A Unified Strategy for Solution Seeking in Graphical $N$-Coalition Noncooperative Games

摘要

This paper aims to reduce the communication and computation costs of the Nashequilibrium seeking strategy for the $N$-coalition non-cooperative gamesproposed in [YEAT]. The objective is achieved in two manners: 1). the Nashequilibrium seeking strategy is re-designed and a new Nash equilibrium seekingalgorithm that yields less communication and computation costs, is proposed.2). an interference graph is introduced to describe the interactions among theagents in each coalition. The newly proposed seeking strategy is then adaptedfor the $N$-coalition non-cooperative games on the interference graph. Asufficient condition on the interference and communication graphs is providedto ensure that the players' actions converge to the Nash equilibrium byutilizing the proposed seeking strategy. Several special cases where there isonly one coalition and/or there are coalitions with only one agent areconsidered. The results for the special cases demonstrate that the proposedseeking strategy achieves the solution seeking for non-cooperative games,social cost minimization problems and single-agent optimization problems in aunified framework. Numerical examples are presented to support the analyticalresults.