On multi-source minimum cost spanning tree problems and agglomeration problems

Resumo

The main purpose of this dissertation is to provide allocation rules for multi-source minimum cost spanning tree problems and for agglomeration problems and is organized in two completely independent chapters. The first chapter is devoted to multi-source minimum cost spanning tree problems. This part studies situations where a group of agents need services provided by several sources. Agents need to be connected, directly or indirectly, to all sources. Every connection entails a cost. Situations of this kind are called multi-source minimum cost spanning tree problems and are extensions of the classical minimum cost spanning tree problem (where there is a single source). We propose a cost allocation rule based on a painting procedure. Agents paint the edges on the paths connecting them to the sources. We prove that the painting rule coincides with the folk rule. Finally, we provide an axiomatic characterization. The second chapter studies agglomeration problems. Agglomeration problems consider that a new firm is planning to open a plant in a country divided into several regions. Each firm receives a positive externality if the new plant is located in its region. In a decentralized mechanism, the plant would be opened in the region where the new firm maximizes its individual benefit. Due to the externalities, it could be the case that the aggregate utility of all firms is maximized in a different region. Thus, the firms in the optimal region could transfer something to the new firm in order to incentivize it to open the plant in that region. We propose several rules that provide different schemes for transfers between firms already located in the country and the newcomer. We define these rules directly and through two different cooperative games with transferable utility. We also analyze several properties of the rules and give axiomatic characterizations.