New results for multi-issue allocation problems and their solutions

In this paper we present a different perspective than the more traditional approaches to study solutions for multi-issue allocation problems. This perspective is based on a direct sum decomposition for the vector space of these problems by identifying those subspaces that are relevant to the study of linear symmetric solutions. We then use such decomposition to derive some basic applications involving characterizations of several classes of solutions. Finally, we present a brief set of results relating coalitional game theory and multi-issue allocation problems.