@techreport{63f19390d8dd4c849b967161ab804989,

title = "The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations",

abstract = "In this paper we analyse the set of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar N-player linear-quadratic differential game. We show that in general there exist maximal 2N - 1 solutions of the (ARE) that give rise to a Nash equilibrium. In particular we analyse the number of equilibria as a function of the state-feedback parameter and present both necessary and sufficient conditions for existence of a unique solution of the (ARE). Furthermore, we derive conditions under which the set of state-feedback parameters for which there is a unique solution grows with the number of players in the game.",

keywords = "Linear quadratic games, feedback Nash equilibrium, solvability conditions, Riccati equations",

author = "J.C. Engwerda",

note = "Pagination: 15",

year = "1999",

language = "English",

volume = "1999-90",

series = "CentER Discussion Paper",

publisher = "Macroeconomics",

type = "WorkingPaper",

institution = "Macroeconomics",

}