Skip to main content

Time, Risk and Conflicts in Economics and Management Science: A Story About Turnpikes

  • Chapter
Decision & Control in Management Science

Part of the book series: Advances in Computational Management Science ((AICM,volume 4))

Abstract

This chapter surveys a class of models in economic theory and management science that deal with decision making in a dynamic environment, under uncertainty and in presence of competition. These models use the paradigms of optimal control, stochastic dynamic programming and dynamic games. They share the consideration of an infinite time horizon and the possibility to exploit an asymptotic stability property called the “turnpike”.

This paper is dedicated to my former PhD students and to my colleagues, around the world, who have participated and helped in the development of my research activity over more than three decades. I thank particularly D.A. Carlson for many helpful suggestions in the presentation of some fundamental ideas in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow, K. and Kurz, M. (1970). Public Investment, The Rate of Return, and Optimal Fiscal Policy. The Johns Hopkins Press.

    Google Scholar 

  2. Bahn, O., Cadena, A., and Kypreos, S. (1999). Joint implementation of CO 2 emission reduction measures between Switzerland and Colombia. E. Fragnière (ed.) Special Issue “Applications of Decision Analysis to Environmental Problems” of Int. J. of Environment and Pollution. 12(2,3).

    Google Scholar 

  3. Bahn, O., Haurie, A., Kypreos, S., and Vial, J.-P. (1998). Advanced mathematical programming modeling to assess the benefits of international C02 abatement cooperation. Environmental Modeling and Assessment, 3(1,2):107–116.

    Article  Google Scholar 

  4. Bellman, R. (1957). Dynamic Programming. Princeton University press, Princeton N.J.

    Google Scholar 

  5. Bellman, R. and Dreyfus, S. (1962). Applied Dynamic Programming. Princeton University press, Princeton N.J.

    Google Scholar 

  6. Berger, C, Dubois, R., Haurie, A., Lessard, E., Loulou, R., and Waaub, J.-P. (1992). Canadian Markal: And advanced linear programming system for energy and environmental modelling. INFOR, 30(2):222–239.

    Google Scholar 

  7. Blaquière, A., and Leitmann, G. (1967). The Geometric Approach. Academic Press, New York.

    Google Scholar 

  8. Boukas, E., Haurie, A., and van Delft, C. (1991). A turnpike improvement algorithm for piecewise deterministic control. Optimal Control Applications and Methods, 12:1–18.

    Article  Google Scholar 

  9. Boukas, E. Haurie, A., and Michel, P. (1990). An optimal control problem with a random stopping time. Journal of Optimization Theory and Applications, 64(3):471–480.

    Article  Google Scholar 

  10. Breton, M., Filar, J., and Haurie, A. (1986). On the computation of equilibria in discounted stochastic dynamic games. Journal of Economic Dynamics and Control, 10:33–36.

    Article  Google Scholar 

  11. Brock, W. (1977). Differential games with active and passive variables. In Henn and Moeschlin, editors, Mathematical Economics and Game Theory: Essays in Honor of Oskar Morgenstern, pages 34–52. Springer Verlag, Berlin.

    Chapter  Google Scholar 

  12. Brock, W. and Scheinkman, J. (1976). Global asymptotic stability of optimal control systems with application to the theory of economic growth. Journal of Economic Theory, 12:164–190.

    Article  Google Scholar 

  13. Brock, W. A. and Haurie, A. (1976). On existence of overtaking optimal trajectories over an infinite time horizon. Mathematics of Operations Research, 1:337–346.

    Article  Google Scholar 

  14. Carlson, D. and Haurie, A. (1995). A turnpike theory for infinite horizon open- loop differential games with decoupled dynamics. In Olsder, G., editor, New Trends in Dynamic Games and Applications, volume 3 of Annals of the Society of Dynamic Games, pages 353–376.

    Chapter  Google Scholar 

  15. Carlson, D. and Haurie, A. (2000). Infinite horizon dynamic games with coupled state constraints. In Filar, J. and eds., V. G., editors, Dynamic Games and Applications, volume 6 of Annals of the International Society of Dynamic Games. Birkhä user.

    Google Scholar 

  16. Carlson, D. and Haurie, A. (1996). A turnpike theory for infinite horizon competitive processes. SIAM Journal on Optimization and Control, 34(4):1405–1419.

    Article  Google Scholar 

  17. Carlson, D., Haurie, A., and Jabrane, A. (1987). Existence of overtaking solutions to infinite dimensional control problems on unbounded time intervals. SIAM Journal on Optimization and Control, 25(6):1517–1541.

    Article  Google Scholar 

  18. Carlson, D., Haurie, A., and Leizarowitz, A. (1991). Infinite Horizon Optimal Control: Deterministic and Stochastic Systems. Springer Verlag.

    Book  Google Scholar 

  19. Case, J. (1969). Toward a theory of many player differential games. SIAM Journal on Optimization and Control, 7(2):179–197.

    Article  Google Scholar 

  20. Cass, D. (1965). Optimum growth in aggregative model of capital accumulation. Review of Economic Studies, 32:233–240.

    Article  Google Scholar 

  21. Cliff, E. and Vincent, T. (1973). An optimal policy for fish harvest. JOTA, 12:485–496.

    Article  Google Scholar 

  22. Dixit, A. and Pindyck, R. (1993). Investment unser Uncertainty. Princeton Univ. Press, Princeton, New Jersey 08540.

    Google Scholar 

  23. Fedra, K. and Haurie, A. (1999). A decision support system for air quality management combining GIS and Optimization techniques. E. Fragnière (ed.) Special Issue “Applications of Decision Analysis to Environmental Problems” of Int. J. of Environment and Pollution. 12(2,3):125–146.

    Google Scholar 

  24. Filar, J., Gaitsgory, V., and Haurie, A. (1996). Control of singularly perturbed hybrid stochastic systems. In Proc. of the 35th IEEE Conference on Decison and Control.

    Google Scholar 

  25. Filar, J. and Haurie, A. (1997). Optimal ergodic control of singularly perturbed hybrid stochastic systems. In Yin, G. and Zhang, Q., editors, Mathematics of Manufacturing Systems, volume 33 of Lectures in Applied Mathematics, pages 101–126. American mathematical Society.

    Google Scholar 

  26. Filar, J. and Vrieze, K. (1997). Competitive Marlov Decision Processes. Springer-Verlag, New York.

    Google Scholar 

  27. Fleming, W., Sethi, S., and Soner, H. (1987). An optimal stochastic production planing problem with randomly fluctuating demand. SI AM Journal on Optimization and Control, 25:1494–1502.

    Article  Google Scholar 

  28. Fragnière, E. and Haurie, A. (1996). A stochastic programming model for energy/environment choices under uncertainty. Int. J. Environment and Pollution, 6(4–6):587–603.

    Google Scholar 

  29. Halkin, H. (1974). Necessary conditions for optimal control problems with infinite horizon. Econometrica, 42(2):267–273.

    Article  Google Scholar 

  30. Hämäläinen, R., Haurie, A., and Kaitala, V. (1985). Equilibria and threats in a fishery management game. Optimal Control Applications and Methods, 6:315–333.

    Article  Google Scholar 

  31. Haurie, A. (1989). Piecewise deterministic differential games. In Ba§ar, T. and Bernhard, P., editors, Differential Games and Applications, volume 119 of Lecture Notes in Control and Information Sciences.

    Google Scholar 

  32. Haurie, A. (1995). Environmental coordination in dynamic oligopolistic markets. Group Decision and Negotiation, 4:39–57.

    Article  Google Scholar 

  33. Haurie, A. and Hung, N. (1976). Further aspects of turnpike theory in continuous time with applications. Journal of Dynamic Systems, Measurement and Control, 98.

    Google Scholar 

  34. Haurie, A. and L’Ecuyer, P. (1986). Approximation and bounds in discrete event dynamic programming. IEEE Transactions on Automatic Control, 31(3):227–235.

    Article  Google Scholar 

  35. Haurie, A., L’Ecuyer, P., and van Delft, C. (1994). Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models. Discrete Event Dynamic Systems: Theory and Applications, 4:87–111.

    Article  Google Scholar 

  36. Haurie, A. and Leitmann, G. (1984). On the global stability of equilibrium solutions for open-loop differential games. Large Scale Systems, 6:107–122.

    Google Scholar 

  37. Haurie, A., Leizarowitz, A., and van Delft, C. (1994). Boundedly optimal control of piecewise deterministic systems. European Journal of Operational Research, 73(2):237–251.

    Article  Google Scholar 

  38. Haurie, A. and Loulou, R. (1997). Modeling Equilibrium and Risk under Global Environmental Constraints in Energy Models. In Martin, W. and Tolwinski, B., editors, Modeling Environmental Policy, Kluwer Acdemic Publishers, Amsterdam.

    Google Scholar 

  39. Haurie, A., Loulou, R., and Savard, G. (1992). A Two-Player Game Model of Power Cogeneration in New England. IEEE Transactions on Automatic Control, 37:1451–1456.

    Article  Google Scholar 

  40. Haurie, A. and Marcotte, P. (1985). On the Relationship Between Nash-Cournot and Wardrop Equilibria. Netwoks, 15:295–309.

    Article  Google Scholar 

  41. Haurie, A. and Roche, M. (1994). Turnpikes and computation of piecewise open-loop equilibria in stochastic differential games. Journal of Economic Dynamics and Control, 18:317–344.

    Article  Google Scholar 

  42. Haurie, A. and Sethi, S. (1984). Decision and forecast horizons, agreeable plans, and the maximum principle for infinite horizon control problems. Operations Research Letters, 3(5):261–265.

    Article  Google Scholar 

  43. Haurie, A., Sethi, S., and Hartl, R. (1984). Optimal control of an age-structured population model with application to social services planning. Large Scale systems, 6:133–158.

    Google Scholar 

  44. Haurie, A. and van Delft, C. (1991). Turnpike properties for a class of piecewise deterministic systems arising in manufacturing flow control. Annals of Operations Research, 29:351–374.

    Article  Google Scholar 

  45. Haurie, A. and van Delft, C. (1995). Turnpikes in flow control models of unreliable manufacturing systems. European Journal of Operational Research, 82(2):338–351.

    Google Scholar 

  46. Haurie, A. and Zaccour, G. (1995). Differential game models of global environmental management. In Carraro, C. and Filar, J., editors, Control and Game-Theoretic Models of the Environment, volume 2 of Annals of the International Society of Dynamic Games, pages 3–23. Birkhäuser, Boston.

    Chapter  Google Scholar 

  47. Howard, R. (1960). Dynamic Programming and Markov Processes. MIT press, Cambridge, Mass.

    Google Scholar 

  48. Isaacs, R. (1964). Differential Games. J. Wiley, New York.

    Google Scholar 

  49. Lee, E. and Markus, L. (1967) Foundations of Optimal Control Theory. Wiley, New-York.

    Google Scholar 

  50. Leitmann, G. (1966). An Introduction to Optimal Control. McGraw-Hill, New-York.

    Google Scholar 

  51. Leizarowitz, A. (1996). Overtaking and almost-sure optimality for infinite horizon Markov decision processes. Mathematics of Operations Research, 21:158–181.

    Article  Google Scholar 

  52. McKenzie, L. (1976). Turnpike theory. Econometrica, pages 841–866.

    Google Scholar 

  53. Michel, P. (1977). Une démonstration élémentaire du principe du maximum. Bulletin de Mathématiques Economiques, 14:9–23.

    Google Scholar 

  54. Nowak, A. (1994). Stationary equilibria for nonzero-sum average ergodic stochastic games with general state space. In Başar, T. and Haurie, A., editors, Advances in Dynamic Games and Applications, volume 1 of Annals of the International Society of Dynamic Games, pages 232–246. Birkhäuser.

    Google Scholar 

  55. Olsder, G. and Suri, R. (1980). Time optimal control of parts-routing in a manufacturing system with failure prone machines. In Proc. Conference on Decision and Control, pages 722–727. IEEE.

    Google Scholar 

  56. Pontryagin et al., L. (1962). The Mathematical Theory of Optimal Processes. Wiley: Interscience, New York.

    Google Scholar 

  57. Ramsey, F. (1928). A mathematical theory of saving. Economic Journal, 38:543–549.

    Article  Google Scholar 

  58. Rockafellar, R. (1973). Saddle points of hamiltonian systems in convex problems of Lagrange. Journal of Optimization Theory and Applications, 12:367–399.

    Article  Google Scholar 

  59. Rogers, P. (1969). Nonzero-sum stochastic games. PhD thesis, University of California, Berkeley 1969, Report ORC 69–8.

    Google Scholar 

  60. Rosen, J. B. (1965). Existence and uniqueness of the equilibrium points for concave n-person games. Econometrica, 33(3):520–534.

    Article  Google Scholar 

  61. Shapley, L. (1953). Stochastic games. Proceedings Nat. Acad, of Science, USA, 39:1095–1100.

    Article  Google Scholar 

  62. Sobel, M. (1971). Noncooperative stochastic games. Ann. Math. Statist, 42:1930–1935.

    Article  Google Scholar 

  63. Starr, A. and Ho, Y. (1969). Nonzero sum differential games (i). Journal of Optimization Theory and Applications, 3:184–206.

    Article  Google Scholar 

  64. von Weizäcker, C. (1965). Existence of optimal programs of accumulation for an infinite time horizon. Review of Economic Studies, 32:85–104.

    Article  Google Scholar 

  65. Whitt, W. (1980). Representation and approximation of noncooperative sequential games. SIAM J. Control, 18:33–48.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Haurie, A. (2002). Time, Risk and Conflicts in Economics and Management Science: A Story About Turnpikes. In: Zaccour, G. (eds) Decision & Control in Management Science. Advances in Computational Management Science, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3561-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3561-1_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4995-0

  • Online ISBN: 978-1-4757-3561-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics