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 vickrey auction with a single duplicate bidder approximates the optimal revenue"):
  Abstract: Bulow and Klemperer's well-known result states that, in a single-item auction where the $n$ bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit $n$ duplicates, one from each distribution, and relaxing its revenue advantage to a $2$-approximation. #R##N#In this work we restore Bulow and Klemperer's number of duplicates in Hartline and Roughgarden's more general setting with a worse approximation ratio. We show that recruiting a duplicate from one of the distributions suffices for the Vickrey auction to $10$-approximate the optimal revenue. We also show that in a $k$-items unit demand auction, recruiting $k$ duplicates suffices for the VCG auction to $O(1)$-approximate the optimal revenue. #R##N#As another result, we tighten the analysis for Hartline and Roughgarden's Vickrey auction with $n$ duplicates for the case with two bidders in the auction. We show that in this case the Vickrey auction with two duplicates obtains at least $3/4$ of the optimal revenue. This is tight by meeting a lower bound by Hartline and Roughgarden. En route, we obtain a transparent analysis of their $2$-approximation for $n$~bidders, via a natural connection to Ronen's lookahead auction.

Includes members:
  Member "99 revenue via enhanced competition":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bulow klemperer style results for welfare maximization in two sided markets")
  Member "the competition complexity of auctions a bulow klemperer result for multi dimensional bidders":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bulow klemperer style results for welfare maximization in two sided markets")
  Member "randomization beats second price as a prior independent auction":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "benchmark design and prior independent optimization")
  Member "optimal auctions vs anonymous pricing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a permutation equivariant neural network architecture for auction design")
  Member "prior independent mechanisms for scheduling":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "an end to end argument in mechanism design prior independent auctions for budgeted agents")
  Member "vickrey auctions for irregular distributions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "bulow klemperer style results for welfare maximization in two sided markets")

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)