Comparative dynamics in differential games: a note on the differentiability of solutions

Chen Ling; Shravan Luckraz; Bruno Antonio Pansera

doi:10.1007/s10957-023-02160-0

Comparative dynamics in differential games: a note on the differentiability of solutions

Chen Ling, Shravan Luckraz, Bruno Antonio Pansera

Research output: Journal Publication › Article › peer-review

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.

Original language	English
Pages (from-to)	1093-1105
Number of pages	13
Journal	Journal of Optimization Theory and Applications
Volume	196
Issue number	3
DOIs	https://doi.org/10.1007/s10957-023-02160-0
Publication status	Published - Mar 2023

Keywords

Differentiability of solutions
Differential games
Local comparative dynamics

ASJC Scopus subject areas

Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10957-023-02160-0

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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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Comparative dynamics in differential games: a note on the differentiability of solutions

Abstract

Keywords

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