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

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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.

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Notes

  1. A common example is a function that has points of inflection in the interior of its domain. Although the latter happen in at most a finite number of points, Zaanen and Luxemburg [12] give an example of a strictly monotonic function whose derivative vanishes almost everywhere.

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Authors and Affiliations

  1. School of Public Finance and Taxation, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Chen Ling & Shravan Luckraz

  2. Department of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, 89124, Reggio Calabria, Italy

    Bruno Antonio Pansera

Authors
  1. Chen Ling
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  2. Shravan Luckraz
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  3. Bruno Antonio Pansera
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Corresponding author

Correspondence to Shravan Luckraz.

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Communicated by Bruce A. Conway .

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We thank two anonymous referees of JOTA for their detailed comments on an earlier version of the paper. We also thank the Associate Editor for useful suggestions. We are grateful to Professor Annamaria Barbagallo for her numerous suggestions and advice. Chen Ling acknowledges the financial support from the National Natural Science Foundation of China (71971193, 71401137) and the Ten-thousand Talents Plan of Zhejiang Province.

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Ling, C., Luckraz, S. & Pansera, B.A. Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions. J Optim Theory Appl 196, 1093–1105 (2023). https://doi.org/10.1007/s10957-023-02160-0

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  • DOI: https://doi.org/10.1007/s10957-023-02160-0

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