Arbres de cost mı́nim i jocs cooperatius

Abstract

[en] In this project we study minimun cost spanning tree problems and how to associate them with a cooperative game of transferable utility. Some real economic situations such as the construction of an electricity network for the supply of energy to an entire village from a common power station can be modelled by these problems. This case was studied by Dutta and Kar (2004). On the one hand, we define two algorithms capable of obtaining a minimum cost spanning tree of a connected graph, namely Prim’s (1957) and Kruskal’s (1956). On the other hand, we explain a series of cost allocation rules, which are interpreted under the prism of cooperative games. A series of properties are detailed to see which of these properties determine them. We also study the irreducible form introduced by Bird (1976) associated with a minimum cost spanning tree problem. We see how to associate one to each problem and analyze the equivalence between rules in this irreducible form.