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This problem pertains to kidney exchange with 0-1 preferences. Four patients are listed with I = (1, 2, 3, 4). Every patient has a donor who is incompatible. As usual, we designate the kidney from the incompatible donor for patient I by ω(i).
 

Keep in mind that a kidney is either compatible or not for a particular patient under 0-1 preferences. Assume that ω(1) is only compatible with patients 3 and 4;  ω(2) is only compatible with patient 1; ω(3) is only compatible with patient 2, and ω(4) is only compatible with patient 1. 

1. Stick with the restriction to two-way trades and suppose the priority order over patients is 1 ≻ 2 ≻ 3 ≻ 4. What is the matching that the priority rule produces?
    
2. Suppose we are now able to handle up to three-way trades. What are the Pareto efficient matchings?

Answer rating: 100% (QA)

Under the restriction of twoway trades and the given priority order the matching that the priority r... View the full answer