The folk solution and Boruvka's algorithm in minimum cost spanning tree problems

The Boruvka's algorithm, which computes the minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature.minimum cost spanning tree; Boruvka's algorithm; folk solution

Cost allocation protocols for network formation on connection situations

International audienceThe issue of embedding cost-awareness in the design of communication network devices and protocols has been growing at a fast rate in last years. Under certain connection situations, however, network design is not enforced by a central authority. This is the case, for instance, of power control for wireless networks, where the cost of a link is a function of the power needed to send a message to a remote node, which increases with the distance. Here each player wishes to consume as few power as possible to send its request and the main question is how to avoid that players deviate from a socially optimal network. In this paper, we study strategic games based on connection situations with the objective to coordinate self-interested agents placed on the nodes of a graph to realize a more efficient communication network. We address the problem of the design of cost allocation protocols that may guarantee the convergence of the best response dynamic and we analyze the effects of cost monotonicity and other state-dependent properties on the optimality of a protocol

The folk solution and Boruvka's algorithm in minimum cost spanning tree problems

The Boruvka's algorithm, which computes the minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature

Cooperative games for minimum cost spanning tree problems

Minimum cost spanning tree problems are well known problems in the Operations Research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory

Optimal equilibria in the non-cooperative game associated with cost spanning tree problems

We study the Pareto optimal equilibria payoffs of the non-cooperative game associated with the cost spanning tree problem. We give two characterisations of these payoffs: one based on the tree they induce and another based on the strategies played by agents. Moreover, an algorithm for computing all these payoffs is provided.Ministerio de Ciencia y Tecnología y FEDER | Ref. BEC2002-04102-C02-01Xunta de Galicia | Ref. PGIDIT03PXIC30002P