IDEAS home Printed from
   My bibliography  Save this paper

Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games


  • Engwerda, J.C.

    (Tilburg University, Center For Economic Research)


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.

Suggested Citation

  • Engwerda, J.C., 2007. "Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games," Discussion Paper 2007-41, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:c7941fef-278b-42ca-a6b8-2b2f340dbeb5

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, December.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Engwerda, J.C., 2007. "A Note on Cooperative Linear Quadratic Control," Discussion Paper 2007-15, Tilburg University, Center for Economic Research.
    5. Engwerda, J.C., 2007. "Necessary and Sufficient Conditions for Solving Cooperative Differential Games," Discussion Paper 2007-42, Tilburg University, Center for Economic Research.
    6. Bas Aarle & Lans Bovenberg & Matthias Raith, 1995. "Monetary and fiscal policy interaction and government debt stabilization," Journal of Economics, Springer, vol. 62(2), pages 111-140, June.
    Full references (including those not matched with items on IDEAS)

    More about this item


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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiucen:c7941fef-278b-42ca-a6b8-2b2f340dbeb5. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.