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Stochastic differential games in economic modeling

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Book cover System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 197))

Abstract

In this paper we present two continuous-time models of economic competition which are based on a stochastic differential game formalism. We focus our presentation on the modeling possibilities offered by the frameworks of piecewise deterministic and switching diffusion control systems respectively. We develop two duopoly models: a dynamic R&D competition model and a stochastic fishery exploitation model with correlated equilibrium. Some indications on the numerical solution of these games are also given.

Research supported by NSERC-Canada, FCAR-Quebec, and FNRS-Switzerland

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References

  1. Akian M., Chancellier J.P. Dynamic Programming Complexity and Applications, Proceedings of the 27th IEEE Conference on Decision and Control, Austin Texas, 1988.

    Google Scholar 

  2. Aumann R.J., 1974, Subjectivity and Correlation in Randomized Strategies, J. Economic Theory, Vol. 1, pp. 67–96.

    MATH  MathSciNet  Google Scholar 

  3. Bertsekas D.P., 1987, Dynamic Programming: Deterministic and Stochastic Models, Prentice Hall.

    Google Scholar 

  4. Boukas E.K., Haurie A. & Michel P., 1990, An optimal control problem with a random stopping time, J. Optim. Theory Appl. 64, 471–480.

    Article  MATH  MathSciNet  Google Scholar 

  5. Boukas E.K., Haurie A. & van Delft Ch., 1991, A Turnpike Improvement Algorithm for Piecewise Deterministic Control, Optimal Control Applications and Methods, Vol. 12, 1–18.

    Article  MATH  MathSciNet  Google Scholar 

  6. Brock W. A., 1977, Differential Games with Active and Passive Variables, in Henn and Moeschlin (Eds.) Mathematical Economics an Game Theory: Essays in Honor of Oskar Morgenstern, Springer Verlag, Berlin, 34–52.

    Chapter  Google Scholar 

  7. Carlson D.A., Haurie A. & Leizarowitz A., 1991, Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, Springer Verlag.

    Google Scholar 

  8. Cass D. & Shell K., 1976, The Hamiltonian Approach to Dynamic Economics, Academic Press.

    Google Scholar 

  9. Clark C.W., Restricted Access to Common-property Resources: a Game Theoretic Analysis, Dynamic Optimization and Mathematical Economics, Edited by P. Liu, Plenum Press, New York, New York, 1980.

    Google Scholar 

  10. Cournot A., 1838,Recherches sur les principes mathématiques de la théorie des richesses, Hachette, Paris.

    Google Scholar 

  11. Feinstein C.D. & Luenberger D.G., 1981, Analysis of the Asymptotic Behaviour of Optimal Control Trajectories: the Implicit Programming Problem, SIAM J. Control Optim. 19, 561–585.

    Article  MATH  MathSciNet  Google Scholar 

  12. Forges F., 1986, An Approach to Communication Equilibria, Econometrica, Vol. 54, pp. 1375–1385.

    Article  MATH  MathSciNet  Google Scholar 

  13. Friedman J. W., Oligopoly and the Theory of Games, North-Holland, Amsterdam, Holland, 1977.

    MATH  Google Scholar 

  14. Ghosh M.K., Arapostathis A. and Marcus S.I., Optimal Control of Switching Diffusions with Application to Flexible Manufacturing Systems, Proceedings of the 30-th IEEE-Conference on Decision and Control, Brighton, England, 1991.

    Google Scholar 

  15. Green E.J. and Porter R.H., Noncooperative Collusion Under Imperfect Price Information, Econometrica, Vol. 52, 1984, pp. 87–100.

    Article  MATH  Google Scholar 

  16. Krylov N.V., Controlled Diffusion Processes, Springer-Verlag, Berlin, Germany, 1980.

    Book  MATH  Google Scholar 

  17. Halkin H. Necessary Conditions for Optimal Control Problems with Infinite Horizon, Econometrica, Vol. 42, 267–273.

    Google Scholar 

  18. Hamalainen R., Haurie A., Kaitala V., Equilibria and Threat in a Fishery Management Game, Optimal Control Applications and Methods, Vol. 6,pp.315–333, 1985.

    Article  MathSciNet  Google Scholar 

  19. Haurie A., 1989, Duopole et Percées Technologiques: un Modèle de Jeu Différentiel Déterministe par Morceaux, L'Actualité Économique, Vol. 65-1, 105–118.

    Article  Google Scholar 

  20. Haurie A., Piecewise Deterministic and Piecewise Diffusion Differential games, in G. Ricci (ed.), Decison Processes in Economics, Springer-Verlag, Berlin, Germany, 1991.

    Google Scholar 

  21. Haurie A., From Repeated to Differential Games: How Time and Uncertainty Pervade the Theory of Games, to appear.

    Google Scholar 

  22. A. Haurie, J.B. Krawczyk, M. Roche, 1992, Monitoring Cooperative Equilibria in a Stochastic Differential Game, Proceedings 31-st IEEE-CDC, Tucson Arizona, Dec. To appear in JOTA.

    Google Scholar 

  23. Haurie A. & Leitmann G., 1984, On the Global Stability of Equilibrium Solutions for Open-Loop Differential Games, Large Scale Systems 6, 107–122.

    MATH  MathSciNet  Google Scholar 

  24. Haurie A. and Leizarowitz A., Overtaking Optimal Regulation and Tracking of Piecewise Diffusion Linear Systems, SIAM J. Control and Optimization, Vol. 30, pp. 816–837, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  25. Haurie A. & Roche M., 1992, Un modèle de concurrence par la R&D: Calcul d'un équilibre stochastique, in Mélanges en l'honneur des professeurs A. Cottier et G. Mentha, Université de Genève, 1992.

    Google Scholar 

  26. Haurie A. & Roche M., 1991, On the Computation of Open-Loop Equilibria in a Class of Differential Games with Random Modal Changes, Journal of Economic Dynamics and Control, to appear, 1993.

    Google Scholar 

  27. Haurie A. and Tolwinski B., Cooperative Equilibria in Discounted Stochastic Sequential Games, Journal of Optimization Theory and Applications, Vol. 64, pp. 511–535, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  28. Haurie A. & van Delft Ch., 1991, Turnpike Properties for a Class of Piecewise Deterministic Systems Arising in Manufacturing Flow Control, Annals of Operations Research 29, 351–374.

    Article  MATH  MathSciNet  Google Scholar 

  29. Henderson J.M. & Quandt R.E., 1987, Microéconomie, Dunod, Paris.

    Google Scholar 

  30. Kushner H.J., Probability Methods for Approximation in Stochastic Control and for Elliptic Equations, Academic Press, New York, New York, 1977.

    Google Scholar 

  31. Munro G.R., The Optimal Management of Transboundary Renewable Resources, Canadian Journal of Economics, Vol. 12, pp. 355–376, 1979.

    Article  Google Scholar 

  32. Porter R.H., Optimal Cartel Trigger Strategies, Journal of Economic Theory, Vol. 29, pp.313–338, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  33. Selten R., Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, Vol. 4, pp. 25–55, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  34. Tirole J., 1989, The Theory of Industrial Organization, MIT Press.

    Google Scholar 

  35. Schmalensee R., 1990, Inter-Industry Studies of Structure and Performance, in Handbook of Industrial organization, ed. R. Schmalensee & R. Willig, Amsterdam North Holland.

    Google Scholar 

  36. Whitt W., 1980, Representation and Approximation of Noncooperative Sequential Games, SIAM J. Control, Vol. 18, pp. 33–48.

    Article  MATH  MathSciNet  Google Scholar 

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Jacques Henry Jean-Pierre Yvon

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© 1994 Springer-Verlag

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Haurie, A. (1994). Stochastic differential games in economic modeling. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035461

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  • DOI: https://doi.org/10.1007/BFb0035461

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19893-2

  • Online ISBN: 978-3-540-39337-5

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