Measuring the Price of Anarchy

• Izabela Komenda

In Critical Care Unit Interactions

• Two hospitals
• number of admissions dependent on current bed occupancy
• delayed discharges if no pressure on CCU beds

so used game theory - prisoner’s dilemma example

• queueing game between 2 hospitals
• each hospital aims to get utliisation rate below 80%
• show equations, and diagram of Markov model
• there is an option to divert a patient from your hospital to the other hospital, but not risk free

results

• look similar to prisoner’s dilemma: if both hospitals act in their own interests, patient throughput is reduced significantly
• “price of anarchy” is ratio of optimal throughput, vs self interest
• play with price changes when target and demand inputs are varied
• try out different models, with demand management, different rules about rejections

complexity was going through the roof, rewrote with python and parallelised it, and took 1 week on supercomputer (rather than 4 months!)