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

Author

Listed:
  • Chen Ling

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

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.

Suggested Citation

  • Chen Ling, 2022. "Comparative Dynamics and Envelope Theorems of Open-Loop Stackelberg Equilibria in Differential Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-25, December.
  • Handle: RePEc:wsi:igtrxx:v:24:y:2022:i:04:n:s0219198922500104
    DOI: 10.1142/S0219198922500104
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