48,610 research outputs found
Network Connectivity Game
We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point
Heterogeneous resource allocation can change social hierarchy in public goods games
Public Goods Games represent one of the most useful tools to study group
interactions between individuals. However, even if they could provide an
explanation for the emergence and stability of cooperation in modern societies,
they are not able to reproduce some key features observed in social and
economical interactions. The typical shape of wealth distribution - known as
Pareto Law - and the microscopic organization of wealth production are two of
them. Here, we introduce a modification to the classical formulation of Public
Goods Games that allows for the emergence of both of these features from first
principles. Unlike traditional Public Goods Games on networks, where players
contribute equally to all the games in which they participate, we allow
individuals to redistribute their contribution according to what they earned in
previous rounds. Results from numerical simulations show that not only a Pareto
distribution for the payoffs naturally emerges but also that if players don't
invest enough in one round they can act as defectors even if they are formally
cooperators. Finally, we also show that the players self-organize in a very
productive backbone that covers almost perfectly the minimum spanning tree of
the underlying interaction network. Our results not only give an explanation
for the presence of the wealth heterogeneity observed in real data but also
points to a conceptual change regarding how cooperation is defined in
collective dilemmas.Comment: 8 pages, 5 figures, 55 reference
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
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
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