### Abstract

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

Place of Publication | Tilburg |

Publisher | Macroeconomics |

Number of pages | 35 |

Volume | 2007-41 |

Publication status | Published - 2007 |

### Publication series

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

Volume | 2007-41 |

### Fingerprint

### Keywords

- Dynamic Optimization
- Pareto Efficiency
- Cooperative Differential Games
- LQ The- ory
- Riccati Equations
- Bargaining

### Cite this

*Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games*. (CentER Discussion Paper; Vol. 2007-41). Tilburg: Macroeconomics.

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**Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games.** / Engwerda, J.C.

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

TY - UNPB

T1 - Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games

AU - Engwerda, J.C.

N1 - Subsequently published in Proceedings of the 5th SEAMS-GMU, 2007 Pagination: 35

PY - 2007

Y1 - 2007

N2 - We survey some recent research results in the field of dynamic cooperative differential games with non-transferable utilities. Problems which fit into this framework occur for instance if a person has more than one objective he likes to optimize or if several persons decide to combine efforts in trying to realize their individual goals. We assume that all persons act in a dynamic environment and that no side-payments take place. For these kind of problems the notion of Pareto efficiency plays a fundamental role. In economic terms, an allocation in which no one can be made better-off without someone else becoming worseoff is called Pareto efficient. In this paper we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex games. These results are elaborated for the special case that the environment can be modeled by a set of linear differential equations and the objectives can be modeled as functions containing just affine quadratic terms. Furthermore we will consider for these games the convex case. In general there exists a continuum of Pareto solutions and the question arises which of these solutions will be chosen by the participating persons. We will flash some ideas from the axiomatic theory of bargaining, which was initiated by Nash [16, 17], to predict the compromise the persons will reach.

AB - We survey some recent research results in the field of dynamic cooperative differential games with non-transferable utilities. Problems which fit into this framework occur for instance if a person has more than one objective he likes to optimize or if several persons decide to combine efforts in trying to realize their individual goals. We assume that all persons act in a dynamic environment and that no side-payments take place. For these kind of problems the notion of Pareto efficiency plays a fundamental role. In economic terms, an allocation in which no one can be made better-off without someone else becoming worseoff is called Pareto efficient. In this paper we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex games. These results are elaborated for the special case that the environment can be modeled by a set of linear differential equations and the objectives can be modeled as functions containing just affine quadratic terms. Furthermore we will consider for these games the convex case. In general there exists a continuum of Pareto solutions and the question arises which of these solutions will be chosen by the participating persons. We will flash some ideas from the axiomatic theory of bargaining, which was initiated by Nash [16, 17], to predict the compromise the persons will reach.

KW - Dynamic Optimization

KW - Pareto Efficiency

KW - Cooperative Differential Games

KW - LQ The- ory

KW - Riccati Equations

KW - Bargaining

M3 - Discussion paper

VL - 2007-41

T3 - CentER Discussion Paper

BT - Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games

PB - Macroeconomics

CY - Tilburg

ER -