Accession Number : AD0710088

Title :   SERIES NASH SOLUTION OF TWO-PERSON NONZERO-SUM LINEAR-QUADRATIC DIFFERENTIAL GAMES,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : Cruz,J. B. , Jr. ; Chen,C. I.

Report Date : JUL 1970

Pagination or Media Count : 29

Abstract : It is well-known that the Nash equilibrium solution of a two-person nonzero-sum linear differential game with a quadratic cost function can be expressed in terms of the solution of coupled generalized Riccati-type matrix differential equations. For high order games the numerical determination of the solution of the nonlinear coupled equations may be difficult or even not possible when the application dictates the use of small memory computers. In this paper a series solution is suggested by means of a parameter imbedding method. Instead of solving a high order Riccati matrix equation a lower order matrix Riccati equation corresponding to a zero-sum game is solved. In addition, lower order linear equations have to be solved. These solutions to lower order equations are the coefficients of the series solution for the nonzero-sum game. Cost functions corresponding to truncated solutions are compared with those for exact Nash equilibrium solutions. (Author)

Descriptors :   (*GAME THEORY, MATHEMATICAL MODELS), COSTS, STOCHASTIC PROCESSES, DECISION MAKING, DIFFERENCE EQUATIONS, LINEAR PROGRAMMING, DIFFERENTIAL EQUATIONS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE