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 "pricing in resource allocation games based on lagrangean duality and convexification"):
  Abstract: We consider a basic resource allocation game, where the players' strategy spaces are subsets of $R^m$ and cost/utility functions are parameterized by some common vector $u\in R^m$ and, otherwise, only depend on the own strategy choice. A strategy of a player can be interpreted as a vector of resource consumption and a joint strategy profile naturally leads to an aggregate consumption vector. Resources can be priced, that is, the game is augmented by a price vector $\lambda\in R^m_+$ and players have quasi-linear overall costs/utilities meaning that in addition to the original costs/utilities, a player needs to pay the corresponding price per consumed unit. We investigate the following question: for which aggregated consumption vectors $u$ can we find prices $\lambda$ that induce an equilibrium realizing the targeted consumption profile?  For answering this question, we revisit a well-known duality-based framework and derive several characterizations of the existence of such $u$ and $\lambda$ using convexification techniques. We show that for finite strategy spaces or certain concave games, the equilibrium existence problem reduces to solving a well-structured LP. We then consider a class of monotone aggregative games having the property that the cost/utility functions of players may depend on the induced load of a strategy profile. For this class, we show a sufficient condition of enforceability based on the previous characterizations. We demonstrate that this framework can help to unify parts of four largely independent streams in the literature: tolls in transportation systems, Walrasian market equilibria, trading networks and congestion control in communication networks.

Includes members:
  Member "nash and wardrop equilibria in aggregative games with coupling constraints":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient estimation of equilibria in large aggregative games with coupling constraints")
  Member "sensitivity analysis for convex separable optimization over integral polymatroids":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "equilibrium computation in resource allocation games")
  Member "totally unimodular congestion games":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "equilibrium computation in resource allocation games")
  Member "combinatorial walrasian equilibrium":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the power and limits of dynamic pricing in combinatorial markets")
  Member "polyhedral clinching auctions and the adwords polytope":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a simple mechanism for a budget constrained buyer")
  Member "optimal pricing in networks with externalities":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "selling a single item with negative externalities")
  Member "congestion games with variable demands":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sensitivity analysis for convex separable optimization over integral polymatroids")

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)