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 "the route to chaos in routing games population increase drives period doubling instability chaos inefficiency with price of anarchy equal to one"):
  Abstract: We study a learning dynamic model of routing (congestion) games to explore how an increase in the total demand influences system performance. We focus on non-atomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative Weights Updates with a fixed learning rate. Previous game-theoretic equilibrium analysis suggests that system performance is close to optimal in the large population limit, as seen by the Price of Anarchy reduction. In this work, however, we reveal a rather undesirable consequence of non-equilibrium phenomena driven by population increase. As the total demand rises, we prove that the learning dynamics unavoidably become non-equilibrating, typically chaotic. The Price of Anarchy predictions of near-optimal performance no longer apply. To the contrary, the time-average social cost may converge to its worst possible value in the large population limit. Every system has a carrying capacity, above which the dynamics is non-equilibrating. If the equilibrium flow is a symmetric $50-50\%$ split, the system exhibits one period-doubling bifurcation. A single periodic attractor of period two replaces the attracting fixed point when the demand exceeds the carrying capacity. In general, for asymmetric equilibrium flows, increasing the demand destabilizes the system, so that the system eventually becomes Li-Yorke chaotic with positive topological entropy. This demand-driven instability emerges from any pair of linear cost functions. Remarkably, in any non-equilibrating regime, the time-average flows on the edges converge {\it exactly} to the equilibrium flows, a property akin to no-regret learning in zero-sum games. Our results extend to any sequence of shrinking learning rates, e.g., $1/\sqrt{T}$, by allowing for a dynamically increasing population size.

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 "cooperation speeds surfing use co bandit":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "periodic bandits and wireless network selection")
  Member "cycles in adversarial regularized learning":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "from poincar e recurrence to convergence in imperfect information games finding equilibrium via regularization")
  Member "multiplicative weights update with constant step size in congestion games convergence limit cycles and chaos":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "learning in games robustness of fast convergence":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "bandits with adversarial scaling")
  Member "on the price of anarchy of highly congested nonatomic network games":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the route to chaos in routing games when is price of anarchy too optimistic")

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)