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Accession Number:
AD0670621
Title:
NONZERO-SUM DIFFERENTIAL GAMES.
Corporate Author:
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
Report Date:
1968-05-01
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
Descriptive Note:
Technical rept.,
Pages:
0036
Contract Number:
N00014-67-A-0298
Contract Number 2:
NGR-22-007-068
File Size:
0.00MB
