1,451 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
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
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
The Price of Anarchy in Cooperative Network Creation Games
In general, the games are played on a host graph, where each node is a
selfish independent agent (player) and each edge has a fixed link creation cost
\alpha. Together the agents create a network (a subgraph of the host graph)
while selfishly minimizing the link creation costs plus the sum of the
distances to all other players (usage cost). In this paper, we pursue two
important facets of the network creation game. First, we study extensively a
natural version of the game, called the cooperative model, where nodes can
collaborate and share the cost of creating any edge in the host graph. We prove
the first nontrivial bounds in this model, establishing that the price of
anarchy is polylogarithmic in n for all values of α in complete host
graphs. This bound is the first result of this type for any version of the
network creation game; most previous general upper bounds are polynomial in n.
Interestingly, we also show that equilibrium graphs have polylogarithmic
diameter for the most natural range of \alpha (at most n polylg n). Second, we
study the impact of the natural assumption that the host graph is a general
graph, not necessarily complete. This model is a simple example of nonuniform
creation costs among the edges (effectively allowing weights of \alpha and
\infty). We prove the first assemblage of upper and lower bounds for this
context, stablishing nontrivial tight bounds for many ranges of \alpha, for
both the unilateral and cooperative versions of network creation. In
particular, we establish polynomial lower bounds for both versions and many
ranges of \alpha, even for this simple nonuniform cost model, which sharply
contrasts the conjectured constant bounds for these games in complete (uniform)
graphs
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