Journal ArticleDOI
The speed of convergence in congestion games under best-response dynamics
TLDR
It is shown that Θ(n log log n) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and nonnull) number of best responses.Abstract:
We investigate the speed of convergence of best response dynamics to approximately optimal solutions in congestion games with linear delay functions. In Ackermann et al. [2008] it has been shown that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players n. Motivated by such a negative result, we focus on the study of the states (not necessarily being equilibria) reached after a limited number of players' selfish moves, and we show that Θ(n log log n) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and nonnull) number of best responses. We show that such result is tight also for the simplest case of singleton congestion games.read more
Citations
More filters
Journal Article
Convergence and approximation in potential games
TL;DR: In this article, the authors study the speed of convergence to approximately optimal states in two classes of potential games and provide bounds in terms of the number of rounds, where a round consists of a sequence of movements, with each player appearing at least once in each round.
Proceedings ArticleDOI
Efficient coordination mechanisms for unrelated machine scheduling
TL;DR: Three new coordination mechanisms for scheduling n selfish jobs on m unrelated machines are presented, one of which is the first that handles anonymous jobs and simultaneously guarantees that the induced game is a potential game and has bounded price of anarchy.
Posted Content
Efficient computation of approximate pure Nash equilibria in congestion games
TL;DR: This work presents a surprisingly simple polynomial-time algorithm that computes $O(1)$-approximate Nash equilibria in non-symmetric congestion games and proves that, for congestion games that deviate from the mild assumptions, computing $\rho$- Approximate Equilibria is {\sf PLS}-complete for any polynomially-time computable $rho$.
Journal ArticleDOI
Circumventing the Price of Anarchy: Leading Dynamics to Good Behavior
TL;DR: In this article, a theory of how well-motivated multiagent dynamics can make use of global information about the game, which might be common knowledge or injected into the system by a helpful central agency, is initiated.
Proceedings ArticleDOI
Concurrent imitation dynamics in congestion games
TL;DR: This paper proposes to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents' strategy if the anticipated latency gain is sufficiently large, and shows rapid convergence to approximate equilibria.
References
More filters
Journal ArticleDOI
Equilibrium points in n-person games
TL;DR: A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
Journal ArticleDOI
REGULAR ARTICLEPotential Games
Dov Monderer,Lloyd S. Shapley +1 more
TL;DR: In this paper, the authors define and discuss several notions of potential functions for games in strategic form, and characterize games that have a potential function, and present a variety of applications.
Journal ArticleDOI
A class of games possessing pure-strategy Nash equilibria
TL;DR: In this paper, a class of noncooperative games (of interest in certain applications) is described and each game in the class is shown to possess at least one Nash equilibrium in pure strategies.
Book ChapterDOI
Worst-case equilibria
TL;DR: In this paper, the authors propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system and derive upper and lower bounds for this ratio in a model in which several agents share a very simple network.
Journal ArticleDOI
How easy is local search
TL;DR: A natural class PLS is defined consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and it is shown that there are complete problems for this class.