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Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions

Author

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  • Chen Ling

    (Zhejiang University of Finance and Economics)

  • Shravan Luckraz

    (Zhejiang University of Finance and Economics)

  • Bruno Antonio Pansera

    (Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria)

Abstract

We revisit the assumption of differentiability of solutions with respect to exogenous variables in the differential games literature (e.g., Ling and Caputo (J Optim Theory Appl 149:151–174, 2011). We show that differentiability can be replaced with a weaker condition that preserves the sign of any comparative dynamics. Although we only consider the Markovian Nash Equilibria in this paper, our result also applies to other concepts of equilibria such as the Stackelberg equilibria.

Suggested Citation

  • Chen Ling & Shravan Luckraz & Bruno Antonio Pansera, 2023. "Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1093-1105, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-023-02160-0
    DOI: 10.1007/s10957-023-02160-0
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    References listed on IDEAS

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    1. Caputo, Michael R., 2007. "The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 198-224, November.
    2. 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.
    3. C. Ling & M. R. Caputo, 2011. "A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 151-174, April.
    4. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    5. Van Gorder, Robert A. & Caputo, Michael R., 2010. "Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1123-1139, June.
    6. Benchekroun, Hassan, 2008. "Comparative dynamics in a productive asset oligopoly," Journal of Economic Theory, Elsevier, vol. 138(1), pages 237-261, January.
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