Skip to main content
SpringerLink
Log in

The dynamics of the strategic capital accumulation

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In a two‐player capital accumulation differential game with reversible investment, wepropose a simplifying method to calculate the open‐loop Nash equilibrium and the centralizedsolution. Then we relate the two outcomes through their dynamic properties, namelythe pattern and the rate of convergence. It is demonstrated that the two outcomes share theproperty that a stock will have a non‐monotonic trajectory as a medium-run consequence ofthe differences in the initial conditions and of the heterogeneity of the agents. On the otherhand, the solutions differ in the speed of convergence of the aggregated variables, which isgreater under the centralized behavior.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Başar and G.J. Olsder, Dynamic Non-Cooperative Game Theory, 2nd ed., Academic Press, 1995.

  2. E.J. Dockner and H. Takahashi, Turnpike properties and comparative dynamics of general capital accumulation games, in: General Equilibrium, Growth, and Trade II: The Legacy of L. McKenzie, eds. M. Boldrin et al., Academic Press, Orlando, FL, 1993, pp. 352-366.

    Google Scholar 

  3. E.J. Dockner, N.V. Long and G. Sorger, Analysis of Nash equilibria in a class of capital accumulation games, Journal of Economic Dynamics and Control 20(1996)1209-1235.

    Google Scholar 

  4. D. Duffie, Y. Geanakoplos, A. MacColell and A. McLennan, Stationary Markov equilibria, Econometrica 62(1994)42-61.

    Google Scholar 

  5. P.K. Dutta and R. Sundaram, The tragedy of the common?, Economic Theory 3(1993)413-426.

    Google Scholar 

  6. P.K. Dutta and R. Sundaram, How different can strategic models be?, Journal of Economic Theory 60(1993)42-61.

    Google Scholar 

  7. C. Fershtman and E. Muller, Capital accumulation game of infinite duration, Journal of Economic Theory 33(1984)322-339.

    Google Scholar 

  8. C. Fershtman and E. Muller, Turnpike properties of capital accumulation game, Journal of Economic Theory 38(1986)167-177.

    Google Scholar 

  9. C. Fershtman and S. Nitzan, Dynamic voluntary provision of public goods, European Economic Review 35(1991)1057-1067.

    Google Scholar 

  10. C. Figuières, P. Gardères and F. Rychen, Infrastructures publiques et politiques de développement décentralisées, GREQAM WP 97A16, 1997.

  11. D. Fudenberg and J. Tirole, Capital as commitment: Strategic investment to deter mobility, Journal of Economic Theory 31(1983)227-256.

    Google Scholar 

  12. R.F. Hartl, A simple proof of the monotonicity of the state trajectories in autonomous control problems, Journal of Economic Theory 41(1987)211-215.

    Google Scholar 

  13. D. Levhari and L. Mirman, The great fish war: An example using a dynamic Cournot Nash solution, Bell Journal of Economics 11(1980)322-334.

    Google Scholar 

  14. E. Maskin and J. Tirole, A theory of oligopoly: I. Overview and quantity competition with large fixed costs, Econometrica 56(1988)549-569.

    Google Scholar 

  15. S.S. Reynolds, Capacity investment, preemption and commitment in an infinite horizon model, Inter-national Economic Review 28(1987)69-88.

    Google Scholar 

  16. R.K. Sundaram, Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games, Journal of Economic Theory 47(1989)153-177.

    Google Scholar 

Download references

Authors
  1. C. Figuières
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Gardères
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Michel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Rychen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Figuières, C., Gardères, P., Michel, P. et al. The dynamics of the strategic capital accumulation. Annals of Operations Research 88, 291–307 (1999). https://doi.org/10.1023/A:1018990615767

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018990615767

Keywords

Search

Navigation