Suppose that there are five agents a1, a2, a3, a4, a5 and five houses h1,h2,h3,h4,h5 in a housing market, where agent ai owns hi for i = 1,...,5 initially. Agents preferences are as follows:

1. Find an allocation that is efficient but not individually rational; otherwise argue/show that no such allocation exists.

h5; P(ai): h2 > h3> h4> h1 > h5; P(az): hi h3 h4> ha P(az): h4 > h2 h1 > h5 > h3; P(04): h1 > h2 h5 > h3 > h4; P(25): h1 > h4> h2> h5> h3. h5; P(ai): h2 > h3> h4> h1 > h5; P(az): hi h3 h4> ha P(az): h4 > h2 h1 > h5 > h3; P(04): h1 > h2 h5 > h3 > h4; P(25): h1 > h4> h2> h5> h3