Distributed Stackelberg Equilibrium Seeking for Networked Multi-Leader Multi-Follower Games with A Clustered Information Structure
CoRR(2024)
摘要
The Stackelberg game depicts a leader-follower relationship wherein decisions
are made sequentially, and the Stackelberg equilibrium represents an expected
optimal solution when the leader can anticipate the rational response of the
follower. Motivated by control of network systems with two levels of
decision-making hierarchy, such as the management of energy networks and power
coordination at cellular networks, a networked multi-leaders and
multi-followers Stackelberg game is proposed. Due to the constraint of limited
information interaction among players, a clustered information structure is
assumed that each leader can only communicate with a portion of overall
followers, namely its subordinated followers, and also only with its local
neighboring leaders. In this case, the leaders cannot fully anticipate the
collective rational response of all followers with its local information. To
address Stackelberg equilibrium seeking under this partial information
structure, we propose a distributed seeking algorithm based on implicit
gradient estimation and network consensus mechanisms. We rigorously prove the
convergence of the algorithm for both diminishing and constant step sizes under
strict and strong monotonicity conditions, respectively. Furthermore, the model
and the algorithm can also incorporate linear equality and inequality
constraints into the followers' optimization problems, with the approach of the
interior point barrier function. Finally, we present numerical simulations in
applications to corroborate our claims on the proposed framework.
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