Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications

Tianyang Nie (), Falei Wang and Zhiyong Yu ()
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Tianyang Nie: Shandong University
Falei Wang: Shandong University
Zhiyong Yu: Shandong University

Dynamic Games and Applications, 2022, vol. 12, issue 2, No 10, 608-631

Abstract: Abstract We study a general kind of partial information nonzero sum two-player stochastic differential games, where the state variable is governed by a stochastic differential equation and the control domain of each player can be non-convex. Moreover, the control variables of both players can enter the diffusion coefficients of the state equation. We establish Pontryagin’s maximum principle for open-loop Nash equilibria of the game. Then, a verification theorem is obtained for Nash equilibria when the control domain is convex. Finally, the theoretical results are applied to studying a linear-quadratic game.

Keywords: Maximum principle; Nonzero sum stochastic differential game; Variational inequality; Backward stochastic differential equation; Partial information; 60H10; 60H30; 91A10; 91A23; 91A25; 93E20 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13235-021-00402-2

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