21 research outputs found
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
Strong stability of Nash equilibria in load balancing games
We study strong stability of Nash equilibria in the load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the
workload of the server it chooses.
A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an
NE approximates an SNE.
Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre-and post-deviation costs. An NE is said to be a ρ-approximate SNE (ρ >= 1) if there is no coalition of jobs such that each job of the coalition
will have an IR more than ρ from coordinated deviations of the coalition.
While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5=4)-approximate SNE, which together with the lower bound already established in the literature implies that the approximation bound is tight. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in the load balancing games. To establish our upper bound, we apply with novelty a powerful graph-theoretic tool
An Upper Bound on the Price of Stability for Undirected Shapley Network Design Games
In this paper, we consider the Shapley network design game on undirected
networks. In this game, we have an edge weighted undirected network
and selfish players where player wants to choose a path from source
vertex to destination vertex . The cost of each edge is equally
split among players who pass it. The price of stability is defined as the ratio
of the cost of the best Nash equilibrium to that of the optimal solution. We
present an upper bound on price of stability for the
single sink case, i.e, for all
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
Approximately Socially-Optimal Decentralized Coalition Formation
Coalition formation is a central part of social interactions. In the emerging
era of social peer-to-peer interactions (e.g., sharing economy), coalition
formation will be often carried out in a decentralized manner, based on
participants' individual preferences. A likely outcome will be a stable
coalition structure, where no group of participants could cooperatively opt out
to form another coalition that induces higher preferences to all its members.
Remarkably, there exist a number of fair cost-sharing mechanisms (e.g.,
equal-split, proportional-split, egalitarian and Nash bargaining solutions of
bargaining games) that model practical cost-sharing applications with desirable
properties, such as the existence of a stable coalition structure with a small
strong price-of-anarchy (SPoA) to approximate the social optimum. In this
paper, we close several gaps on the previous results of decentralized coalition
formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show
several previously known fair cost-sharing mechanisms are the best practical
mechanisms with minimal SPoA. (2) We improve the SPoA of egalitarian and Nash
bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the
SPoA of a mix of different cost-sharing mechanisms. (4) We present a
decentralized algorithm to form a stable coalition structure. (5) Finally, we
apply our results to a novel application of peer-to-peer energy sharing that
allows households to jointly utilize mutual energy resources. We also present
and analyze an empirical study of decentralized coalition formation in a
real-world P2P energy sharing project