We adopt a non-cooperative approach to bankruptcy problems by studying a Rubinstein-like multilateral bargaining game where players bargain over efficient estate allocations satisfying claims-boundedness and order-preservation. We analyze the subgame perfect equilibria in stationary strategies (SSPE).We prove that an equilibrium always exists and that there can be no delay in agreement. As the players become increasingly patient, players with sufficiently small claims are fully compensated. Additionally, we provide an example of a game with infinitely many equilibria, even in the limit when players are arbitrarily patient. Still, in the limit the expected payoff is at least the minimum of the claim and an equal share in the estate.We introduce a selection of bargaining equilibrium called robust bargaining equilibrium (RBE), and show that every game has a unique RBE. As the players become increasingly patient, every proposal of the RBE converges to the constrained equal awards rule applied to the underlying bankruptcy problem. Lastly, we show that this allocation equals the Nash bargaining solution of the feasible set.