Approximate stable solutions in infinite tree problems

Abstract

In this article infinite minimum cost spanning tree situations and related TU-games are studied. Since an optimal tree for these situations does not always exist, it is impossible in such situations to implement core solutions based on a particular tree. Therefore, we study core-like solutions and deal with three cases concerning the total cost of connection: when it is zero, when it is finite but larger than zero, and when it is infinite.

Keywords:

• countable infinite number of players
• spanning trees
• core-like solutions

AMS Subject Classification::

• 91A12

Acknowledgments

We are grateful to an anonymous refree for her/his useful comments. We thank Rodica Branzei for her helpful comments and valuable suggestions that have substantially improved this article. This research has been partially supported by MIUR through grant IT1114. Financial support from the Government of Spain and FEDER, under projects MTM2005-09184-C02-02 and MTM2008-06778-C02-01 is gratefully acknowledged.