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<p>This paper addresses the finite horizon Stackelberg game involving a backward stochastic system of mean-field type under partial information. The necessary and sufficient optimality conditions for the follower and the leader are first established for the nonlinear problem using the stochastic maximum principles of mean-field backward stochastic differential equations and mean-field forward-backward stochastic differential equations, respectively. In this context, the leader’s information is a sub-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> </InlineEquation>-algebra of the follower’s information. Next, a linear quadratic Stackelberg game involving a mean-field backward stochastic differential equation is examined. For the linear case, we first solve the optimal control problem for the follower and obtain the state feedback representation of the follower’s optimal control using four Riccati equations. Subsequently, utilizing the optimal control obtained for the follower, we proceed to solve the problem for the leader. Through the utilization of the stochastic maximum principle and stochastic filtering technique, we derive four Riccati equations along with the filtering equation of state for the leader’s optimal control problem. Finally, the Stackelberg equilibrium in feedback form is achieved.</p>

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A Stackelberg Game for Mean-Field Backward Stochastic System Under Partial Information

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • G. Saranya,
  • P. Muthukumar

摘要

This paper addresses the finite horizon Stackelberg game involving a backward stochastic system of mean-field type under partial information. The necessary and sufficient optimality conditions for the follower and the leader are first established for the nonlinear problem using the stochastic maximum principles of mean-field backward stochastic differential equations and mean-field forward-backward stochastic differential equations, respectively. In this context, the leader’s information is a sub- \(\sigma \) -algebra of the follower’s information. Next, a linear quadratic Stackelberg game involving a mean-field backward stochastic differential equation is examined. For the linear case, we first solve the optimal control problem for the follower and obtain the state feedback representation of the follower’s optimal control using four Riccati equations. Subsequently, utilizing the optimal control obtained for the follower, we proceed to solve the problem for the leader. Through the utilization of the stochastic maximum principle and stochastic filtering technique, we derive four Riccati equations along with the filtering equation of state for the leader’s optimal control problem. Finally, the Stackelberg equilibrium in feedback form is achieved.