EQUILIBRIUM POINTS OF N-PERSON DIFFERENTIAL GAMES.
Abstract
Consider a differential game G between the players 1, 2, ..., N whose state is governed by the equation x dot = f(t, x, u sub 1, ..., u sub N), where u sub i is a control vector belonging to player i, and suppose that each player i wishes to manipulate his control vector u sub i in such a way as to minimize a functional J sub i = K sub i (x(t sub f)) + the integral from t sub 0 to t sub f of the quantity L sub i (t, x(t), u sub 1 (t), ..., u sub n (t)) dt. Here t sub 0 and t sub f are respectively the times at which the game begins and ends. A strategy N-tuple u sub 1 = phi* sub 1 (t, x), ..., u sub N = phi* sub N (t, x) is called an equilibrium point for G if the inequalities J sub i (phi* sub 1, ..., phi* sub N) J sub i (..., phi* sub (i-1), phi sub i, phi* (i + 1), ...) hold for each i = 1, ..., N and for each admissible strategy u sub i = phi sub i (t, x) for the player i. We seek methods of finding equilibrium points for the game G. Thus the problem is a generalization of that considered first by Isaacs and later by Berkovitz and Fleming, Pontryagin, and others.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD0661097
Entities
People
- James Howard Case
Organizations
- University of Michigan