the first week consisted of a survey of two person zero sum differential games by L. D. Berkovitz and four integrated lectures by R. J. Elliott and N. J. Kalton, who have made important contributions to the concept of "value" of a differential game. Applications were featured during the second week and included tactical air games, pursuit and evasion problems, as well as computational aspects. A closing lecture with historical perspectives was given by Rufus Issacs, the recognised pioneer of differential games theory.

Contenu

The Past and Some Bits of the Future.- Two Person Zero Sum Differential Games: An Overview.- to Differential Games I Competitive Dynamic Situations, Strategies, and Values.- to Differential Games II: Stochastic Games and Parabolic equations.- Differential Games of Survival.- Solution Sets for N-Person Games.- Alternatives to the Tree Model for Extensive Games.- Cooperative and Non-Cooperative Differential Games.- N-Person Stochastic Differential Games.- Quantitative Games: Problem Statement and Examples, New Geometric Aspects.- Strategic "Prejudgments" and Decision Criteria in N-Person Games.- Many Player Differential Games with Coalitions.- Extension of 2 Person Zero Sum Game.- Differential Games with Partial Differential Equations.- The Tactical Air Game: A Multimove Game with Mixed Strategy Solution.- Impulsively Controlled D.G..- The Theory of Hamiltonian Dynamical Systems, And an Application to Economics.- Averaged Hamiltonians in Differential Games.- Computational Aspects in two-Level Differential Games.- Computed Solutions of Differential Games.- Optimality and Transition Surfaces Using the Reprisal Concept.- Pursuit of A Faster Evader.- Aerial Turning Chases.- Avoidance of Guided Projectiles.- Pursuit Games: A Survey.- Values of Positional Games.- Catastrophe Theory in Differentiable Games.