Cooperative games and mechanisms for division problems

Cooperative games describe situations where players collaborate in coalitions and generate profits. Cooperative game theory analyses how to allocate profits generated by the grand coalition among the players in a fair way, and provides several significant solutions. This thesis introduces a new class of cooperative games, and studies explicit expressions of these solutions in this class. Moreover, these solutions are characterized using the axiomatic method. Next, this thesis focuses on non-cooperative games and mechanism design. Based on a sequential partition method, this thesis gives a new non-cooperative interpretation of the constrained equal awards rule for bankruptcy problems. Then, a particular mechanism is considered to solve division problems with single-dipped preferences. The Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by so-called maximal coalitions: non-involved agents prefer getting zero over an equal coalition share, whereas for agents in the coalition the opposite holds.