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 "capacitated caching games"):
  Abstract: Capacitated Caching (CC) Games are motivated by P2P and web caching applications, and involve nodes on a network making strategic choices regarding the content to replicate in their caches. Caching games were introduced by Chun et al [6], who analyzed the uncapacitated case leaving the capacitated version as an open direction. In this work, we study pure Nash equilibria of both fractional (FCC) and integral (ICC) versions of CC games. Using erasure codes we present a compelling realization of FCC games in content distribution. We show that every FCC game instance possesses an equilibrium. We also show, however, that finding an equilibrium in an FCC game is PPAD-complete. For ICC games we delineate the boundary between intractability and effective computability in terms of the network structure, object preferences, and the total number of objects. A central result of this paper is the existence (and poly-time computability) of equilibria for hierarchical networks. Using a potential function argument, we also show the existence of equilibria for general symmetric networks when object preferences are binary. For general ICC games, however, equilibria may not exist. In fact, we show that it is NP-hard to determine whether equilibria exist, even when either the network is symmetric and there are only three objects in the system, or the network is arbitrary and there are only two objects in the system. Finally, we show that the existence of equilibria in strongly connected networks with two objects and binary object preferences can be determined in polynomial time, via a reduction to the even-cycle problem. A significant feature of our work is the development of the above results in a general framework of natural preference orders, orders that are entirely arbitrary except for two benign constraints - “Nearer is better” and “Irrelevance of alternatives”. A novel aspect of our framework is that the results apply even to the situation where different nodes have utility functions of completely different functional forms (e.g. one node’s utility could depend on the sum of distances to the objects of interest whereas another’s could depend on the maximum distance).

Includes members:
  Member "optimal data placement on networks with a constant number of clients":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "cache me if you can capacitated selfish replication games in networks")
  Member "reducibility among fractional stability problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the classes ppa k existence from arguments modulo k")
  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)