4,714 research outputs found
Enforcing efficient equilibria in network design games via subsidies
The efficient design of networks has been an important engineering task that
involves challenging combinatorial optimization problems. Typically, a network
designer has to select among several alternatives which links to establish so
that the resulting network satisfies a given set of connectivity requirements
and the cost of establishing the network links is as low as possible. The
Minimum Spanning Tree problem, which is well-understood, is a nice example.
In this paper, we consider the natural scenario in which the connectivity
requirements are posed by selfish users who have agreed to share the cost of
the network to be established according to a well-defined rule. The design
proposed by the network designer should now be consistent not only with the
connectivity requirements but also with the selfishness of the users.
Essentially, the users are players in a so-called network design game and the
network designer has to propose a design that is an equilibrium for this game.
As it is usually the case when selfishness comes into play, such equilibria may
be suboptimal. In this paper, we consider the following question: can the
network designer enforce particular designs as equilibria or guarantee that
efficient designs are consistent with users' selfishness by appropriately
subsidizing some of the network links? In an attempt to understand this
question, we formulate corresponding optimization problems and present positive
and negative results.Comment: 30 pages, 7 figure
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
Matroids are Immune to Braess Paradox
The famous Braess paradox describes the following phenomenon: It might happen
that the improvement of resources, like building a new street within a
congested network, may in fact lead to larger costs for the players in an
equilibrium. In this paper we consider general nonatomic congestion games and
give a characterization of the maximal combinatorial property of strategy
spaces for which Braess paradox does not occur. In a nutshell, bases of
matroids are exactly this maximal structure. We prove our characterization by
two novel sensitivity results for convex separable optimization problems over
polymatroid base polyhedra which may be of independent interest.Comment: 21 page
Designing Network Protocols for Good Equilibria
Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs
Fair Tree Connection Games with Topology-Dependent Edge Cost
How do rational agents self-organize when trying to connect to a common
target? We study this question with a simple tree formation game which is
related to the well-known fair single-source connection game by Anshelevich et
al. (FOCS'04) and selfish spanning tree games by Gourv\`es and Monnot
(WINE'08). In our game agents correspond to nodes in a network that activate a
single outgoing edge to connect to the common target node (possibly via other
nodes). Agents pay for their path to the common target, and edge costs are
shared fairly among all agents using an edge. The main novelty of our model is
dynamic edge costs that depend on the in-degree of the respective endpoint.
This reflects that connecting to popular nodes that have increased internal
coordination costs is more expensive since they can charge higher prices for
their routing service.
In contrast to related models, we show that equilibria are not guaranteed to
exist, but we prove the existence for infinitely many numbers of agents.
Moreover, we analyze the structure of equilibrium trees and employ these
insights to prove a constant upper bound on the Price of Anarchy as well as
non-trivial lower bounds on both the Price of Anarchy and the Price of
Stability. We also show that in comparison with the social optimum tree the
overall cost of an equilibrium tree is more fairly shared among the agents.
Thus, we prove that self-organization of rational agents yields on average only
slightly higher cost per agent compared to the centralized optimum, and at the
same time, it induces a more fair cost distribution. Moreover, equilibrium
trees achieve a beneficial trade-off between a low height and low maximum
degree, and hence these trees might be of independent interest from a
combinatorics point-of-view. We conclude with a discussion of promising
extensions of our model.Comment: Accepted at FSTTCS 2020, full versio
Network Creation Games: Think Global - Act Local
We investigate a non-cooperative game-theoretic model for the formation of
communication networks by selfish agents. Each agent aims for a central
position at minimum cost for creating edges. In particular, the general model
(Fabrikant et al., PODC'03) became popular for studying the structure of the
Internet or social networks. Despite its significance, locality in this game
was first studied only recently (Bil\`o et al., SPAA'14), where a worst case
locality model was presented, which came with a high efficiency loss in terms
of quality of equilibria. Our main contribution is a new and more optimistic
view on locality: agents are limited in their knowledge and actions to their
local view ranges, but can probe different strategies and finally choose the
best. We study the influence of our locality notion on the hardness of
computing best responses, convergence to equilibria, and quality of equilibria.
Moreover, we compare the strength of local versus non-local strategy-changes.
Our results address the gap between the original model and the worst case
locality variant. On the bright side, our efficiency results are in line with
observations from the original model, yet we have a non-constant lower bound on
the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication
in the proceedings of the 40th International Conference on Mathematical
Foundations on Computer Scienc
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
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