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A dynamical neural network approach for solving stochastic two-player zero-sum games.

Dawen Wu1, Abdel Lisser1

  • 1Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, 3, rue Joliot Curie, 91190 Gif-sur-Yvette, France.

Neural Networks : the Official Journal of the International Neural Network Society
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Summary
This summary is machine-generated.

This study models a stochastic Nash game using a dynamical neural network (DNN). The DNN approach finds better optimal points and solves large-scale problems, outperforming traditional convex solvers.

Keywords:
Dynamical neural networkSaddle pointStochastic two-player zero-sum game

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Area of Science:

  • Game Theory
  • Machine Learning
  • Dynamical Systems

Background:

  • Stochastic two-player zero-sum Nash games present complex computational challenges.
  • Existing methods may struggle with convergence or large problem instances.

Purpose of the Study:

  • To introduce a novel dynamical neural network (DNN) model for solving stochastic Nash games.
  • To analyze the stability and equilibrium properties of the proposed DNN model.
  • To compare the DNN approach against state-of-the-art convex solvers.

Main Methods:

  • Formulating the Nash game as a dynamical neural network.
  • Analyzing the global asymptotic stability of the DNN equilibrium point.
  • Conducting numerical experiments comparing DNN with Splitting Conic Solver (SCS) and Cvxopt.

Main Results:

  • The saddle point of the game corresponds to the equilibrium of the DNN.
  • The DNN model demonstrates convergence to superior optimal points.
  • The DNN method successfully solves problems irrespective of their size, including large-scale instances.

Conclusions:

  • Dynamical neural networks offer a powerful alternative for solving stochastic Nash games.
  • The DNN approach provides enhanced accuracy and scalability compared to conventional solvers.