# Lipschitz Continuity and Approximate Equilibria

@inproceedings{Deligkas2016LipschitzCA, title={Lipschitz Continuity and Approximate Equilibria}, author={Argyrios Deligkas and John Fearnley and Paul G. Spirakis}, booktitle={SAGT}, year={2016} }

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…

## 11 Citations

Efficient algorithms for computing approximate equilibria in bimatrix, polymatrix and Lipschitz games

- Economics, Computer Science
- 2016

This thesis designs algorithms for computing approximate equilibria that beat the cur- rent best algorithms for these problems and constructs an approximation-preserving reduction from the problem of computing an approximate Bayesian Nash equilibrium (e-BNE) for a two-player Bayesian game to the problemof computing an e-NE of a polymatrix game and shows that the algorithm of Chapter 4 can be applied to two- player Bayesian games.

Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games

- Economics, MathematicsSAGT
- 2021

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.

Computing Equilibria in Atomic Splittable Polymatroid Congestion Games with Convex Costs

- EconomicsArXiv
- 2018

It is shown that there is a polynomial time transformation to atomic splittable polymatroid congestion games implying that one can compute $\epsilon$-approximate Cournot-Nash equilibria within pseudo-polynomial time.

G T ] 8 A ug 2 01 8 Equilibrium Computation in Resource Allocation Games

- Economics
- 2018

We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion…

Equilibrium Computation in Atomic Splittable Singleton Congestion Games

- Computer ScienceIPCO
- 2017

We devise the first polynomial time algorithm computing a pure Nash equilibrium for atomic splittable congestion games with singleton strategies and player-specific affine cost functions. Our…

Distance-based Equilibria in Normal-Form Games

- EconomicsAAAI
- 2020

We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of “possible profiles” that are within a certain…

Distance-Based Equilibria in Normal-Form Games

- Economics
- 2020

We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of “possible profiles” that are within a certain…

Approximating the Existential Theory of the Reals

- Mathematics, Computer ScienceWINE
- 2018

The main theorem is a sampling theorem, similar to those that have been proved for approximate equilibria in normal form games, that states that if an ETR problem has an exact solution, then it has a k-uniform approximate solution, where k depends on various properties of the formula.

Algorithms and complexity of problems arising from strategic settings

- Computer Science, Mathematics
- 2019

This thesis deals with an evolutionary setting where it is shown that for a wide range of symmetric bimatrix games, deciding ESS existence is intractable, and presents a general framework for constructing approximation schemes for problems that can be written as an Existential Theory of the Reals formula with variables constrained in a bounded convex set.

Uniqueness and computation of equilibria in resource allocation games

- Economics
- 2019

The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.

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