IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v133y2007i1d10.1007_s10957-007-9180-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9180-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-007-9180-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 60-73, April.
    2. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 60-73.
    3. I. Zeiler & J.P. Caulkins & G. Tragler, 2011. "Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use," Post-Print hal-00978258, HAL.
    4. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    5. G. Feichtinger & A. Steindl, 2006. "DNS Curves in a Production/Inventory Model," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 295-308, February.
    6. Yegorov, Yury & Wirl, Franz & Grass, Dieter & Eigruber, Markus & Feichtinger, Gustav, 2022. "On the matthew effect on individual investments in skills in arts, sports and science," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 178-199.
    7. Francesco Bartaloni, 2021. "Existence of the Optimum in Shallow Lake Type Models with Hysteresis Effect," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 358-392, August.
    8. Wirl, Franz, 2009. "OPEC as a political and economical entity," European Journal of Political Economy, Elsevier, vol. 25(4), pages 399-408, December.
    9. Levy, Amnon & Neri, Frank & Grass, Dieter, 2006. "Macroeconomic Aspects Of Substance Abuse: Diffusion, Productivity And Optimal Control," Macroeconomic Dynamics, Cambridge University Press, vol. 10(2), pages 145-164, April.
    10. Yuri Yegorov & Dieter Grass & Magda Mirescu & Gustav Feichtinger & Franz Wirl, 2020. "Growth and Collapse of Empires: A Dynamic Optimization Model," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 620-643, August.
    11. Herbert Dawid & Michel Y. Keoula & Peter M. Kort, 2017. "Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms," Dynamic Games and Applications, Springer, vol. 7(4), pages 555-577, December.
    12. Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
    13. Seidl, Andrea & Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2018. "Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs," European Journal of Operational Research, Elsevier, vol. 267(2), pages 700-715.
    14. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.
    15. Haunschmied, Josef L. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2005. "Keeping up with the technology pace: A DNS-curve and a limit cycle in a technology investment decision problem," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 509-529, August.
    16. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
    17. 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.
    18. Dockner, Engelbert J. & Nishimura, Kazuo, 2005. "Capital accumulation games with a non-concave production function," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 408-420, August.
    19. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    20. Wirl, Franz, 2016. "Indeterminacy and history dependence of strategically interacting players," Economics Letters, Elsevier, vol. 145(C), pages 19-24.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9180-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.