In an estate division problem an estate has to be divided among several players whose total entitlement to the estate exceeds its size. This paper extends the non-cooperative approach through a claim game, as initiated by o'neill (1982), by allowing players to put multiple claims on the same part of the estate, and by considering the case where individual entitlements may exceed the estate. A full characterization of the set of nash equilibria of the claim game is obtained both for restricted estate division problems, where individual entitlements do not exceed the estate, and for the general case. Variations on the claim game are considered, which result in proportional division in equilibrium.
Atlamaz, M., Berden, C., Peters, H. J. M., & Vermeulen, A. J. (2011). Non-Cooperative solutions for estate division problems. Games and Economic Behavior, 73, 39-51. https://doi.org/10.1016/j.geb.2010.12.008