474,875 research outputs found
Multilevel Network Games
We consider a multilevel network game, where nodes can improve their
communication costs by connecting to a high-speed network. The nodes are
connected by a static network and each node can decide individually to become a
gateway to the high-speed network. The goal of a node is to minimize its
private costs, i.e., the sum (SUM-game) or maximum (MAX-game) of communication
distances from to all other nodes plus a fixed price if it
decides to be a gateway. Between gateways the communication distance is ,
and gateways also improve other nodes' distances by behaving as shortcuts. For
the SUM-game, we show that for , the price of anarchy is
and in this range equilibria always exist. In range
the price of anarchy is , and
for it is constant. For the MAX-game, we show that the
price of anarchy is either , for ,
or else . Given a graph with girth of at least , equilibria always
exist. Concerning the dynamics, both the SUM-game and the MAX-game are not
potential games. For the SUM-game, we even show that it is not weakly acyclic.Comment: An extended abstract of this paper has been accepted for publication
in the proceedings of the 10th International Conference on Web and Internet
Economics (WINE
Network Games
In a variety of contexts - ranging from public goods provision to information collection - a player's well-being depends on own action as well as on the actions taken by his or her neighbors. We provide a framework to analyze such strategic interactions when neighborhood structure, modeled in terms of an underlying network of connections, a¤ects payo¤s. We provide results characterizing how the network structure, an individual.s position within the network, the nature of games (strategic substitutes versus complements and positive versus negative externalities), and the level of information, shape individual behavior and payoffs.Networks, Network Games, Graphical Games, Diffusion, Incomplete Information
The Least-core and Nucleolus of Path Cooperative Games
Cooperative games provide an appropriate framework for fair and stable profit
distribution in multiagent systems. In this paper, we study the algorithmic
issues on path cooperative games that arise from the situations where some
commodity flows through a network. In these games, a coalition of edges or
vertices is successful if it enables a path from the source to the sink in the
network, and lose otherwise. Based on dual theory of linear programming and the
relationship with flow games, we provide the characterizations on the CS-core,
least-core and nucleolus of path cooperative games. Furthermore, we show that
the least-core and nucleolus are polynomially solvable for path cooperative
games defined on both directed and undirected network
Stackelberg Network Pricing Games
We study a multi-player one-round game termed Stackelberg Network Pricing
Game, in which a leader can set prices for a subset of priceable edges in a
graph. The other edges have a fixed cost. Based on the leader's decision one or
more followers optimize a polynomial-time solvable combinatorial minimization
problem and choose a minimum cost solution satisfying their requirements based
on the fixed costs and the leader's prices. The leader receives as revenue the
total amount of prices paid by the followers for priceable edges in their
solutions, and the problem is to find revenue maximizing prices. Our model
extends several known pricing problems, including single-minded and unit-demand
pricing, as well as Stackelberg pricing for certain follower problems like
shortest path or minimum spanning tree. Our first main result is a tight
analysis of a single-price algorithm for the single follower game, which
provides a -approximation for any . This can
be extended to provide a -approximation for the
general problem and followers. The latter result is essentially best
possible, as the problem is shown to be hard to approximate within
\mathcal{O(\log^\epsilon k + \log^\epsilon m). If followers have demands, the
single-price algorithm provides a -approximation, and the
problem is hard to approximate within \mathcal{O(m^\epsilon) for some
. Our second main result is a polynomial time algorithm for
revenue maximization in the special case of Stackelberg bipartite vertex cover,
which is based on non-trivial max-flow and LP-duality techniques. Our results
can be extended to provide constant-factor approximations for any constant
number of followers
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