Competitive Fair Division under Linear Preferences

The fair division of a bundle of goods (manna) among agents with heterogenous preferences is an important challenge for normative economic analysis. The difficulty is to combine e¢ ciency (Pareto optimality) with some convincing notion of fairness. When agents are responsible for their ordinal preferences, and cardinal measures of utility are not relevant, the division rule favored by economist is the Competitive equilibrium with equal incomes, thereafter CEEI, invented almost 50 years ago (Varian, Kolm). Here we discuss this rule in the important special case where individual preferences are linear. This means that the goods are perfect substitutes and each participant in the division needs only report p1 rates of substitution if there are p goods to share. This assumption is less drastic than may appear.