Consider an exchange economy, in which there are two goods. The rst good is indivisible, i.e. its quantity is described by an integer. There is also a perfectly divisible medium of exchange between traders called money. A bundle of goods is therefore described by a vector (x; m), where x 2 X = f0; 1g, and m 2 R . The economy is populated by n individuals, indexed by i 2 I = f1; :::; ng. Preferences are such that each trader does not value consumption of more than one unit of the indivisible good, and are additively separable in money and the indivisible good. Thus the utility function of each individual i 2 I can be written as