We consider estate division problems, a generalization of bankruptcy problems. We show that in
a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment
of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal
division. Next, we consider division rules satisfying efficiency, equal treatment of equals, and
claims monotonicity. For claim games with at most three agents, again all Nash equilibria
induce equal division. Surprisingly, this result does not extend to claim games with more than
three agents. However, if nonbossiness is added, then equal division is restored.