We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source.

In multi-issue allocation situations we have to divide a resource among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present an axiomatic characterization of the proportional rule.

Multi-issue allocation situations study problems where we have to divide an estate among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present several axiomatic characterizations of the constrained equal awards rule generalizing some characterizations of these rules in bankruptcy situations. Keywords multi-issue allocation situations • constrained equal awards We thank Juan Moreno-Ternero for helpful comments. Financial support from Ministerio de Ciencia y Tecnología and FEDER through grant ECO2008-03484-C02-01/ECON and from Xunta de Galicia through grants PGIDIT06PXIB362390PR and INCITE08PXIB300005PR is gratefully acknowledged.

In Tijs et al. (2006) a new family of cost allocation rules is introduced. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity in the context of cost spanning tree problems.

In this paper, we introduce minimum cost spanning tree problems with multiple sources. This new setting is an extension of the classical model where there is a single source. We extend several definitions of the folk rule, the most prominent rule in the classical model, to this new context: first as the Shapley value of the irreducible game; second as an obligation rule; third as a partition rule and finally through a cone-wise decomposition. We prove that all the definitions provide the same cost allocation and present two axiomatic characterizations.