• Computer Science, Mathematics
  • Published in ArXiv 2019

On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games

@article{Mazumdar2019OnFL,
  title={On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games},
  author={Eric V. Mazumdar and Michael I. Jordan and S. Shankar Sastry},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.00838}
}
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differential structure of the game, we construct an algorithm for which the local Nash equilibria are the only attracting fixed points. We also show that the algorithm exhibits no… CONTINUE READING

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