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Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games

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Author Info
Engwerda, J.C. (Tilburg University, Center for Economic Research)

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Abstract

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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-41.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200741

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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

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  1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April. [Downloadable!] (restricted)
  2. Engwerda, J.C., 2007. "Necessary and Sufficient Conditions for Solving Cooperative Differential Games," Discussion Paper 2007-42, Tilburg University, Center for Economic Research. [Downloadable!]
  3. Engwerda, J.C., 2007. "A Note on Cooperative Linear Quadratic Control," Discussion Paper 2007-15, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Aarle, B. van & Bovenberg, L. & Raith, M., 1995. "Monetary and Fiscal Policy Interaction and Government Debt Stabilization," Discussion Paper 1, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier. [Downloadable!] (restricted)
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  1. Engwerda, J.C., 2007. "Necessary and Sufficient Conditions for Solving Cooperative Differential Games," Discussion Paper 2007-42, Tilburg University, Center for Economic Research. [Downloadable!]
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