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Bifurcating DNS Thresholds in a Model of Organizational Bridge Building

Author

Listed:
  • J. P. Caulkins

    (Carnegie Mellon University)

  • G. Feichtinger

    (Vienna University of Technology)

  • D. Grass

    (Vienna University of Technology)

  • G. Tragler

    (Vienna University of Technology)

Abstract

A simple optimal control model is introduced, where “bridge building” positions are rewarded. Optimal solutions can be classified with regard to the two parameters (i) the cost of adjusting one’s position in a social network and (ii) the discount rate. A complete analytical description is derived for the bifurcation lines in parameter space, which separate regions with different optimal behavior. These behaviors are always approaching the organizational boundary, always falling away from the boundary, and deciding based on one’s initial state. The latter case gives rise to the emergence of so-called Dechert–Nishimura–Skiba (DNS) points describing optimal solution strategies. Furthermore the bifurcation from a single DNS point into two DNS points is analyzed in parameter space. All these strategies have a sensible interpretation within the context of the model.

Suggested Citation

  • J. P. Caulkins & G. Feichtinger & D. Grass & G. Tragler, 2007. "Bifurcating DNS Thresholds in a Model of Organizational Bridge Building," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 19-35, April.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9180-6
    DOI: 10.1007/s10957-007-9180-6
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    References listed on IDEAS

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    1. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    2. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, October.
    3. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    4. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    5. Gernot Tragler & Jonathan P. Caulkins & Gustav Feichtinger, 2001. "Optimal Dynamic Allocation of Treatment and Enforcement in Illicit Drug Control," Operations Research, INFORMS, vol. 49(3), pages 352-362, June.
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    Cited by:

    1. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    2. Grass, D., 2012. "Numerical computation of the optimal vector field: Exemplified by a fishery model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1626-1658.
    3. Moghayer, S. & Wagener, F.O.O., 2009. "Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems," CeNDEF Working Papers 09-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2011. "Monotonicity and continuity of the critical capital stock in the Dechert–Nishimura model," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 677-682.
    5. Kiseleva, T. & Wagener, F.O.O., 2011. "Bifurcations of Optimal Vector Fields," CeNDEF Working Papers 11-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    6. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.

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