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On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games

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  • S. J. Rubio

    (University of Valencia)

Abstract

The scope of the applicability of the feedback Stackelberg equilibrium concept in differential games is investigated. First, conditions for obtaining the coincidence between the stationary feedback Nash equilibrium and the stationary feedback Stackelberg equilibrium are given in terms of the instantaneous payoff functions of the players and the state equations of the game. Second, a class of differential games representing the underlying structure of a good number of economic applications of differential games is defined; for this class of differential games, it is shown that the stationary feedback Stackelberg equilibrium coincides with the stationary feedback Nash equilibrium. The conclusion is that the feedback Stackelberg solution is generally not useful to investigate leadership in the framework of a differential game, at least for a good number of economic applications

Suggested Citation

  • S. J. Rubio, 2006. "On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 203-220, January.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:1:d:10.1007_s10957-005-7565-y
    DOI: 10.1007/s10957-005-7565-y
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    Citations

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    Cited by:

    1. S. Kostyunin & A. Palestini & E. Shevkoplyas, 2014. "On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 660-673, November.
    2. E. Bacchiega & L. Lambertini & A. Palestini, 2010. "On the Time Consistency of Equilibria in a Class of Additively separable Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 415-427, June.
    3. Karray, Salma & Martín-Herrán, Guiomar, 2009. "A dynamic model for advertising and pricing competition between national and store brands," European Journal of Operational Research, Elsevier, vol. 193(2), pages 451-467, March.
    4. Martín-Herrán, Guiomar & Rubio, Santiago J., 2016. "The Strategic Use of Abatement by a Polluting Monopoly," ETA: Economic Theory and Applications 244532, Fondazione Eni Enrico Mattei (FEEM).
    5. Ekaterina Gromova & Anastasiya Malakhova & Arsen Palestini, 2018. "Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration," Mathematics, MDPI, vol. 6(9), pages 1-17, September.
    6. Mikhail I. Krastanov & Rossen Rozenov & Boyan K. Stefanov, 2023. "On a Constrained Infinite-Time Horizon Linear Quadratic Game," Dynamic Games and Applications, Springer, vol. 13(3), pages 843-858, September.
    7. Lu, Lijue & Navas, Jorge, 2021. "Advertising and quality improving strategies in a supply chain when facing potential crises," European Journal of Operational Research, Elsevier, vol. 288(3), pages 839-851.
    8. Martín-Herrán, Guiomar & Rubio, Santiago J., 2021. "On coincidence of feedback and global Stackelberg equilibria in a class of differential games," European Journal of Operational Research, Elsevier, vol. 293(2), pages 761-772.
    9. Alexander Moll & Meir Pachter & Eloy Garcia & David Casbeer & Dejan Milutinović, 2020. "Robust Policies for a Multiple-Pursuer Single-Evader Differential Game," Dynamic Games and Applications, Springer, vol. 10(1), pages 202-221, March.
    10. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    11. Guiomar Martín-Herrán & Santiago J. Rubio, 2016. "The Strategic Use of Abatement by a Polluting Monopoly," Working Papers 2016.58, Fondazione Eni Enrico Mattei.
    12. Caputo, Michael R. & Ling, Chen, 2013. "The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1982-1994.
    13. Thomas Eichner & Gilbert Kollenbach & Mark Schopf, 2023. "Demand- Versus Supply-Side Climate Policies with a Carbon Dioxide Ceiling," The Economic Journal, Royal Economic Society, vol. 133(652), pages 1371-1406.
    14. Lu, Lijue & Marín-Solano, Jesús & Navas, Jorge, 2019. "An analysis of efficiency of time-consistent coordination mechanisms in a model of supply chain management," European Journal of Operational Research, Elsevier, vol. 279(1), pages 211-224.

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