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 "complexity and parametric computation of equilibria in atomic splittable congestion games via weighted block laplacians"):
  Abstract: We show that computing an equilibrium in atomic splittable congestion games with player-specific affine cost functions $l_{e,i}(x) = a_{e,i} x + b_{e,i}$ is $\mathsf{PPAD}$-complete. To prove that the problem is contained in $\mathsf{PPAD}$, we develop a homotopy method that traces an equilibrium for varying flow demands of the players. A key technique for this method is to describe the evolution of the equilibrium locally by a novel block Laplacian matrix. Using the properties of this matrix give rise to a path following formulation for computing an equilibrium where states correspond to supports that are feasible for some demands. A closer investigation of the block Laplacian system further allows to orient the states giving rise to unique predecessor and successor states thus putting the problem into $\mathsf{PPAD}$. For the $\mathsf{PPAD}$-hardness, we reduce from computing an approximate equilibrium of a bimatrix win-lose game. As a byproduct of our reduction we further show that computing a multi-class Wardrop equilibrium with class dependent affine cost functions is $\mathsf{PPAD}$-complete as well. #R##N#On our way, we obtain new results regarding the multiplicity of equilibria. When the coefficients $a_{e,i}$ are in general position, every game has a finite set of equilibria while without this assumption there may be a continuum of equilibria. When the additive constants $b_{e,i}$ are in general position, games have an odd number of equilibria except for a nullset of demand values. #R##N#As another byproduct of our $\mathsf{PPAD}$-completeness proof, we obtain an algorithm that computes a continuum of equilibria parametrized by the players' flow demand. For player-specific costs, the algorithm runs in polynomial space. For games with player-independent costs, we obtain an algorithm computing all equilibria as a function of the flow demand that runs in time polynomial in the output.

Includes members:
  Member "computing all wardrop equilibria parametrized by the flow demand":
    also connected through other hyperedges:
      (none)
  Member "uniqueness of equilibria in atomic splittable polymatroid congestion games":
    also connected through other hyperedges:
      (none)
  Member "computing solutions of the multiclass network equilibrium problem with affine cost functions":
    also connected through other hyperedges:
      (none)
  Member "constant rank bimatrix games are ppad hard":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "consenus halving does it ever get easier")
  Member "the complexity of the homotopy method equilibrium selection and lemke howson solutions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a generalized training approach for multiagent learning")
  Member "settling the complexity of computing two player nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "learning zero sum simultaneous move markov games using function approximation and correlated equilibrium")

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)