JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: VoL 27, No. 2, FEBRUARY 1979 TECHNICAL NOTE On the Uniqueness of Nash Strategies for a Class of Analytic Differential Games I G. P. PAPAVASSILOPOULOS 2 AND J. B. CRUZ, JR. 3 Communicated by G. Leitmann Abstract. The uniqueness of Nash equilibria is shown for the case where the data of the problem are analytic functions and the admissible strategy spaces are restricted to analytic functions of the current state and time. Key Words. Nash games, partial differential equations, differential games. 1. Introduction Nonzero-sum Nash differential games have attracted considerable interest during the last few years. Despite the many results available in this area, those concerning existence and uniqueness of optimal strategies are far from being satisfactory. This holds true especially if the strategies take into account information about the present and past values of the state of the system. In this context, Refs. 1 and 2 can be pointed out. In these papers, the nonuniqueness of the Nash equilibrium strategies was demonstrated when the current state x (t) and the initial state x0 are available to at least one of the 1This work was supported in part by the Joint Services Electronics Program (US Army, US Navy, and US Air Force) under Contract No, DAAB-07-72-C-0259, in part by the National Science Foundation under Grant No. ENG-74-20091, and in part by the Department of Energy, Electric Energy Systems Division under Contract No. US ERDA EX-76-C-01- 2088. 2 Graduate Student, Decision and Control Laboratory, Coordinated Science Laboratory, and Department of Electrical Engineering, University of Illinois, Urbana, Illinois. 3professor, Decision and Control Laboratory, Coordinated Science Laboratory, and Department of Electrical Engineering, University of Illinois, Urbana, Illinois. 309 0022-3239/79/0200-0309503.00/0 © I979 Plenum Publishing Corporation