A strategic approach to estate division problems with non-homogenous preferences

The classical bankruptcy problem (O''Neill, 1982) is extended by assuming that the agents have non-homogenous preferences over several estates. A special case is the one in which there are finitely many estates and the agents have homogenous preferences, i.e., constant utilities, per estate. 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 anestate. 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 proportionally according to 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. 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.