Alternative axiomatic characterizations of the Shapley and Banzhaf values

Game Theory

The nucleolus and kernel of veto-rich transferable utility games

Game Theory

Controlled communication networks

Game Theory;game theory

On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems in which an existing network has to be extended to connect users to a source. This paper generalizes the definition of irreducible core to minimum cost spanning extension problems and introduces an algorithm generating all elements of the irreducible core. Moreover, the equal remaining obligations rule, a one-point refinement of the irreducible core ispresented. Finally, the paper characterizes these solutions axiomatically. The classical Bird tree allocation of minimum cost spanning tree problems is obtained as a particular case in our algorithm for the irreducible core.Networks;Cost Allocation;costs and cost price

Bird's tree allocations revisited

Game Theory;Cost Allocation

Minimum cost spanning extension problems: The proportional rule and the decentralized rule

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems (see Bird 1976) where an existing network has to be extended to connect users to a source. In this paper, we present two cost allocation rules for these problems, viz. the proportional rule and the decentralized rule. We introduce algorithms that generate these rules and prove that both rules are refinements of the irreducible core, as defined in Feltkamp, Tijs and Muto (1994b). We then proceed to axiomatically characterize the proportional rule.Networks;Cost Allocation;costs and cost price