Advertisement

Group Decision and Negotiation

, Volume 4, Issue 1, pp 71–97 | Cite as

Strategic bargaining for the control of a dynamic system in state-space form

  • Harold Houba
  • Aart de Zeeuw
Article

Abstract

The partition of a pie model is integrated into a two-player difference game in state-space form with a finite horizon, in order to derive strategic bargaining outcomes in the framework of difference games. It is assumed that agreements are binding. In contrast to the model for the partition of a pie, the outcomes are not necessarily Pareto-efficient. For one-dimensional, linear-quadratic difference games, the subgame perfect bargaining outcome is unique, Paretoefficient, and analytically tractable. However, for higher dimensions the linear-quadratic structure breaks down and one has to resort to numerical methods.

Key Words

difference games strategic bargaining subgame perfectness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Başar, T., and G.-J. Olsder. (1982).Dynamic Noncooperative Game theory. New York: Academic Press.Google Scholar
  2. Ehtamo, H., J. Ruusunen, and R. Hämäläinen. (1990). “On a Class of Cooperative Feedback Solutions for Differential Games”. In N. Christodoulakis (ed.),Dynamic Modeling and Control of National Economies 1989, Selected Papers from the 6th IFAC Symposium, Edinburg. Oxford: Pergamon Press, pp. 33–35.Google Scholar
  3. Fernandez, R., and J. Glazer. (1991). “Striking for a Bargain Between Two Completely Informed Agents”,American Economic Review 81, 240–252.Google Scholar
  4. Fershtman, Ch., and M. Kamien. (1987). “Dynamic Duopolistic Competition with Sticky Prices”,Econometrica 55, 1151–1164.Google Scholar
  5. Fischer, S. (1980). “Dynamic Inconsistency, Cooperation and the Benevolent Dissembling Government”,Journal of Economic Dynamics and Control 2, 93–108.Google Scholar
  6. Haller, H., and S. Holden. (1991). “A Letter to the Editor on Wage Bargaining”,Journal of Economic Theory 52, 232–236.Google Scholar
  7. Haurie, A., and B. Tolwinski. (1984). “Acceptable Equilibria in Dynamic Bargaining Games”,Large Scale Systems 6, 73–89.Google Scholar
  8. Houba, H. (1992). “Non-Cooperative Bargaining in Infinitely Repeated Games with Binding Contracts. Working paper, Free University, Amsterdam.Google Scholar
  9. Houba, H., and A. de Zeeuw. (1991). “Strategic Bargaining and Difference Games”. In R. Hämäläinen and H. Ehtamo (eds.),Dynamic Games in Economic Analysis (Lecture Notes in Control and Information Sciences, Vol. 157). Berlin: Springer-Verlag, pp. 68–77.Google Scholar
  10. Kreps, D. (1990).A Course in Microeconomic Theory. New York/London: Harvester Wheatsheaf.Google Scholar
  11. Lancaster, K. (1973). “The Dynamic Inefficiency of Capitalism”,Journal of Political Economy 81, 1092–1109.Google Scholar
  12. Nash, J. (1953). “Two-Person Cooperative Games”,Econometrica 21, 128–140.Google Scholar
  13. van der Ploeg, F., and A. de Zeeuw. (1992). “International Aspects of Pollution Control”,Environmental and Resource Economics 2, 117–139.Google Scholar
  14. Reinganum, J., and N. Stokey. (1985). “Oligopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games”,International Economic Review 26, 161–173.Google Scholar
  15. Reynolds, S. (1987). “Capacity Investiments, Preemption and Commitment in an Infinite Horizon Model”,Interinational Economic Review 28, 69–88.Google Scholar
  16. Roth, A. (1979).Axiomatic Models of Bargaining (Lecture Notes in Economics and Mathematical Systems, Vol. 170). Berlin: Springer-Verlag.Google Scholar
  17. Rubinstein, A. (1982). “Perfect Equilibrium in a Bargaining Model”,Econometrica 50, 97–109.Google Scholar
  18. Starr, A., and Y. Ho (1969). “Further Properties of Nonzero-Sum Differential Games”,Journal of Optimization Theory and Applications 3, 207–219.Google Scholar
  19. Stefanski, J., and K. Cichocki. (1986). “Strategic Bargaining in a Dynamic Economy.” Discussion Paper, Systems Research Institute, Polish Academy of Sciences, Warsaw.Google Scholar
  20. Strang, G. (1980).Linear Algebra and Its Applications, 2nd ed. New York/London: Academic Press.Google Scholar
  21. Tolwinski, B. (1982). “A Concept of Cooperative Equilibrium for Dynamic Games”,Automatica 18, 431–441.Google Scholar
  22. de Zeeuw, A. (1984). “Policy Solutions for a Linked Model for Two Common Market Countries. In T. Başar and L.F. Pau (eds.),Dynamic Modeling and Control of National Economies 1983. Oxford: Pergamon Press, pp. 9–14.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Harold Houba
    • 1
    • 2
  • Aart de Zeeuw
    • 3
  1. 1.Free UniversityAmsterdam
  2. 2.Department of EconometricsTilburg UniversityTilburgthe Netherlands
  3. 3.Tilburg Universitythe Netherlands

Personalised recommendations