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 "designing networks with good equilibria under uncertainty"):
  Abstract: We consider the problem of designing network cost-sharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree. We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model). #R##N#In the adversarial model, the designer's goal is to choose a single, universal protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design? We first demonstrate that there exist graphs (outerplanar) where knowledge of the underlying metric can dramatically improve the performance of good network design. Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of $\Omega(\log k)$, which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes. #R##N#Then we switch to the stochastic model, where each player is independently activated. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol with constant PoA.

Includes members:
  Member "online network design algorithms via hierarchical decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the power of recourse better algorithms for facility location in online and dynamic models")
  Member "potential games are necessary to ensure pure nash equilibria in cost sharing games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "cost sharing games for energy efficient multi hop broadcast in wireless networks")
  Member "improving the price of anarchy for selfish routing via coordination mechanisms":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "when does diversity of user preferences improve outcomes in selfish routing")
  Member "efficient coordination mechanisms for unrelated machine scheduling":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the price of anarchy of cost sharing in real time scheduling systems")
  Member "inner product spaces for minsum coordination mechanisms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximating generalized network design under dis economies of scale with applications to energy efficiency")
  Member "an o lognloglogn upper bound on the price of stability for undirected shapley network design games":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficient black box reductions for separable cost sharing")

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)