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Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games

CentER Discussion Paper Series No. 2007-41

35 Pages Posted: 13 Jun 2007  

Jacob C. Engwerda

Tilburg University - Department of Economics

Date Written: June 2007


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 worse off 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.

Keywords: Dynamic Optimization, Pareto Efficiency, Cooperative Differential Games, LQ Theory, Riccati Equations, Bargaining

JEL Classification: C61, C71, C73

Suggested Citation

Engwerda, Jacob C., Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games (June 2007). Available at SSRN: or

Jacob Engwerda (Contact Author)

Tilburg University - Department of Economics ( email )

P.O. Box 90153
Tilburg, 5000 LE
+31 13 466 2174 (Phone)
+31 13 466 3280 (Fax)

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