# Game Theory, The Prisoners Dilemma and OHIP Clawbacks

Before I became a medical student, I spent 2 years as an undergraduate studying mathematics. I’ve always been interested in the junction of mathematics and human behaviour.

The Stanford University student syllabus describes Game Theory as “the mathematical modeling of strategic interaction among rational (and irrational) agents.”

A classic example is the prisoner’s dilemma. Here 2 suspects of a crime are apprehended. There is enough evidence to convict both of a lesser crime but to convict either of a more serious crime, the testimony of the other prisoner is required.

Both prisoners are offered a deal. Inform on the other and go free. If the other prisoner informs but you don’t then you serve 4 years in jail. If both inform each will get 2 years and if neither informs then both serve 1 year for the lesser crime. It is assumed that both prisoners are rational and that there will be no secondary repercussions for informing.

In this simplified example it is thought that both are better off informing.

Ontario Doctors face a very similar dilemma today.

The Government of Ontario has put a hard cap on the physician services budget. It the budget is overspent, then each and every service will be paid in full (well in full is an exageration) but a ‘reconciliation’ or claw back of fees will occur. Fees that have already been reduced by 3.15% will face a second reduction to keep the total spend under the hard cap.

The reconciliation will be made according to the government’s fiscal year, April 1 to March 31. How do things stand five months into the fiscal year? Doctors have no idea as the government refuses to share utilization data.

If doctors decided to act in a mutually advantageous manner then they would each reduce their clinical activity so as keep under the hard cap.

The dilemma is that no doctor knows what the other doctors are doing. So if an individual doctor maintains or reduces her activity to keep the spend down to target but her colleagues increase their activity to maintain revenue, she will have the double hit of reduced billings while still facing a claw-back.

Like the prisoner in the game theory example she is much better off working harder so that she does not have to pay for everyone else’s increase out of proportion to her billings. It’s best to get on a billing treadmill and race against everyone else.

We saw this pattern in the early 90’s when the Rae Government used the same strategy as the Wynne Government. Each quarter saw increasing clinical activity and larger and larger claw-backs. In the end claw-backs reached %10 of gross billings and a much larger reduction in after expense income.

I don’t know what the billings have been over the past 5 months but I’ll bet dollars to donuts that they have exceeded expectations and that a large claw-back is pending.

Doctors, like the prisoners have no other choice.

I admit that the Wynne Government’s strategy will work in the short term to reduce spending. But it will make impossible rational system changes that could maintain curent spending levels and patient care. The current strategy of a hard cap and claw-backs will do nothing to improve or even maintain quality.

Scott D Wooder, MD

## 5 thoughts on “Game Theory, The Prisoners Dilemma and OHIP Clawbacks”

1. Matthew says:

This is a refreshingly different view of events, Scott. The game theory model has some interesting implications:

1. There are multiple agents in “our” game with competing interests
2. The government is allowed to act simultaneously as agent and arbiter. In the prisoners’ dilemma analogy, this is tantamount to being the police and the other prisoner–it has an inherent conflict.
3. Each negotiation seems like a discrete event to us–we treat them as such in good faith; however, they are actually sequential games for the agents, and repeating games for the government. This has implications for strategy.
4. The arbiter can, and does, change the rules during and after the game. Thus the two-year sentence that a prisoner receives in one scenario may end up much worse than expected… “Oh, by the way, that’s in solitary, and the turncoat gets your earnings.”

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2. I am fascinated to know about your mathematical background. The logic of the prisoners dilemma seems to be a great analogy.

Everything else being equal the conclusion of doctors working harder and harder on the treadmill makes sense and I suspect that is what the government is counting on.

Also the prisoners choices only affect the prisoners themselves. The choices made by individual doctors will affect patients as well as the doctors themselves. With a large shortage of physicians in Ontario, only a few leaving practice will make a big impression on their patients. As many are aware, doctors have already retired and made decisions about moving away because of the recent fee imposition by government that’s includes a global cap. Once the clawback happens I suspect that a larger efflux of physicians from practice in Ontario will occur. Many more will retire and many more will leave.

Patients are already feeling the effects of government healthcare rationing. We ain’t seen nothing yet as the clawbacks are coming.

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3. Max says:

Great analogy Dr.Wooder. However, it only seems to address the situation in which the doctors can actually make a choice about their billings and the amount they work. Primary care physicians, ER and trauma staff, as well as physicians of all disciplines in under serviced areas around the province are handcuffed by patient demand and can only limit their billings by working less. A choice that is frequently not possible from either a practical or ethical standpoint as it would result in the sickest and often most vulnerable patients without care. These ‘prisoners’ of the government cannot limit their billings and will be punished with the claw back if and when the hard cap is broken without having any chance of contributing to the ‘solution’ of self regulating their billing. Not a great recruitment and retention strategy by the Ontario government if they are interested in the health of their citizens.

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1. Frankly, Ontario has been considered doctor-unfriendly for years because of the actions of government.

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4. M Newhouse says:

Good point Scott.
Do all healthcare administrators and the minister of health fall under the hard cap also? If not, why not?
And should not all government departments and employees, including Ms Wynne not be subjected to the same hard cap? If they go over budget, as they always do, should not the deficit be clawed back from all those working in each department?

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