Alternating Bid Bargaining with a Smallest Money Unit

In a seminal paper, Ariel Rubinstein has shown that impatience implies determinateness of the 2-person bargaining problem. In this note we show that this result depends also on the assumption that the set of alternatives is a continuum. If the pie can be divided only in finitely many different ways, (for example, because the pie is an amount of money and there is a smallest money unit), any partition can be obtained as the result of a subgame perfect equilibrium if the time interval between successive offers is sufficiently small.