Fair Division in Cournot Markets

Abstract

Fair division is discussed on the basis of a cooperative oligopoly game without transferable technologies. In a first step an oligopoly situation is introduced from which the corresponding oligopoly game in normal from can be derived. In a second step the associated cooperative games, the so-called α- and β-value games, are introduced. In order to study the fair division of the proceeds, as produced to the members of a cartel, important properties of cooperative oligopoly games must be recalled. In respect thereof the notion of convexity or super-modularity is crucial to expect that firms have strong incentives to merge their economic activities into a monopoly. This property has a strong impact on how an agreement can be stabilized by dividing the proceeds of a mutual cooperation fairly. As we pursue a better and more comprehensive understanding of a fair compromise, a set of principles of distributive justice (axioms) is presented. On the one hand the axiomatic foundation of the Shapley value is given that lets one consider this solution scheme as a fair division rule. On the other hand the axiomatic foundation of the pre-kernel is presented to set a counter-point to what subjects consider as fair or unfair. Beside its attractive axiomatic characterization, it is argued that an efficient and easy computability of a proposed solution is a desirable feature to qualify as a fair division rule. It is established on the basis of the introduced cooperative oligopoly game that the pre-kernel is technically more complicated and is therefore difficult to compute. A clear disadvantage with regard to the Shapley value which possesses a simple, efficient, and systematic computation procedure.