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The estate division problem considers the issue of dividing an estate when the sum of entitlements is larger than the estate. This paper studies the estate division problem from a noncooperative perspective. The integer claim game introduced by O'Neill (1982) and extended by Atlamaz et al. (2011) is generalized by specifying a sharing rule to divide every interval among the claimants. We show that for all problems for which the sum of entitlements is at most twice the estate the existence of a Nash equilibrium is guaranteed for a general class of sharing rules. Moreover, the corresponding set of equilibrium payoffs is independent of which sharing rule in the class is used. Well-known division rules that always assign a payoff vector in this set of equilibrium payoffs are the adjusted proportional rule, the random arrival rule and the Talmud rule.