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 "fictitious play convergence smoothness and optimism"):
  Abstract: We consider the dynamics of two-player zero-sum games, with the goal of understanding when such dynamics lead to equilibrium behavior at a fast rate. In particular, we study the dynamic known as \emph{fictitious play} (FP) in which each player simultaneously best-responds to the empirical distribution of the historical plays of their opponent. Nearly 70 years ago it was shown by Robinson that FP does converge to the Nash Equilibrium, although the rate she proved was exponential in the total number of actions of the players. In 1959, Karlin conjectured that FP converges at the more natural rate of $O(1/\epsilon^2)$. However, Daskalakis and Pan disproved a version of this conjecture in 2014, showing that an exponentially-slow rate can occur, although their result relied on adversarial tie-breaking. In this paper, we show that Karlin's conjecture is indeed correct in two major instances if you appropriately handle ties. First, we show that if the game matrix is diagonal and ties are broken lexicographically, then FP converges at a $O(1/\epsilon^2)$ rate, and we also show a matching lower bound under this tie-breaking assumption. Our second result shows that FP converges at a rate of $O(1/\epsilon^2)$ when the players' decision sets are smooth, and $\tilde{O}(1/\epsilon)$ under an additional assumption. In this last case, we also show that a modification of FP, known as Optimistic FP, converges at a rate of $O(1/\epsilon)$.

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 "finite regret and cycles with fixed step size via alternating gradient descent ascent":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "introduction to online convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "beyond ucb optimal and efficient contextual bandits with regression oracles")
  Member "multi agent learning in network zero sum games is a hamiltonian system":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the route to chaos in routing games when is price of anarchy too optimistic")
  Member "on the exponential rate of convergence of fictitious play in potential games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "smooth fictitious play in n times 2 potential games")
  Member "a counter example to karlin s strong conjecture for fictitious play":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "payoff performance of fictitious play":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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)