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The authors consider estate division problems, a generalization of bankruptcy problems. They 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 equilibrium induce equal division. Next, they consider division rules satisfying efficiency, equal treatment of equals, and claims monotonicity. For claim games with at most three agents, again all Nash equilibrium induces equal division. Surprisingly, this result does not extend to claim games with more than three agents. However, if no bossiness is added, then equal division is restored.
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