Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games
@inproceedings{Goldberg2021LowerBF, title={Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games}, author={Paul W. Goldberg and Matthew J. Katzman}, booktitle={SAGT}, year={2021} }
Nearly a decade ago, Azrieli and Shmaya introduced the class of λ-Lipschitz games in which every player’s payoff function is λ-Lipschitz with respect to the actions of the other players. They showed that such games admit -approximate pure Nash equilibria for certain settings of and λ. They left open, however, the question of how hard it is to find such an equilibrium. In this work, we develop a query-efficient reduction from more general games to Lipschitz games. We use this reduction to show a…
References
SHOWING 1-10 OF 20 REFERENCES
Logarithmic Query Complexity for Approximate Nash Computation in Large Games
- Economics, Computer ScienceTheory of Computing Systems
- 2018
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.
Bounds for the Query Complexity of Approximate Equilibria
- Computer Science, EconomicsACM Trans. Economics and Comput.
- 2013
The number of payoff queries needed to compute approximate equilibria of multi-player games is analyzed, and it is found that query complexity is an effective tool for distinguishing the computational difficulty of alternative solution concepts, and new techniques for upper- and lower bounding the query complexity are developed.
Settling the Complexity of Computing Approximate Two-Player Nash Equilibria
- Computer Science2016 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…
Lipschitz Continuity and Approximate Equilibria
- EconomicsAlgorithmica
- 2020
The key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in games with continuous action spaces and non-linear payoff functions.
Query Complexity of Approximate Equilibria in Anonymous Games
- Computer Science, EconomicsWINE
- 2015
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.
Lipschitz Continuity and Approximate Equilibria
- EconomicsSAGT
- 2016
This paper studies games with continuous action spaces and non-linear payoff functions, and shows that if the penalty function is Lipschitz continuous, then it can provide a quasi-polynomial time approximation scheme.
Query complexity of approximate equilibria in anonymous games
- Computer Science, EconomicsJ. Comput. Syst. Sci.
- 2017
Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games
- Computer ScienceITCS
- 2017
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.