
Accession Number : AD0670621
Title : NONZEROSUM DIFFERENTIAL GAMES.
Descriptive Note : Technical rept.,
Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
Personal Author(s) : Starr,A. W. ; Ho,Y. C.
Report Date : MAY 1968
Pagination or Media Count : 36
Abstract : The theory of differential games is extended to the situation where there are N players and where the game is nonzerosum, i.e., the players wish to minimize different performance criteria. Dropping the usual zerosum condition adds several interesting new features. It is no longer obvious what should be demanded of a 'solution,' and three types of solutions are discussed: the 'Nash equilibrium,' the 'minimax,' and the 'noninferior set of strategies.' For one special case, the linearquadratic game, all three of these solutions can be obtained by solving sets of ordinary matrix differential equations. To illustrate the differences between zerosum and nonzerosum games, the results are applied to a nonzerosum version of a simple pursuitevasion problem first considered by Ho, Bryson and Baron in 1965. 'Negotiated' solutions are found to exist which give better results for both players than the usual 'saddlepoint' solution. To illustrate that the theory may find interesting applications in economic analysis, a problem is outlined involving the dividend policies of firms operating in an imperfectly competitive market. (Author)
Descriptors : (*GAME THEORY, BEHAVIOR), (*MANAGEMENT PLANNING AND CONTROL, *ECONOMICS), MINIMAX TECHNIQUE, DECISION MAKING, PERFORMANCE(HUMAN), MOTIVATION, OPTIMIZATION, COSTS
Subject Categories : Administration and Management
Economics and Cost Analysis
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE