Differential Games

Differential Games

 

a branch of the mathematical theory of control, dealing with the control of an object in conflict situations. In differential games the possibilities of the players are described by differential equations containing control vectors, manipulated by the players. In choosing his control, each player can use only current information on the behavior of other players. There are two categories of differential games: those for two players and those for many players. The most thoroughly studied games are the differential games of pursuit, in which there are two players—the pursuer and the pursued. The goal of the pursuer is to guide a vector z(t) to a given set M in the shortest possible time. The goal of the pursued is to delay the moment of arrival of the vector z(t) in M. Fundamental results in the study of differen-tail games were obtained during the 1960’s in the USSR by L. S. Pontriagin, N. N. Krasovskii, E. F. Mishchenko, and B. N. Pshenichnyi and in the USA by R. Isaacs, L. Berkovitz, and W. Fleming.

M. S. NIKOL’SKII

References in periodicals archive ?
Cooperative game theory, mechanism design/implementation, political economy, learning, equilibrium selection, experimental economics, axiomatic decision theory, and differential games are among the areas addressed.
The 11 papers in this collection apply stochastic differential games to technological innovation timing, compare the Nash equilibria for static and dynamic public good games, and examine a Bayesian learning process leading to a mixed strategy Nash equilibrium.
Other areas covered include dynamic programming, optimal control for polynomial systems, multi-variable frequency-domain techniques, and differential games.
Chapters cover general optimal control problems, finite-dimensional optimization, optimization of dynamic systems with general performance criteria, terminal equality constraints, the linear quadratic control problem, and linear quadratic differential games.
The first is based on the mathematical theory of differential games.
Closed-loop (feedback) equilibria are usually preferred, but there are no general existence theorems for closed-loop equilibria in differential games with a freely chosen terminal date.
Hence, in this paper I analyze the intrafirm diffusion of a new process innovation in a differential game model of an oligopoly.
Section 2 presents the differential game model of intrafirm diffusion, and section 3 provides the details of its equilibrium.
The appropriate framework for analyzing this problem is a differential game.
To determine the open-loop equilibrium of this differential game, the standard approach is to form, for each firm i, the Hamiltonian
Russia) have organized the material in this text into two sections: an elementary but systematic exposition of the main ideas of modern game theory with only secondary school level mathematics required and a more detailed discussion of the mathematical methods of the theory that discusses such advanced analysis topics as the differential geometry approach to stability, the abstract dynamic system approach to the analysis of differential games, Bellman type equations for multi-criteria optimization, turnpikes for stochastic games, and statistical physics (this latter section requires familiarity with calculus, differential equations, linear algebra, and probability).
Other topics covered include differential games, the use of chaos indicators in rigid body motion, and single-point optimal attitude determination using modified Rodrigues parameters.

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