56,690 research outputs found
Price of Anarchy in Bernoulli Congestion Games with Affine Costs
We consider an atomic congestion game in which each player participates in
the game with an exogenous and known probability , independently
of everybody else, or stays out and incurs no cost. We first prove that the
resulting game is potential. Then, we compute the parameterized price of
anarchy to characterize the impact of demand uncertainty on the efficiency of
selfish behavior. It turns out that the price of anarchy as a function of the
maximum participation probability is a nondecreasing
function. The worst case is attained when players have the same participation
probabilities . For the case of affine costs, we provide an
analytic expression for the parameterized price of anarchy as a function of
. This function is continuous on , is equal to for , and increases towards when . Our work can be interpreted as
providing a continuous transition between the price of anarchy of nonatomic and
atomic games, which are the extremes of the price of anarchy function we
characterize. We show that these bounds are tight and are attained on routing
games -- as opposed to general congestion games -- with purely linear costs
(i.e., with no constant terms).Comment: 29 pages, 6 figure
The Price of Anarchy for Minsum Related Machine Scheduling
We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e-1). This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature
Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability
The price of anarchy and price of stability are three well-studied
performance metrics that seek to characterize the inefficiency of equilibria in
distributed systems. The distinction between these two performance metrics
centers on the equilibria that they focus on: the price of anarchy
characterizes the quality of the worst-performing equilibria, while the price
of stability characterizes the quality of the best-performing equilibria. While
much of the literature focuses on these metrics from an analysis perspective,
in this work we consider these performance metrics from a design perspective.
Specifically, we focus on the setting where a system operator is tasked with
designing local utility functions to optimize these performance metrics in a
class of games termed covering games. Our main result characterizes a
fundamental trade-off between the price of anarchy and price of stability in
the form of a fully explicit Pareto frontier. Within this setup, optimizing the
price of anarchy comes directly at the expense of the price of stability (and
vice versa). Our second results demonstrates how a system-operator could
incorporate an additional piece of system-level information into the design of
the agents' utility functions to breach these limitations and improve the
system's performance. This valuable piece of system-level information pertains
to the performance of worst performing agent in the system.Comment: 14 pages, 4 figure
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