Comparative Dynamics and Envelope Theorems of Open-Loop Stackelberg Equilibria in Differential Games

Chen Ling ()
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Chen Ling: School of Public Finance and Taxation, Zhejiang University of Finance and Economics, 18 Xueyuan Street, Hangzhou, Zhejiang 310018, P. R. China

International Game Theory Review (IGTR), 2022, vol. 24, issue 04, 1-25

Abstract: A direct proof of the envelope theorems and intrinsic comparative dynamics of locally differentiable open-loop Stackelberg equilibria (OLSE) is given using an extended primal-dual method. It is shown that the follower’s envelope and comparative dynamics results agree in form with those of any player in an open-loop Nash equilibrium, while those of the leader differ. This difference allows, in principle, an empirical test of the leader–follower role in a differential game. Separability conditions are identified on the instantaneous payoff and transition functions under which, for certain parameters, the intrinsic comparative dynamics of the leader’s time-inconsistent OSLE and those in the corresponding optimal control problem are qualitatively identical. However, similar conditions do not exist for time-consistent OSLE.

Keywords: Comparative dynamics; open-loop Stackelberg equilibria; differential games (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0219198922500104

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