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.
Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions / Ling, Chen; Luckraz, Shravan; Pansera, Bruno Antonio. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 196:3(2023), pp. 1093-1105. [10.1007/s10957-023-02160-0]
Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions
Pansera, Bruno Antonio
2023-01-01
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.| File | Dimensione | Formato | |
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