The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games

Alain Bensoussan · Shaokuan Chen · SURESH P. SETHI

144 citations0/0 files storedSIAM Journal on Control and Optimization

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Game Theory and Applications Stochastic processes and financial applications Guidance and Control Systems

Abstract

For stochastic Stackelberg differential games played by a leader and a follower, there are several solution concepts in terms of the players' information sets. In this paper we derive the maximum principle for the leader's global Stackelberg solution under the adapted closed-loop memoryless information structure, where the term global signifies the leader's domination over the entire game duration. As special cases, we study linear quadratic Stackelberg games under both adapted open-loop and adapted closed-loop memoryless information structures, as well as the resulting Riccati equations.

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References

1982Dynamic Noncooperative Game Theory 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2000Differential Games in Economics and Management Science 1998Arbitrage Theory in Continuous Time 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme 2007Forward-Backward Stochastic Differential Equations and their Applications 1999Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control

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2018ON A NEW PARADIGM OF OPTIMAL REINSURANCE: A STOCHASTIC STACKELBERG DIFFERENTIAL GAME BETWEEN AN INSURER AND A REINSURER 2015Leader–follower stochastic differential game with asymmetric information and applications 2019Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework 2021A hybrid stochastic differential reinsurance and investment game with bounded memory 2018A leader-follower stochastic linear quadratic differential game with time delay

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