### 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.

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Macroeconomics |

Number of pages | 15 |

Volume | 1999-90 |

Publication status | Published - 1999 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 1999-90 |

### Keywords

- Linear quadratic games
- feedback Nash equilibrium
- solvability conditions
- Riccati equations

## Fingerprint Dive into the research topics of 'The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations'. Together they form a unique fingerprint.

## Cite this

Engwerda, J. C. (1999).

*The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations*. (CentER Discussion Paper; Vol. 1999-90). Macroeconomics.