Skip to main content
SpringerLink
Log in

A Historical Perspective on Cooperative Differential Games

  • Chapter
Advances in Dynamic Games and Applications

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 6))

Abstract

This paper provides a brief historical perspective on the use of cooperative solution concepts in the theory of differential and dynamic games. The paper surveys the publications that appeared in control journals, likeAutomaticatheJournal of Optimization and Applications (JOTA), theSIAM Journal on Control and OptimizationtheIEEE Transactions on Automatic Controland the proceedings of the successive Differential Games Symposia, during a period that spans from the origin of differential game theory, in the early 1960s, until 1990. The survey concentrates on solution concepts that imply Pareto optimality with respect to the reward criteria of the different players. The survey does not include the topic of team theory.

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

Access this chapter

Log in via an institution
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. Aumann, R. Acceptable points in general cooperative n-person gamesAnnals of Mathematical Studies 40 287–324, 1954.

    MathSciNet  Google Scholar 

  2. Aumann, R. A survey of cooperative games without side payments, in M. Shubiked., Essays in Mathematical Economics Princeton University Press, 1969.

    Google Scholar 

  3. Basile, G. and Vincent, T. L. Absolutely cooperative solution for a linear, multiplayer differential gameJOTA6 (1):41–46, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  4. Case, J. Toward a theory of many-player differential gamesSIAM J. Cont. and Opt.7 (2):179–197, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  5. Case, J. A class of games having Pareto optimal nash equilibriaJOTA13 (3):379–386, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  6. DaCunha, N. O. and Polak, E. Constrained minimization under vector-valued criterion in finite-dimensional spacesUC Berkeley, Electronics Research Laboratory Memorandum no. ERL-M188, 1966.

    Google Scholar 

  7. DaCunha, N O and Polak, E. Constrained minimization under vector-valued criterion in linear topological spaces, in A. V. Balakrishnan and L. W. Neustadt, eds.Mathematical Theory of ControlAcademic Press, New York, 1967.

    Google Scholar 

  8. Isaacs, R.Differential GamesJohn Wiley, New York, 1964.

    Google Scholar 

  9. Edgeworth, E Y.Mathematical PsychicsC. Kegan Paul & Co., London, 1881. See also Francis Ysidro Edgeworth, by Peter Newman,The New Palgrave Utility and Probability W. W. Norton & Co., New York, 1990.

    Google Scholar 

  10. Ehtamo, H., Ruusunen, J., and Hämäläinen, R. P. Solution for a dynamic bargaining problem with application to resource managementJOTA59 (2):391–405, 1988.

    Article  MATH  Google Scholar 

  11. Ehtamo, H., Ruusunen, J., and Hämäläinen, R. P. A hierarchical approach to bargaining in power pool managementIEEE Trans. on Auto. Cont.Ac-34, pp. 666–669, 1989.

    Google Scholar 

  12. Friedman, A.Differential GamesWiley-Interscience, New-York, 1971.

    MATH  Google Scholar 

  13. Fudenberg, D. and Maskin, E. The Folk theorem in repeated games with discounting and with incomplete informationEconometrica54, pp. 533–554, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  14. Gao, L., Jakubowski, A., Klompstra, M. B., and Olsder, G. J. Time-dependent cooperation in games, in T. Basar and P. Bernhard, eds.Differential Games and ApplicationsLecture Notes in Control and Information Sciences, Vol. 119, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  15. Goffin, J. L. and Haurie A. Necessary conditions and sufficient conditions for Pareto optimality in a multicriterion perturbed systemProc. 5th IFIP Conference on Optimization TechniquesRome, Springer-Verlag, 1973.

    Google Scholar 

  16. Hämäläinen, R. H., Kaitala, V., and Haurie, A. Bargaining on whales: A differential game model with Pareto optimal equilibriaOper. Res. Let.3 (1):5–11, 1984.

    Article  MATH  Google Scholar 

  17. Hämäläinen, R. P., Kaitala., V., and Haurie, A. Equilibria and threats in a fishery management gameOptimal Cont. Appl. Meth.6 (1):315–333, 1985.

    Article  MATH  Google Scholar 

  18. Haurie, A. On Pareto optimal decision for a coalition of a subset of players IEEE Trans. Auto. Cont., AC-18 (2), April 1973.

    Google Scholar 

  19. Haurie, A. On some properties of the characteristic function and the Core of a multistage game of coalitions, IEEE Trans. Auto. Cont., AC-20 (2), April 1975.

    Google Scholar 

  20. Haurie, A. A note on Nonzero-sum differential games with bargaining solutionsJOTA13 (1):31–39, 1976.

    Article  MathSciNet  Google Scholar 

  21. Haurie, A. and Delfour, M. Individual and collective rationality in a dynamic pareto equilibriumJOTA13 (3):290–302, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  22. Haurie, A. and Pohjola, M. Efficient equilibria in a differential game of capitalismJ. Econ. Dyn. Cont.11, pp. 65–78, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  23. Haurie, A. and Tolwinski, B. Acceptable equilibria in dynamic bargaining gamesLarge Scale Systems6, pp. 73–89, 1984.

    MathSciNet  MATH  Google Scholar 

  24. Haurie, A. and Tolwinski, B. Definition and properties of cooperative equilibria in a two-player game of infinite durationJOTA46 (4):525–534, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  25. Ho, Y. C. Differential games, dynamic optimization, and generalized control theoryJOTA6 (3):179–207, 1970.

    Article  MATH  Google Scholar 

  26. Ho, Y. C. Comment on a paper by Medanic and AndjelicJOTA10 (3):187–189, 1972.

    Article  MATH  Google Scholar 

  27. Hogan, H. L. Preferred coalitions in cooperative differential gamesJOTA 13 (2):186–202, 1974.

    Article  Google Scholar 

  28. Krassovski, N. N. and Subbotin, A. I.Jeux DifférentielsNauka, Moscow, 1977.

    Google Scholar 

  29. Klinger, A. Vector-valued performance criteria, IEEE Trans. Auto. Cont., AC-9 (1), 1964.

    Google Scholar 

  30. Kwon, Y. K. and Yu, P. L. Stabilization through taxation in n-person gamesJOTA23 (2):277–284, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  31. Leitmann, G., Rocklin, S., and Vincent, T. L. A note on control space properties of cooperative gamesJOTA9 (6):379–390, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  32. Lin, J. G. Maximal vectors and multi-objective optimizationJOTA18 (1):41–64, 1976.

    Article  MATH  Google Scholar 

  33. Liu, P. T. Nonzero-sum differential games with bargaining solutionsJOTA11 (3):284–292, 1973.

    Article  MATH  Google Scholar 

  34. Medanic, J. and Andjelic, M. On a class of differential games without saddle-point solutionsJOTA8 (6):413–430, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  35. Nash, J. The bargaining problemEconometrica18, 155–162, 1950.

    Article  MathSciNet  MATH  Google Scholar 

  36. Nash, J. Two-person cooperative gamesEconometrica21, 128–140, 1953.

    Article  MathSciNet  MATH  Google Scholar 

  37. Pareto, V.Cours d’conomie PolitiqueSapurious Rouge, Lausanne, 1896.

    Google Scholar 

  38. Petrosjan, L. A. and Murzov, N. V. Game of overpulling with many participants (in Russian)Viestnik Leningradskogo Univ.13, 1967.

    Google Scholar 

  39. Ray, A. and Blaquière, A. Sufficient conditions for optimality of threat strategies in a differential gameJOTA30 (1):99–109,1981.

    Article  Google Scholar 

  40. Reid, R. W. and Citron, S. J. On noninferior performance index vectorsJOTA7 (1):11–27, 1969.

    Article  MathSciNet  Google Scholar 

  41. Salukvadze, M. On the existence of solutions in problems of optimization under vector-valued criteriaJOTA13 (2):203–217, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  42. Tolwinski, B. A concept of cooperative equilibrium for dynamic gamesAutomatica18, (4):431–441, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  43. Scarf, H. The Core of a n-person gameEconometrica35, 50–69, 1967.

    Article  MathSciNet  MATH  Google Scholar 

  44. Schmitendorf, W. E. and Moriarty, G. A sufficiency condition for coalitive Pareto-optimal solutionsJOTA18 (1):93–102,1976.

    Article  MathSciNet  MATH  Google Scholar 

  45. Stadler, W. Sufficient conditions for preference optimalityJOTA18 (1):119–140, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  46. Starr, A. W. and Ho, Y. C. Nonzero-sum differential gamesJOTA3 (4):207–219, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  47. Starr, A. W. and Ho, Y. C. Nonzero-sum differential gamesJOTA3 (3):184–206, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  48. Tolwinski, B., Haurie, A., and Leitmann, G. Cooperative equilibria in differential gamesJ. Math. Anal. Appl.119, pp. 182–202, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  49. Varaiya, P. N-player stochastic differential gamesSIAM J. Cont. and Opt. 14 (3):538–545, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  50. Vincent, T. L. and Leitmann, G. Control space properties of cooperative gamesJOTA6 (2):91–113, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  51. von Neumann, J. and Morgenstern, O. Theory of Games and Economic Behavior, Princeton University Press, 1944.

    Google Scholar 

  52. Yu, P. L. and Leitmann, G. Compromise solutions, domination structures and salukvadze’s solutionJOTA13 (3):362–378, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  53. Zadeh, L. A. Optimality of non-scalar-valued performance criteria, IEEE Trans. Auto. Cont., AC-8 (1), 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Geneva LOGILAB/HEC, Geneva, Switzerland

    Alain Haurie

Authors
  1. Alain Haurie
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, 06902, France

    Eitan Altman  & Odile Pourtallier  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Haurie, A. (2001). A Historical Perspective on Cooperative Differential Games. In: Altman, E., Pourtallier, O. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0155-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0155-7_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6637-2

  • Online ISBN: 978-1-4612-0155-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation