157. STACKELBERG EQUILIBRIUM SEEKING IN NONCOOPERATIVE GAMES

Department: Mechanical & Aerospace Engineering
Research Institute Affiliation: Center for Control Systems and Dynamics (CCSD)
Faculty Advisor(s): Miroslav Krstic

Primary Student
Name: Paul A Frihauf
Email: pfrihauf@ucsd.edu
Phone: 858-534-5670
Grad Year: 2012

Abstract
We introduce a non-model based learning approach to stably attain the equilibrium solution in Stackelberg noncooperative games. Stackelberg games have a hierarchical structure where a leader enforces its strategy on the other players, known as followers, who react rationally to the leader's action. The leader maximizes its payoff function by choosing its action with the expectation of the followers' rational response. The proposed strategy is based on the extremum seeking method, which employs sinusoidal perturbations to estimate the gradient of an unknown payoff function, and extends our earlier results in Nash equilibrium seeking. For a two-player Stackelberg game, we assume that the leader knows its payoff function and can observe the follower's action, but not its payoff function. The follower can only measure its payoff value and has no knowledge of the leader's action or payoff function. Hence, to maximize their respective payoffs, the leader employs a learning strategy to estimate the follower's response based on its observed action, and the follower utilizes a Nash seeking strategy. By predicting the follower's response, the leader is able to improve upon its Nash equilibrium value. We consider games with quadratic payoff functions and prove convergence to a neighborhood of the the Stackelberg equilibrium.

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