311 research outputs found
Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games
We study coordination mechanisms for Scheduling Games (with unrelated
machines). In these games, each job represents a player, who needs to choose a
machine for its execution, and intends to complete earliest possible. Our goal
is to design scheduling policies that always admit a pure Nash equilibrium and
guarantee a small price of anarchy for the l_k-norm social cost --- the
objective balances overall quality of service and fairness. We consider
policies with different amount of knowledge about jobs: non-clairvoyant,
strongly-local and local. The analysis relies on the smooth argument together
with adequate inequalities, called smooth inequalities. With this unified
framework, we are able to prove the following results.
First, we study the inefficiency in l_k-norm social costs of a strongly-local
policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy
of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all
deterministic, non-preemptive, strongly-local and non-waiting policies
(non-waiting policies produce schedules without idle times). These results
ensure that SPT is close to optimal with respect to the class of l_k-norm
social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price
of anarchy O(2^k).
Second, we consider the makespan (l_infty-norm) social cost by making
connection within the l_k-norm functions. We revisit some local policies and
provide simpler, unified proofs from the framework's point of view. With the
highlight of the approach, we derive a local policy Balance. This policy
guarantees a price of anarchy of O(log m), which makes it the currently best
known policy among the anonymous local policies that always admit a pure Nash
equilibrium.Comment: 25 pages, 1 figur
On the Impact of Fair Best Response Dynamics
In this work we completely characterize how the frequency with which each
player participates in the game dynamics affects the possibility of reaching
efficient states, i.e., states with an approximation ratio within a constant
factor from the price of anarchy, within a polynomially bounded number of best
responses. We focus on the well known class of congestion games and we show
that, if each player is allowed to play at least once and at most times
any best responses, states with approximation ratio times the
price of anarchy are reached after best
responses, and that such a bound is essentially tight also after exponentially
many ones. One important consequence of our result is that the fairness among
players is a necessary and sufficient condition for guaranteeing a fast
convergence to efficient states. This answers the important question of the
maximum order of needed to fast obtain efficient states, left open by
[9,10] and [3], in which fast convergence for constant and very slow
convergence for have been shown, respectively. Finally, we show
that the structure of the game implicitly affects its performances. In
particular, we show that in the symmetric setting, in which all players share
the same set of strategies, the game always converges to an efficient state
after a polynomial number of best responses, regardless of the frequency each
player moves with
Consciousness science : real progress and lingering misconceptions.
Link_to_subscribed_fulltex
The Price of Anarchy for Selfish Ring Routing is Two
We analyze the network congestion game with atomic players, asymmetric
strategies, and the maximum latency among all players as social cost. This
important social cost function is much less understood than the average
latency. We show that the price of anarchy is at most two, when the network is
a ring and the link latencies are linear. Our bound is tight. This is the first
sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
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
The sequential price of anarchy for atomic congestion games
In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, here we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos then relates the quality of any subgame perfect equilibrium to the quality of a global optimum. The effect of sequential decision making on the quality of equilibria, however, depends on the specific game under consideration.\ud
Here we analyze the sequential price of anarchy for atomic congestion games with affine cost functions. We derive several lower and upper bounds, showing that sequential decisions mitigate the worst case outcomes known for the classical price of anarchy. Next to tight bounds on the sequential price of anarchy, a methodological contribution of our work is, among other things, a "factor revealing" integer linear programming approach that we use to solve the case of three players
A polynomial oracle-time algorithm for convex integer minimization
In this paper we consider the solution of certain convex integer minimization
problems via greedy augmentation procedures. We show that a greedy augmentation
procedure that employs only directions from certain Graver bases needs only
polynomially many augmentation steps to solve the given problem. We extend
these results to convex -fold integer minimization problems and to convex
2-stage stochastic integer minimization problems. Finally, we present some
applications of convex -fold integer minimization problems for which our
approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur
Malicious Bayesian Congestion Games
In this paper, we introduce malicious Bayesian congestion games as an
extension to congestion games where players might act in a malicious way. In
such a game each player has two types. Either the player is a rational player
seeking to minimize her own delay, or - with a certain probability - the player
is malicious in which case her only goal is to disturb the other players as
much as possible.
We show that such games do in general not possess a Bayesian Nash equilibrium
in pure strategies (i.e. a pure Bayesian Nash equilibrium). Moreover, given a
game, we show that it is NP-complete to decide whether it admits a pure
Bayesian Nash equilibrium. This result even holds when resource latency
functions are linear, each player is malicious with the same probability, and
all strategy sets consist of singleton sets. For a slightly more restricted
class of malicious Bayesian congestion games, we provide easy checkable
properties that are necessary and sufficient for the existence of a pure
Bayesian Nash equilibrium.
In the second part of the paper we study the impact of the malicious types on
the overall performance of the system (i.e. the social cost). To measure this
impact, we use the Price of Malice. We provide (tight) bounds on the Price of
Malice for an interesting class of malicious Bayesian congestion games.
Moreover, we show that for certain congestion games the advent of malicious
types can also be beneficial to the system in the sense that the social cost of
the worst case equilibrium decreases. We provide a tight bound on the maximum
factor by which this happens.Comment: 18 pages, submitted to WAOA'0
Nash Equilibria in Discrete Routing Games with Convex Latency Functions
In a discrete routing game, each of n selfish users employs a mixed strategy to ship her (unsplittable) traffic over m parallel links. The (expected) latency on a link is determined by an arbitrary non-decreasing, non-constant and convex latency function φ. In a Nash equilibrium, each user alone is minimizing her (Expected) Individual Cost, which is the (expected) latency on the link she chooses. To evaluate Nash equilibria, we formulate Social Cost as the sum of the users ’ (Expected) Individual Costs. The Price of Anarchy is the worst-case ratio of Social Cost for a Nash equilibrium over the least possible Social Cost. A Nash equilibrium is pure if each user deterministically chooses a single link; a Nash equilibrium is fully mixed if each user chooses each link with non-zero probability. We obtain: For the case of identical users, the Social Cost of any Nash equilibrium is no more than the Social Cost of the fully mixed Nash equilibrium, which may exist only uniquely. Moreover, instances admitting a fully mixed Nash equilibrium enjoy an efficient characterization. For the case of identical users, we derive two upper bounds on the Price of Anarchy: For the case of identical links with a monomial latency function φ(x) = x d, the Price of Anarchy is the Bell number of order d + 1. For pure Nash equilibria, a generic upper bound from the Wardrop model can be transfered to discrete routing games. For polynomial latency functions with non-negative coefficients and degree d, this yields an upper bound of d + 1. For th
- …