A strategic approach to multiple estate division problems

The classical bankruptcy problem (O’Neill, 1982) is extended by assuming that there are multiple estates to be divided. In the finite case, there are finitely many estates and the agents have homogenous preferences, i.e., constant utilities, per estate, but preferences may differ across estates. In the general case, i.e., the infinite estate problem, players have arbitrary preferences over an interval of real numbers each of which is regarded as an estate. The finite estate problem is a special case of the infinite estate problem. A strategic game is formulated in which each agent/player distributes his legal entitlement over the estates, resulting in individual claims per estate: each estate is then divided according to some allocation rule based on these individual claims. The focus of the paper is on the study of Nash equilibria, in particular on their existence, in finite and infinite estate games; and on computational aspects of Nash equilibrium, in particular for the special but natural case of proportional allocation. For this case, it is also shown that, generally speaking, Nash equilibria are not unique nor Pareto optimal but that they are Pareto optimal in a second best sense: they do not Pareto dominate each other. The paper concludes with a brief consideration of envy-freeness. JEL Classification numbers: C72, D63