Lipschitz Continuity and Approximate Equilibria

@article{Deligkas2020LipschitzCA,
  title={Lipschitz Continuity and Approximate Equilibria},
  author={Argyrios Deligkas and John Fearnley and Paul G. Spirakis},
  journal={Algorithmica},
  year={2020},
  pages={1-28}
}
In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these games. We begin by studying Lipschitz games, which encompass, for example, all concave games with Lipschitz continuous payoff functions. We provide an efficient algorithm for computing approximate equilibria in these games. Then we turn our attention to penalty… 
1 Citations
Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games
TLDR
This work develops a query-efficient reduction from more general games to Lipschitz games, and provides an exponential lower bound on the deterministic query complexity of finding -approximate correlated equilibria of n-player, m-action, λ-Lipschitzer games for strong values of , motivating the consideration of explicitly randomized algorithms in the above results.

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