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 "existence and complexity of approximate equilibria in weighted congestion games"):
  Abstract: We study the existence of approximate pure Nash equilibria ($\alpha$-PNE) in weighted atomic congestion games with polynomial cost functions of maximum degree $d$. Previously it was known that $d$-approximate equilibria always exist, while nonexistence was established only for small constants, namely for $1.153$-PNE. We improve significantly upon this gap, proving that such games in general do not have $\tilde{\Theta}(\sqrt{d})$-approximate PNE, which provides the first super-constant lower bound. #R##N#Furthermore, we provide a black-box gap-introducing method of combining such nonexistence results with a specific circuit gadget, in order to derive NP-completeness of the decision version of the problem. In particular, deploying this technique we are able to show that deciding whether a weighted congestion game has an $\tilde{O}(\sqrt{d})$-PNE is NP-complete. Previous hardness results were known only for the special case of exact equilibria and arbitrary cost functions. #R##N#The circuit gadget is of independent interest and it allows us to also prove hardness for a variety of problems related to the complexity of PNE in congestion games. For example, we demonstrate that the question of existence of $\alpha$-PNE in which a certain set of players plays a specific strategy profile is NP-hard for any $\alpha < 3^{d/2}$, even for unweighted congestion games. #R##N#Finally, we study the existence of approximate equilibria in weighted congestion games with general (nondecreasing) costs, as a function of the number of players $n$. We show that $n$-PNE always exist, matched by an almost tight nonexistence bound of $\tilde\Theta(n)$ which we can again transform into an NP-completeness proof for the decision problem.

Includes members:
  Member "on approximate pure nash equilibria in weighted congestion games with polynomial latencies":
    also connected through other hyperedges:
      (none)
  Member "an improved algorithm for computing approximate equilibria in weighted congestion games":
    also connected through other hyperedges:
      (none)
  Member "the price of stability of weighted congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on approximate pure nash equilibria in weighted congestion games with polynomial latencies")
  Member "computing approximate pure nash equilibria in shapley value weighted congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on approximate pure nash equilibria in weighted congestion games with polynomial latencies")
  Member "efficient computation of approximate pure nash equilibria in congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the efficiency of best response dynamics")
  Member "approximate pure nash equilibria in weighted congestion games existence efficient computation and structure":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on approximate pure nash equilibria in weighted congestion games with polynomial latencies")
  Member "on the performance of approximate equilibria in congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the price of satisficing in network user equilibria")

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)