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 "from darwin to poincar e and von neumann recurrence and cycles in evolutionary and algorithmic game theory"):
  Abstract: Replicator dynamics, the continuous-time analogue of Multiplicative Weights Updates, is the main dynamic in evolutionary game theory. In simple evolutionary zero-sum games, such as Rock-Paper-Scissors, replicator dynamic is periodic \cite{zeeman1980population}, however, its behavior in higher dimensions is not well understood. We provide a complete characterization of its behavior in zero-sum evolutionary games. We prove that, if and only if, the system has an interior Nash equilibrium, the dynamics exhibit Poincare recurrence, i.e., almost all orbits come arbitrary close to their initial conditions infinitely often. If no interior equilibria exist, then all interior initial conditions converge to the boundary. Specifically, the strategies that are not in the support of any equilibrium vanish in the limit of all orbits. All recurrence results furthermore extend to a class of games that generalize both graphical polymatrix games as well as evolutionary games, establishing a unifying link between evolutionary and algorithmic game theory. We show that two degrees of freedom, as in Rock-Paper-Scissors, is sufficient to prove periodicity.

Includes members:
  Member "fast and furious learning in zero sum games vanishing regret with non vanishing step sizes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the route to chaos in routing games when is price of anarchy too optimistic")
  Member "alpha rank multi agent evaluation by evolution":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "neural replicator dynamics")
  Member "vortices instead of equilibria in minmax optimization chaos and butterfly effects of online learning in zero sum games":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "combining no regret and q learning")
  Member "finite regret and cycles with fixed step size via alternating gradient descent ascent":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "multi agent learning in network zero sum games is a hamiltonian system":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the route to chaos in routing games when is price of anarchy too optimistic")
  Member "learning dynamics and the co evolution of competing sexual species":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the route to chaos in routing games when is price of anarchy too optimistic")
  Member "cycles in adversarial regularized learning":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "from poincar e recurrence to convergence in imperfect information games finding equilibrium via regularization")
  Member "average case performance of replicator dynamics in potential games via computing regions of attraction":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "proportional dynamics in exchange economies")

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)