Medicine and Game Theory: How to win


You have to learn the rules of the game; then learn to play better than anyone else - Albert Einstein

Game theory is a field of mathematics which emerged in the 20th century looking at how players in a game interact. In game theory any interaction between two or more people can be described as a game. In this musing I’m looking at how game theory can influence healthcare both in the way we view an individual patient as well as future policy.

There are at least two kinds of games. One could be called finite, the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.     

James P. Carse Author of Finite and Infinite Games

Game theory is often mentioned in sports and business

In a finite game all the players and all the rules are known. The game also has a known end point. A football match would therefore be an example of a finite game. There are two teams of eleven players with their respective coaches. There are two halves of 45 minutes and clear laws of football officiated by a referee. After 90 minutes the match is either won, lost or drawn and is definitely over.

Infinite games have innumerable players and no end points. Players can stop playing or join or be absorbed by other teams. The goal is not an endpoint but to keep playing. A football season or even several football seasons could be described as an infinite game. Key to infinite games then is a vision and principles. A team may lose one match but success is viewed by the team remaining consistent to that vision; such as avoiding relegation every season or promoting young talent. Athletic Club in Spain are perhaps the prime example of this. Their whole raison d'être is that they only use players from the Basque Region of Spain. This infinite game of promoting local talent eschews any short term game. In fact their supporters regularly report they’d rather get relegated than play non-Basque players.

Problems arise by confusing finite and infinite games. When Sir Alex Ferguson retired as Manchester United manager after 27 years in 2013 the club attempted to play an infinite game. They chose as his replacement David Moyes, a manager with a similar background and ethics to Ferguson, giving him a 9 year contract. 6 months into that he was fired and since then United have been playing a finite game choosing more short term appointments, Louis van Gaal and Jose Mourinho, rather than following a vision.

It’s easy to see lessons for business from game theory. You may get a deal or not. You may have good quarters or bad quarters. But whilst those finite games are going on you have your overall business plan, an infinite game. You’re playing to keep playing by staying in business.

What about healthcare?

So a clinician and patient could be said to be players in a finite game competing against whatever illness the patient has. In this game the clinician and patient have to work together and use their own experiences to first diagnose and then treat the illness. The right diagnosis is made and the patient gets better. The game is won and over. Or the wrong diagnosis is made and the patient doesn’t get better. The game is lost and over. But what about if the right diagnosis is made but for whatever reason the patient doesn’t get better? That finite game is lost. But what about the infinite game?

Let’s say our patient has an infection. That infection has got worse and now the patient has sepsis. In the United Kingdom we have very clear guidelines on how to manage sepsis from the National Institute of Clinical Excellence. Management is usually summed up as the ‘Sepsis Six’. There are clear principles about how to play this game. So we follow these principles as we treat our patient. We follow the Sepsis Six. But they aren’t guarantees. We use them because they give us the best possible chance to win this particular finite game. Sometimes it will work and the patient will get better and we win. Sometimes it won’t and the patient may die. Even if all the ‘rules’ are followed, due to reasons beyond any of the players. But whilst each individual patient may be seen as a finite game there is a larger infinite game being played. By making sure we approach each patient with these same principles we not only give them the best chance of winning their finite game but we also keep the infinite game going; of ensuring each patient with sepsis is managed in the same optimum way. By playing the infinite game well we have a better chance of winning finite games.

This works at the wider level too. For example, if we look at pneumonia we know that up to 70% of patients develop sepsis. We know that smokers who develop chronic obstructive pulmonary disease (COPD) have up to 50% greater risk of developing pneumonia. We know that the pneumococcal vaccine has reduced pneumonia rates especially amongst patients in more deprived areas. Reducing smoking and ensuring vaccination are infinite game goals and they work. This is beyond the control of one person and needs a coordinated approach across healthcare policy.


Are infinite games the future of healthcare?

In March 2015 just before the UK General Election the Faculty of Public Health published their manifesto called ‘Start Well, Live Better’ for improving general health. The manifesto consisted of 12 points:

The Start Well, Live Better 12 priorities from Lindsey Stewart, Liz Skinner, Mark Weiss, John Middleton, Start Well, Live Better—a manifesto for the public's health, Journal of Public Health, Volume 37, Issue 1, March 2015, Pages 3–5,

There’s a mixture of finite goals here - establishing a living wage for example - and some infinite goals as well such as universal healthcare. The problem is that finite game success is much more short-term and easier to measure than with infinite games. We can put a certain policy in place and then measure impact. However, infinite games aimed improving a population’s general health take years if not decades to show tangible benefit. Politicians who control healthcare policy and heads of department have a limited time in office and need to show benefits immediately. The political and budgetary cycles are short. It is therefore tempting to choose to play finite games only rather than infinite.

The National Health Service Long Term Plan is an attempt to commit to playing an infinite game. The NHS England Chief Simon Stevens laid out five priorities for the NHS focusing health spending over the next 5 years: mental health, cardiovascular disease, cancer, child services and reducing inequalities. This comes after a succession of NHS plans since 2000 which all focused on increasing competition and choice. The Kings Fund have been ambivalent about the benefit those plans made.

Since its inception the National Health Service has been an infinite game changing how we view illness and the relationship between the state and patients. Yet if we chase finite games that are incongruous to our finite game we risk that infinite game. There is a very clear link between the effect of the UK government’s austerity policy on social care and its impact on the NHS.

We all need to identify the infinite game we want to play and make sure it fits our principles and vision. We have to accept that benefits will often be intangible and appreciate the difficulties and scale we’re working with. We then have to be careful with the finite games we choose to play and make sure they don’t cost us the infinite game.

Playing an infinite game means committing to values at both a personal and institutional level. It says a lot about us and where we work. It means those in power putting aside division and ego. Above all it would mean honesty.

Thanks for reading

- Jamie