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 "the price of stability of weighted congestion games"):
  Abstract: We give exponential lower bounds on the Price of Stability (PoS) of weighted congestion games with polynomial cost functions. In particular, for any positive integer $d$ we construct rather simple games with cost functions of degree at most $d$ which have a PoS of at least $\varOmega(\Phi_d)^{d+1}$, where $\Phi_d\sim d/\ln d$ is the unique positive root of equation $x^{d+1}=(x+1)^d$. This asymptotically closes the huge gap between $\varTheta(d)$ and $\Phi_d^{d+1}$ and matches the Price of Anarchy upper bound. We further show that the PoS remains exponential even for singleton games. More generally, we also provide a lower bound of $\varOmega((1+1/\alpha)^d/d)$ on the PoS of $\alpha$-approximate Nash equilibria. All our lower bounds extend to network congestion games, and hold for mixed and correlated equilibria as well. #R##N#On the positive side, we give a general upper bound on the PoS of approximate Nash equilibria, which is sensitive to the range $W$ of the player weights. We do this by explicitly constructing a novel approximate potential function, based on Faulhaber's formula, that generalizes Rosenthal's potential in a continuous, analytic way. From the general theorem, we deduce two interesting corollaries. First, we derive the existence of an approximate pure Nash equilibrium with PoS at most $(d+3)/2$; the equilibrium's approximation parameter ranges from $\varTheta(1)$ to $d+1$ in a smooth way with respect to $W$. Secondly, we show that for unweighted congestion games, the PoS of $\alpha$-approximate Nash equilibria is at most $(d+1)/\alpha$.

Includes members:
  Member "computing approximate pure nash equilibria in shapley value weighted congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "existence and complexity of approximate equilibria in weighted congestion games")
  Member "efficient computation of approximate pure nash equilibria in congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "existence and complexity of approximate equilibria in weighted congestion games")
  Member "approximate pure nash equilibria in weighted congestion games existence efficient computation and structure":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "existence and complexity of approximate equilibria in weighted congestion games")
  Member "a unifying tool for bounding the quality of non cooperative solutions in weighted congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "optimal mechanisms for distributed resource allocation")
  Member "on the performance of approximate equilibria in congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "existence and complexity of approximate equilibria in weighted congestion games")

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)