From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory

@article{Papadimitriou2018FromNE,
  title={From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory},
  author={Christos H. Papadimitriou and Georgios Piliouras},
  journal={Entropy},
  year={2018},
  volume={20}
}
In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of… 

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