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Necessary and Sufficient Conditions for Pareto Optimality in Infinite Horizon Cooperative Differential Games
Contributions to game theory and management, Tome 3 (2010), pp. 322-341 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an $N$ player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto solutions as solving $N$ constrained optimal control subproblems. We derive some weak sufficient conditions which entail one to find all Pareto solutions by solving a weighted sum optimal control problem. Further, we observe that these sufficient conditions are related to transversality conditions of the associated subproblems. We consider games defined by nonautonomous and discounted autonomous systems. 
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     author = {Puduru Viswanadha Reddy and Jacob Engwerda},
     title = {Necessary and {Sufficient} {Conditions} for {Pareto} {Optimality} in {Infinite} {Horizon} {Cooperative} {Differential} {Games}},
     journal = {Contributions to game theory and management},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a25/}
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Puduru Viswanadha Reddy; Jacob Engwerda. Necessary and Sufficient Conditions for Pareto Optimality in Infinite Horizon Cooperative Differential Games. Contributions to game theory and management, Tome 3 (2010), pp. 322-341. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a25/

[1] Aseev S., Kryazhimskiy V., “The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons”, SIAM Journal on Control and Optimization, 43:3 (2004), 1094–1119 | DOI | MR | Zbl

[2] Aubin J. P., Clarke F. H., “Shadow prices and duality for a class of optimal control problems”, SIAM Journal on Control and Optimization, 17:5 (1979), 567–586 | DOI | MR | Zbl

[3] Blaquiere A., Juricek L., Wiese K. E., “Geometry of Pareto equilibria and maximum principle in $N$ person differential games”, Journal of Optimization Theory and Applications, 38 (1972), 223–243 | MR | Zbl

[4] Chang S. S. L., “General theory of optimal processes”, SIAM Journal of Control, 4:1 (1966), 46–55 | DOI | MR | Zbl

[5] Engwerda J. C., LQ dynamic optimization and differential games, Wiley, Chichester, 2005

[6] Engwerda J. C., “The regular convex cooperative linear quadratic control problem”, Automatica, 44:9 (2008), 2453–2457 | DOI | MR | Zbl

[7] Engwerda J. C., Necessary and sufficient conditions for Pareto optimal solutions of cooperative differential games, Submitted, 2009 | MR

[8] Fan K., Glicksberg I., Hoffman A. J., “Systems of inequalities involving convex functions”, American Mathematical Society Proceedings, 8:3 (1957), 617–622 | DOI | MR | Zbl

[9] Grass D., Calkins J. P., Feichtinger G., Tragler G., Behrens D., Optimal Control of Nonlinear Processes: with Applications in Drugs, Corruption and Terror, Springer, 2008 | MR

[10] Halkin H., “Necessary conditions for optimal control problems with infinite horizons”, Econometrica, 42 (1974), 267–272 | DOI | MR | Zbl

[11] Hartman P., Ordinary Differential Equations, John Wiley Sons, 1964 | MR | Zbl

[12] Kamien M. I., Schwartz N. L., Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Elsevier Science, 1991 | MR

[13] Leitmann G., Rocklin S., Vincent T. L., “A note on control space properties of cooperative games”, Journal of Optimization Theory and Applications, 9 (1972), 379–390 | DOI | MR | Zbl

[14] Leitmann G., Cooperative and Non cooperative Many Player Differential Games, Springer Verlag, Berlin, 1974 | Zbl

[15] Mitchel P., “On the transversality conditions in infinite horizon optimal problems”, Econometrica, 50 (1982), 975–985 | DOI | MR

[16] Seierstad A., Sydsaeter K., Optimal control theory with economic applications, North-Holland, Amsterdam, 1986 | MR

[17] Seierstad A., “Necessary conditions for nonsmooth, infinite-horizon, optimal control problems”, Journal of Optimization Theory and Applications, 103 (1999), 201–229 | DOI | MR | Zbl

[18] Simon C. P., Blume L., Mathematics for Economists, Norton Company, New York, 1994 | Zbl

[19] Stalford H. L., “Criteria for Pareto optimality in cooperative differential games”, Journal of Optimization Theory and Applications, 9 (1972), 391–398 | DOI | MR | Zbl

[20] Vincent T. L., Leitmann G., “Control space properties of cooperative games”, Journal of Optimization Theory and Applications, 6 (1970), 91–104 | DOI | MR

[21] Zadeh L. A., “Optimality and non-scalar-valued performance criteria”, IEEE Transactions on Automatic Control, 8:1 (1963), 59–60 | DOI