Skip to main content

A Tutorial on Dynamic and Differential Games

  • Conference paper
Book cover Dynamic Games and Applications in Economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 265))

Abstract

A general formulation of dynamic and differential games is given, which includes both discrete and continuous time problems as well as deterministic and stochastic games. Solution concepts are introduced in two categories, depending on whether the dynamic game is defined in normal or extensive form. For the former, we present the Nash, Stackelberg and Consistent Conjectural Variations (CCV) equilibria, with considerable discussion devoted to the CCV solution, including comparisons with other more specific definitions found in the literature. For games in extensive form, we discuss the feedback solution concepts, and elaborate on the time consistency issue, which is currently of major interest in the economics literature. The chapter concludes with a discussion which puts into proper perspective the topics and contributions of the ten papers to follow, and their relationships with each other.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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 and Selective Bibliography

  • Basar, T. (1984), “Affine Incentive Schemes for Stochastic Systems with Dynamic Information,” SIAM J. Control and Optimization, vol. 22, no. 2, pp. 199–210.

    Article  Google Scholar 

  • Basar, T. (1985), “Dynamic Games and Incentives,” in Systems and Optimization, Lecture Notes in Control and Information Sciences, A. Bagchi and H. Th. Jongen (edts.), Springer-Verlag, vol. 66, pp. 1–13.

    Google Scholar 

  • Basar, T. and A. Haurie (1984), “Feedback Equilibria in Differential Games with Structural and Modal Uncertainties,” in Advances in Large Scale Systems, vol. 1, J. B. Cruz, Jr. (ed.) JAI Press Inc., pp. 163–201.

    Google Scholar 

  • Basar, T., A. Haurie and G. Ricci (1985), “On the Dominance of Capialists Leadership in a Feedback Stackelberg Solution of a Differential Game Model of Capitalism,” J. Economic Dynamics and Control, to appear.

    Google Scholar 

  • Basar, T. and G. J. Olsder (1982), Dynamic Noncooperative Game Theory, Academic Press, London/New York.

    Google Scholar 

  • Basar, T. and H. Selbuz (1979), “Closed-Loop Stackelberg Strategies with Applications in the Optimal Control of Multilevel Systems,” IEEE Transactions on Automatic Control, vol. AC-24, no. 2, pp. 166–179.

    Article  Google Scholar 

  • Baudet, G. M. (1978), “Asynchronous Iterative Methods for Multiprocessors,” J. Association for Computing Machines, vol. 25, no. 2, pp. 226–244.

    Google Scholar 

  • Bertsekas, D. P. (1983), “Distributed Asynchronous Computation of Fixed Points,” Mathematical Programming, vol. 27, North-Holland, pp. 107–120.

    Article  Google Scholar 

  • Bresnahan, T. F. (1981), “Duopoly Models with Consistent Conjectures,” American Economic Review, vol 71, pp. 934–945.

    Google Scholar 

  • Cansever, D. H. and T. Basar (1985), “Optimum/Near-Optimum Incentive Policies for Stochastic Decision Problems in the Presence of Parametric Uncertainty,” Automatica, vol. 24, no. 5.

    Google Scholar 

  • Feichtinger, G. and S. Jørgensen (1983), “Differential Game Models in Management,” European J. Operational Research, vol. 14, pp. 137–155.

    Article  Google Scholar 

  • Fershtman, C. and M. I. Kamien (1985), “Conjectural Equilibrium and Strategy Spaces in Differential Games,” in Optimal Control Theory and Economic Analysis, vol. 2, G. Feichtinger (ed.), North-Holland.

    Google Scholar 

  • Hallett, A. J. H. (1984), “Non-cooperative Strategies for Dynamic Policy Games and the Problem of Time Inconsistency,” Oxford Economic Papers, vol. 36, pp. 381–399.

    Google Scholar 

  • Ho, Y. C, P. B. Luh and G. J. Olsder, “A Control Theoretic View on Incentives,” Automatica, vol. 18, pp. 167–179.

    Google Scholar 

  • Kamien, M. I. and N. L. Schwartz (1983), “Conjectural Variations,” Canadian J. Economics, vol. 16, pp. 191–211.

    Article  Google Scholar 

  • Miller, M. and M. Salmon (1983), “Dynamic Games and Time Inconsistency of Optimal Policies in Open Economies,” preprint.

    Google Scholar 

  • Ortega, J. M. and W. C. Rheinboldt (1970), Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York.

    Google Scholar 

  • Papavassilopoulos, G. P. and J. B. Cruz, Jr. (1979), “Nonclassical Control Problems and Stackelberg Games,” IEEE Transactions on Automatic Control, vol. AC-24, no. 2, pp. 155–166.

    Article  Google Scholar 

  • Zheng, Y. P. and T. Basar, “Existence and Derivation of Optimal Affine Incentive Schemes for Stackelberg Games with Partial Information: A Geometric Approach,” International J. Control, vol. 35, no. 6, pp. 997–1012.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Başar, T. (1986). A Tutorial on Dynamic and Differential Games. In: Başar, T. (eds) Dynamic Games and Applications in Economics. Lecture Notes in Economics and Mathematical Systems, vol 265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61636-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-61636-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16435-7

  • Online ISBN: 978-3-642-61636-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics