Bounds for the Query Complexity of Approximate Equilibria

@article{Goldberg2013BoundsFT,
  title={Bounds for the Query Complexity of Approximate Equilibria},
  author={Paul W. Goldberg and Aaron Roth},
  journal={ACM Transactions on Economics and Computation (TEAC)},
  year={2013},
  volume={4},
  pages={1 - 25}
}
  • P. Goldberg, Aaron Roth
  • Published 26 August 2016
  • Computer Science, Economics
  • ACM Transactions on Economics and Computation (TEAC)
We analyze the number of payoff queries needed to compute approximate equilibria of multi-player games. We find that query complexity is an effective tool for distinguishing the computational difficulty of alternative solution concepts, and we develop new techniques for upper- and lower bounding the query complexity. For binary-choice games, we show logarithmic upper and lower bounds on the query complexity of approximate correlated equilibrium. For well-supported approximate correlated… 
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Query Complexity of Approximate Equilibria in Anonymous Games
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It is proved that $$\varOmega n \log {n}$$ payoffs must be queried in order to find any $$epsilon $$-well-supported Nash equilibrium, even by randomized algorithms, which is the first one to obtain an inverse polynomial approximation in poly-time.
Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games
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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.
Finding Approximate Nash Equilibria of Bimatrix Games via Payoff Queries
TLDR
It is shown that randomized algorithms require Ω(k2) payoff queries in order to find an ϵ-Nash equilibrium with ϵ < 1/4k, even in zero-one constant-sum games, which rules out query-efficient randomized algorithms for finding exact Nash equilibria.
Logarithmic Query Complexity for Approximate Nash Computation in Large Games
TLDR
A randomised algorithm is presented that achieves ε approaching 18$\frac {1}{8}$ for 2-strategy games in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players’ payoffs/actions.
Finding approximate nash equilibria of bimatrix games via payoff queries
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It is shown that randomized algorithms require Omega(k2) payoff queries in order to find a 1/6k-Nash equilibrium, even in zero-one constant-sum games, which rules out query-efficient randomized algorithms for finding exact Nash equilibria.
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…
Simple Approximate Equilibria in Games with Many Players
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This work considers ε-equilibria notions for a constant value of ε in n-player m-action games and proves its equivalence to the well-known Beck-Fiala conjecture from discrepancy theory, the first result that introduces a connection between game theory and discrepancy theory.
Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games
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It is proved that, for some constant $\epsilon>0$, any randomized oracle algorithm that computes an $\epSilon$-ANE in a binary-action, $n$-player game must make $2^{\Omega(n/\log n)}$ payoff queries.
Smoothed Efficient Algorithms and Reductions for Network Coordination Games
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The approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case and defines a notion of smoothness-preserving reduction among search problems, which allows for the extension of smoothed efficient algorithms from one problem to another.
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best-response Queries
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Two algorithms for Constant-Dimension Generalised Binary Search provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies.
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It is proved that $$\varOmega n \log {n}$$ payoffs must be queried in order to find any $$epsilon $$-well-supported Nash equilibrium, even by randomized algorithms, which is the first one to obtain an inverse polynomial approximation in poly-time.
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