human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "distributed resource allocation through utility design part i optimizing the performance certificates via the price of anarchy"):
  Abstract: Game theory has emerged as a novel approach for the coordination of multiagent systems. A fundamental component of this approach is the design of a local utility function for each agent so that their selfish maximization achieves the global objective. In this paper we propose a novel framework to characterize and optimize the worst case performance (price of anarchy) of any resulting equilibrium as a function of the chosen utilities, thus providing a performance certificate for a large class of algorithms. More specifically, we consider a class of resource allocation problems, where each agent selects a subset of the resources with the goal of maximizing a welfare function. First, we show that any smoothness argument is inconclusive for the design problems considered. Motivated by this, we introduce a new approach providing a tight expression for the price of anarchy (PoA) as a function of the chosen utility functions. Leveraging this result, we show how to design the utilities so as to maximize the PoA through a tractable linear program. In Part II we specialize the results to submodular and supermodular welfare functions, discuss complexity issues and provide two applications.

Includes members:
  Member "nash and wardrop equilibria in aggregative games with coupling constraints":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "pricing in resource allocation games based on lagrangean duality and convexification")
  Member "game efficiency through linear programming duality":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "utility design for distributed resource allocation part i characterizing and optimizing the exact price of anarchy")
  Member "multiagent maximum coverage problems the trade off between anarchy and stability":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "when smoothness is not enough toward exact quantification and optimization of the price of anarchy")
  Member "the price of anarchy in auctions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "a unifying tool for bounding the quality of non cooperative solutions in weighted congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "optimal mechanisms for distributed resource allocation")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.GT(Computer Science and Game Theory)