Incentive Stackelberg Games for Stochastic Linear Systems With H_∞ Constraint.

Area of Science:

• Control Theory
• Game Theory
• Stochastic Systems

Background:

• Investigates Stackelberg games with one leader and multiple followers in stochastic linear systems.
• Addresses challenges posed by external disturbances in dynamic systems.
• Highlights limitations of existing ordinary Stackelberg games in achieving team-optimal and Nash equilibrium simultaneously.

Purpose of the Study:

• To develop an incentive Stackelberg strategy set for stochastic linear systems.
• To enable the leader to achieve a team-optimal solution and followers to reach a Nash equilibrium.
• To simultaneously attenuate external disturbances within the system.

Main Methods:

• Formulation of incentive Stackelberg games for stochastic linear systems.
• Design of a strategy set balancing leader's optimality and follower's equilibrium.
• Utilizes cross-coupled stochastic Riccati differential equations (finite-horizon) and algebraic Riccati equations (infinite-horizon).

Main Results:

• The incentive Stackelberg strategy set is derived by solving specific sets of cross-coupled stochastic Riccati equations.
• Demonstrates the ability to achieve leader's team-optimal solution and followers' Nash equilibrium.
• Shows effective attenuation of external disturbances in the stochastic system.

Conclusions:

• The proposed incentive Stackelberg strategy set is effective for stochastic linear systems with disturbances.
• Provides a method to solve complex game-theoretic problems in dynamic environments.
• Numerical examples validate the effectiveness of the developed strategy set.