On the solution set of the scalar feedback Nash algebraic Riccati equations

Author

Engwerda, Jacob C.

Author_Institution

Dept. of Econ., Tilburg Univ., Tilburg, Netherlands

fYear

1999

fDate

Aug. 31 1999-Sept. 3 1999

Firstpage

3468

Lastpage

3476

Abstract

In this note we analyse Uie sei of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar multi-player linear-quadratic differential game. We show that in general there exists more than one solution of the (ARE) that gives rise to a Nash equilibrium. In particular we analyse the number of equilibria as a function of the state-feedback parameter.

Keywords

Riccati equations; feedback; game theory; linear quadratic control; ARE; Nash algebraic Riccati equations; scalar multiplayer linear-quadratic differential game; state-feedback parameter; Econometrics; Games; Jacobian matrices; Mathematical model; Nash equilibrium; Riccati equations; Linear quadratic games; Riccati equations; feedback Nash equilibrium; solvability conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 1999 European

Conference_Location

Karlsruhe

Print_ISBN

978-3-9524173-5-5

Type

conf

Filename

7099866

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=706921