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 "on computability of equilibria in markets with production"):
  Abstract: Although production is an integral part of the Arrow-Debreu market model, most of the work in theoretical computer science has so far concentrated on markets without production, i.e., the exchange economy. This paper takes a significant step towards understanding computational aspects of markets with production. #R##N#We first define the notion of separable, piecewise-linear concave (SPLC) production by analogy with SPLC utility functions. We then obtain a linear complementarity problem (LCP) formulation that captures exactly the set of equilibria for Arrow-Debreu markets with SPLC utilities and SPLC production, and we give a complementary pivot algorithm for finding an equilibrium. This settles a question asked by Eaves in 1975 of extending his complementary pivot algorithm to markets with production. #R##N#Since this is a path-following algorithm, we obtain a proof of membership of this problem in PPAD, using Todd, 1976. We also obtain an elementary proof of existence of equilibrium (i.e., without using a fixed point theorem), rationality, and oddness of the number of equilibria. We further give a proof of PPAD-hardness for this problem and also for its restriction to markets with linear utilities and SPLC production. Experiments show that our algorithm runs fast on randomly chosen examples, and unlike previous approaches, it does not suffer from issues of numerical instability. Additionally, it is strongly polynomial when the number of goods or the number of agents and firms is constant. This extends the result of Devanur and Kannan (2008) to markets with production. #R##N#Finally, we show that an LCP-based approach cannot be extended to PLC (non-separable) production, by constructing an example which has only irrational equilibria.

Includes members:
  Member "the complexity of non monotone markets":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "consenus halving does it ever get easier")
  Member "a combinatorial polynomial algorithm for the linear arrow debreu market":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "proportional dynamics in exchange economies")
  Member "concave generalized flows with applications to market equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "algorithms for competitive division of chores")
  Member "settling the complexity of arrow debreu equilibria in markets with additively separable utilities":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the complexity of interactively learning a stable matching by trial and error")
  Member "spending is not easier than trading on the computational equivalence of fisher and arrow debreu equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "dynamics of distributed updating in fisher 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)