Differential games

In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors - the pursuer . Principles of Autonomy and Decision Making.

Lecture 25: Differential Games.

Massachusetts Institute of Technology. L25: Differential Games. In fact, differential game problems represent a generalization of optimal control problems in cases where there are more than one con- troller or player. However, differential games are conceptually far more complex than optimal control . One of the definitive works in game theory, this volume takes an original and expert look at conflict solutions.

Drawing on game theory, the calculus of variations, and control theory, the author solves an amazing array of problems relating to military situations, pursuit and evasion tactics, athletic contests, and many more. Buy Differential Games : A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (Dover Books on Mathematics) on Amazon. FREE SHIPPING on qualified orders.

These notes provide a brief introduction to the theory of noncooperative differential games. After the Introduction, Section reviews the theory of static games. Different concepts of solution are discusse including Pareto optima, Nash and Stackelberg equi- libria, and the co-co (cooperative-competitive) . A frequently adopted approach to dynamic optimization problems is the tech- nique of dynamic programming. The technique was developed by Bellman. Zaccour, Dynamic Games in the.

Invited contribution, special issue, 50th anniversary of . A branch of the mathematical theory of control (cf. Automatic control theory), the subject of which is control in conflict situations. The theory of differential games is also related to the general theory of games (cf.

Games, theory of). A state transition equation can be defined. A comprehensive, self-contained survey of the theory and applications of differential games , one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is . A mathematical theory with applications to warfare and pursuit, control and optimization.

Combining the principles of game theory, the calculus of variations, and control theory, the author considers and solves an amazing array of problems: military, pursuit and evasion, . Furthermore, stochastic differential games have extensive applications in many fields such as engineering, economics, and management science. On the definition of differential games and the existence of value and saddle points.

Existence of value and of saddle points for differential games of pursuit and evasion. The paper deals with N-person nonzero-sum games in which the dynamics is described by Ito stochastic differential equations. Sufficient conditions are found guaranteeing the Nash-equilibrium for the strategies of the players. The optimal strategies are solutions of certain partial initial value problems analogous to the . The online version of Pursuit-Evasion Differential Games by Y. Pachter on ScienceDirect.

In this paper we study zero-sum two-player stochastic differential games with the help of the theory of backward stochastic differential equations (BSDEs). At the one hand we generalize the of the pioneer work of Fleming and Souganidis by considering cost functionals defined by controlled . Adaptive Control for avoidance or evasion in an uncertain environment, M Corless et al. Stochastic guidance laws in satellite .