Short trading cycles: Paired kidney exchange with strict ordinal preferences

I study kidney exchange with strict ordinal preferences and with constraints on the lengths of the exchange cycles. Efficient deterministic mechanisms have poor fairness properties in this environment. Instead, I propose an individually rational, ordinally efficient and anonymous random mechanism for two-way kidney exchange based on Bogomolnaia and Moulin’s (2001) Probabilistic Serial mechanism. Individual rationality incentivizes patient-donor pairs who are compatible with each other to participate in the exchange, thus increasing the overall transplantation rate. Finally, individual rationality, ex-post efficiency and weak strategyproofness are incompatible for any mechanism