1,938 research outputs found
Computer Science and Game Theory: A Brief Survey
There has been a remarkable increase in work at the interface of computer
science and game theory in the past decade. In this article I survey some of
the main themes of work in the area, with a focus on the work in computer
science. Given the length constraints, I make no attempt at being
comprehensive, especially since other surveys are also available, and a
comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic
Random Access Game and Medium Access Control Design
Motivated partially by a control-theoretic viewpoint, we propose a game-theoretic model, called random access game, for contention control. We characterize Nash equilibria of random access games, study their dynamics, and propose distributed algorithms (strategy evolutions) to achieve Nash equilibria. This provides a general analytical framework that is capable of modeling a large class of system-wide quality-of-service (QoS) models via the specification of per-node utility functions, in which system-wide fairness or service differentiation can be achieved in a distributed manner as long as each node executes a contention resolution algorithm that is designed to achieve the Nash equilibrium. We thus propose a novel medium access method derived from carrier sense multiple access/collision avoidance (CSMA/CA) according to distributed strategy update mechanism achieving the Nash equilibrium of random access game. We present a concrete medium access method that adapts to a continuous contention measure called conditional collision probability, stabilizes the network into a steady state that achieves optimal throughput with targeted fairness (or service differentiation), and can decouple contention control from handling failed transmissions. In addition to guiding medium access control design, the random access game model also provides an analytical framework to understand equilibrium and dynamic properties of different medium access protocols
Convergence of Large Atomic Congestion Games
We consider the question of whether, and in what sense, Wardrop equilibria
provide a good approximation for Nash equilibria in atomic unsplittable
congestion games with a large number of small players. We examine two different
definitions of small players. In the first setting, we consider a sequence of
games with an increasing number of players where each player's weight tends to
zero. We prove that all (mixed) Nash equilibria of the finite games converge to
the set of Wardrop equilibria of the corresponding nonatomic limit game. In the
second setting, we consider again an increasing number of players but now each
player has a unit weight and participates in the game with a probability
tending to zero. In this case, the Nash equilibria converge to the set of
Wardrop equilibria of a different nonatomic game with suitably defined costs.
The latter can also be seen as a Poisson game in the sense of Myerson (1998),
establishing a precise connection between the Wardrop model and the empirical
flows observed in real traffic networks that exhibit stochastic fluctuations
well described by Poisson distributions. In both settings we give explicit
upper bounds on the rates of convergence, from which we also derive the
convergence of the price of anarchy. Beyond the case of congestion games, we
establish a general result on the convergence of large games with random
players towards Poisson games.Comment: 34 pages, 3 figure
On the impact of heterogeneity and back-end scheduling in load balancing designs
Load balancing is a common approach for task
assignment in distributed architectures. In this paper, we show
that the degree of inefficiency in load balancing designs is highly
dependent on the scheduling discipline used at each of the backend
servers. Traditionally, the back-end scheduler can be modeled
as Processor Sharing (PS), in which case the degree of inefficiency
grows linearly with the number of servers. However, if the back-end
scheduler is changed to Shortest Remaining Processing Time
(SRPT), the degree of inefficiency can be independent of the
number of servers, instead depending only on the heterogeneity
of the speeds of the servers. Further, switching the back-end
scheduler to SRPT can provide significant improvements in
the overall mean response time of the system as long as the
heterogeneity of the server speeds is small
Scheduling Games with Machine-Dependent Priority Lists
We consider a scheduling game in which jobs try to minimize their completion
time by choosing a machine to be processed on. Each machine uses an individual
priority list to decide on the order according to which the jobs on the machine
are processed. We characterize four classes of instances in which a pure Nash
equilibrium (NE) is guaranteed to exist, and show, by means of an example, that
none of these characterizations can be relaxed. We then bound the performance
of Nash equilibria for each of these classes with respect to the makespan of
the schedule and the sum of completion times. We also analyze the computational
complexity of several problems arising in this model. For instance, we prove
that it is NP-hard to decide whether a NE exists, and that even for instances
with identical machines, for which a NE is guaranteed to exist, it is NP-hard
to approximate the best NE within a factor of for all
. In addition, we study a generalized model in which players'
strategies are subsets of resources, each having its own priority list over the
players. We show that in this general model, even unweighted symmetric games
may not have a pure NE, and we bound the price of anarchy with respect to the
total players' costs.Comment: 19 pages, 2 figure
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