Accession Number : AD0670621

Title :   NONZERO-SUM 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 nonzero-sum, i.e., the players wish to minimize different performance criteria. Dropping the usual zero-sum 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 linear-quadratic game, all three of these solutions can be obtained by solving sets of ordinary matrix differential equations. To illustrate the differences between zero-sum and nonzero-sum games, the results are applied to a nonzero-sum version of a simple pursuit-evasion 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 'saddle-point' 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