Lipschitz Continuity and Approximate Equilibria

  title={Lipschitz Continuity and Approximate Equilibria},
  author={Argyrios Deligkas and John Fearnley and Paul G. Spirakis},
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
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.


An Optimization Approach for Approximate Nash Equilibria
An efficient algorithm is provided that computes 0.3393-approximate Nash equilibria, the best approximation to date, based on the formulation of an appropriate function of pairs of mixed strategies reflecting the maximum deviation of the players' payoffs from the best payoff each player could achieve given the strategy chosen by the other.
Playing large games using simple strategies
The existence of ε-Nash equilibrium strategies with support logarithmic in the number of pure strategies is proved and it is proved that if the payoff matrices of a two person game have low rank then the game has an exact Nash equilibrium with small support.
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This paper provides the first polynomial time algorithms constructing ε-SuppNE for normalized or win lose bimatrix games, for any nontrivial constant 0≤ε<1, bounded away from 1.
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It is proved that in every normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium in which each player randomizes uniformly among a set of O(log m + log n) pure actions, and an inverse connection between the entropy of Nash equilibria in the game, and the time it takes to find such an approximation using the random sampling method is established.
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A new, distributed method to compute approximate Nash equilibria in bimatrix games that first solves two independent LPs, each of which is derived from one of the two payoff matrices, and then computes an approximate Nash equilibrium using only limited communication between the players.
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Settling the Complexity of Computing Approximate Two-Player Nash Equilibria
  • A. Rubinstein
  • Computer Science
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2016
We prove that there exists a constant ε > 0 such that, assuming the Exponential Time Hypothesis for PPAD, computing an ε-approximate Nash equilibrium in a two-player (n × n) game requires