249 research outputs found
On the Impact of Singleton Strategies in Congestion Games
To what extent does the structure of the players\u27 strategy space influence the efficiency of decentralized solutions in congestion games? In this work, we investigate whether better performance is possible when restricting to load balancing games in which players can only choose among single resources. We consider three different solutions concepts, namely, approximate pure Nash equilibria, approximate one-round walks generated by selfish players aiming at minimizing their personal cost and approximate one-round walks generated by cooperative players aiming at minimizing the marginal increase in the sum of the players\u27 personal costs. The last two concepts can also be interpreted as solutions of simple greedy online algorithms for the related resource selection problem. Under fairly general latency functions on the resources, we show that, for all three types of solutions, better bounds cannot be achieved if players are either weighted or asymmetric. On the positive side, we prove that, under mild assumptions on the latency functions, improvements on the performance of approximate pure Nash equilibria are possible for load balancing games with weighted and symmetric players in the case of identical resources. We also design lower bounds on the performance of one-round walks in load balancing games with unweighted players and identical resources (in this case, solutions generated by selfish and cooperative players coincide)
Computing Approximate Equilibria in Weighted Congestion Games via Best-Responses
We present a deterministic polynomial-time algorithm for computing
-approximate (pure) Nash equilibria in weighted congestion games
with polynomial cost functions of degree at most . This is an exponential
improvement of the approximation factor with respect to the previously best
deterministic algorithm. An appealing additional feature of our algorithm is
that it uses only best-improvement steps in the actual game, as opposed to
earlier approaches that first had to transform the game itself. Our algorithm
is an adaptation of the seminal algorithm by Caragiannis et al. [FOCS'11, TEAC
2015], but we utilize an approximate potential function directly on the
original game instead of an exact one on a modified game.
A critical component of our analysis, which is of independent interest, is
the derivation of a novel bound of for the
Price of Anarchy (PoA) of -approximate equilibria in weighted congestion
games, where is the Lambert-W function. More specifically, we
show that this PoA is exactly equal to , where
is the unique positive solution of the equation . Our upper bound is derived via a smoothness-like argument,
and thus holds even for mixed Nash and correlated equilibria, while our lower
bound is simple enough to apply even to singleton congestion games
Exact Price of Anarchy for Weighted Congestion Games with Two Players
This paper gives a complete analysis of worst-case equilibria for various
versions of weighted congestion games with two players and affine cost
functions. The results are exact price of anarchy bounds which are parametric
in the weights of the two players, and establish exactly how the primitives of
the game enter into the quality of equilibria. Interestingly, some of the
worst-cases are attained when the players' weights only differ slightly. Our
findings also show that sequential play improves the price of anarchy in all
cases, however, this effect vanishes with an increasing difference in the
players' weights. Methodologically, we obtain exact price of anarchy bounds by
a duality based proof mechanism, based on a compact linear programming
formulation that computes worst-case instances. This mechanism yields
duality-based optimality certificates which can eventually be turned into
purely algebraic proofs.Comment: 17 pages, 9 figures, 4 table
On Linear Congestion Games with Altruistic Social Context
We study the issues of existence and inefficiency of pure Nash equilibria in
linear congestion games with altruistic social context, in the spirit of the
model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a
framework, given a real matrix specifying a particular
social context, each player aims at optimizing a linear combination of the
payoffs of all the players in the game, where, for each player , the
multiplicative coefficient is given by the value . We give a broad
characterization of the social contexts for which pure Nash equilibria are
always guaranteed to exist and provide tight or almost tight bounds on their
prices of anarchy and stability. In some of the considered cases, our
achievements either improve or extend results previously known in the
literature
Uniform Mixed Equilibria in Network Congestion Games with Link Failures
Motivated by possible applications in fault-tolerant routing, we introduce the notion of uniform mixed equilibria in network congestion games with adversarial link failures, where players need to route traffic from a source to a destination node. Given an integer rho >= 1, a rho-uniform mixed strategy is a mixed strategy in which a player plays exactly rho edge disjoint paths with uniform probabilities, so that a rho-uniform mixed equilibrium is a tuple of rho-uniform mixed strategies, one for each player, in which no player can lower her cost by deviating to another rho-uniform mixed strategy. For games with weighted players and affine latency functions, we show existence of rho-uniform mixed equilibria and provide a tight characterization of their price of anarchy. For games with unweighted players, instead, we extend the existential guarantee to any class of latency functions and, restricted to games with affine latencies, we derive a tight characterization of both the prices of anarchy and stability
Non-Atomic One-Round Walks in Polynomial Congestion Games
Abstract. In this paper we study the approximation ratio of the solutions achieved after an -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions onl
Project Games
International audienceWe consider a strategic game called project game where each agent has to choose a project among his own list of available projects. The model includes positive weights expressing the capacity of a given agent to contribute to a given project The realization of a project produces some reward that has to be allocated to the agents. The reward of a realized project is fully allocated to its contributors, according to a simple proportional rule. Existence and computational complexity of pure Nash equilibria is addressed and their efficiency is investigated according to both the utilitarian and the egalitarian social function
Congestion Games with Multisets of Resources and Applications in Synthesis
In classical congestion games, players\u27 strategies are subsets of resources. We introduce and study multiset congestion games, where players\u27 strategies are multisets of resources. Thus, in each strategy a player may need to use each resource a different number of times, and his cost for using the resource depends on the load that he and the other players generate on the resource.
Beyond the theoretical interest in examining the effect of a repeated use of resources, our study enables better understanding of non-cooperative systems and environments whose behavior is not covered by previously studied models. Indeed, congestion games with multiset-strategies arise, for example, in production planing
and network formation with tasks that are more involved than reachability. We study in detail the application of synthesis from component libraries: different users synthesize systems by gluing together components from a component library. A component may be used in several systems and may be used several times in a system. The performance of a component and hence the system\u27s quality depends on the load on it.
Our results reveal how the richer setting of multisets congestion games affects the stability and equilibrium efficiency compared to standard congestion games. In particular, while we present very simple instances with no pure Nash equilibrium and prove tighter and simpler lower bounds for equilibrium inefficiency, we are also able to show that some of the positive results known for affine and weighted congestion games apply to the richer setting of multisets
Improving Approximate Pure Nash Equilibria in Congestion Games
Congestion games constitute an important class of games to model resource
allocation by different users. As computing an exact or even an approximate
pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011)
present a polynomial-time algorithm that computes a ()-approximate pure Nash equilibria for games with linear cost
functions and further results for polynomial cost functions. We show that this
factor can be improved to and further improved results for
polynomial cost functions, by a seemingly simple modification to their
algorithm by allowing for the cost functions used during the best response
dynamics be different from the overall objective function. Interestingly, our
modification to the algorithm also extends to efficiently computing improved
approximate pure Nash equilibria in games with arbitrary non-decreasing
resource cost functions. Additionally, our analysis exhibits an interesting
method to optimally compute universal load dependent taxes and using linear
programming duality prove tight bounds on PoA under universal taxation, e.g,
2.012 for linear congestion games and further results for polynomial cost
functions. Although our approach yield weaker results than that in Bil\`{o} and
Vinci (2016), we remark that our cost functions are locally computable and in
contrast to Bil\`{o} and Vinci (2016) are independent of the actual instance of
the game
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