A strategic approach to multiple estate division problems

- A claim game is proposed for estate division problems with non-homogeneous preferences.
- The existence of Nash equilibrium is established.
- Welfare properties of equilibria are studied.

The classical bankruptcy problem is extended by assuming that there are multiple estates. In the finite estate case, the agents have homogeneous preferences per estate, which may differ across estates. In the more general infinite estate problem, players have arbitrary preferences over an interval of real numbers each of which is regarded as an estate. A strategic estate game is formulated in which each agent distributes his legal entitlement over the estates, resulting in individual claims per estate: each estate is then divided according to some allocation rule. The paper focuses on existence and on computational aspects of Nash equilibria in finite and infinite estate games, with some focus on the proportional allocation rule. For this rule, it also studies Pareto optimality and envy-freeness of equilibrium allocations.