### Abstract

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 |
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Volume | 1999-90 |

### Fingerprint

### Keywords

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

### Cite this

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

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**The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations.** / Engwerda, J.C.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations

AU - Engwerda, J.C.

N1 - Pagination: 15

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Linear quadratic games

KW - feedback Nash equilibrium

KW - solvability conditions

KW - Riccati equations

M3 - Discussion paper

VL - 1999-90

T3 - CentER Discussion Paper

BT - The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations

PB - Macroeconomics

CY - Tilburg

ER -