Social Networks 101 P ROF. J ASON H ARTLINE AND P ROF. N ICOLE I MMORLICA

Lecture Twenty-Three: Kidney transplants.

Kidney failure Sometimes people find themselves without a kidney. Diabetes Hypovolemia Dehydration Sepsis Rhabdomyolysis High blood pressure Without a transplant, they will die.

Kidney supply 1. Cadavers

Kidney supply 2. Live donors

Kidney supply 3. Pigs (maybe)

Kidney demand There are currently waiting for a kidney transplant in the US. 80,000 people

In 2008, 5,920 patients died or became too sick for a transplant.

In 2008, 10,526 patients received cadaver kidneys. 4,857 patients received live donor kidneys.

Making supply meet demand The economic approach 101: Buying kidneys. I have an extra kidney. I need a kidney. My value for it is my value for my life.

Repugnance Often x + $ is repugnant, even when x alone is not. Interest on loans Prostitution Organ donation

“We didn’t have time to pick up a bottle of wine, but this is what we would have spent.”

Legality Section 301 of the National Organ Transplant Act, “Prohibition of organ purchases” imposes criminal penalties on any person who “knowingly acquire[s], receive[s], or otherwise transfer[s] any human organ for valuable consideration for use in human transplantation”

Making supply meet demand Take two: Kidney exchange.

Compatibility Blood “O”, “A”, “B”, “AB” Tissue (crossmatch test)

Kidney exchange Sick, blood type A Sick, blood type B Healthy, blood type A Healthy, blood type B

To be less morbid, Pretend that a kidney is a house.

Housing exchange Each person has a house. Each person has a strict set of preferences over all houses. House C House AHouse B House D A > B > C > D

Housing exchange Question: Can we design a set of trades to make all agents better off?

Top trading cycles 1.Each agent points to her most preferred house that is still on the market. 2.Select a cycle and have those agents trade houses. These houses leave the market. 3.Repeat until each agent has transacted.

Top trading cycles House C House A House B House D A > B > D > C

Top trading cycles House C House A House B House D A > B > D > C

Top trading cycles 1.Each agent points to her most preferred house that is still on the market. 2.Select a cycle and have those agents trade houses. These houses leave the market. 3.Repeat until each agent has transacted. What if there are no cycles after step 1? What if there are multiple cycles?

Top trading cycles Each node has only one out-going arrow.  there is at least one cycle, and cycles don’t conflict.

Top trading cycles A 1.Each agent points to her most preferred house that is still on the market. 2. Select a cycle and have those agents trade houses. These houses leave the market.

Properties Dominant strategy: Each agent’s best strategy is to point to his most preferred house. Pareto efficiency: No agent can be made better off without making some agent worse off.

Dominant strategy A “Chains” never disappear  you don’t lose options as time goes by.

Pareto efficiency No one can be made better off without making someone worse off.

Group deviations Pareto efficiency  even groups can’t form coalitions to get better allocations!

Back to kidneys … Idea: Each node in the graph is an incompatible donor-recipient pair.

Back to kidneys … Cute, but …. What is the right thing to optimize? Can we find these cycles easily? Are preferences really strict? What if people change their mind? What about angel donors/cadaver queues?

NEPKE (or the New England Program for Kidney Exchange) 1.Patients register in database. 2.Doctors classify kidneys as compatible or incompatible. 3.Short cycles/chains are found. 4.Operations are performed simultaneously.

NEPKE 38 exchanges performed to date. (also Alliance for Paired Donations)

Next time Stable marriage.