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Posts Tagged ‘probability’

Game Theory: Rafa is the King

Together with Formula 1, tennis is the other sport I love – and my favourite player by far is Rafa!

We often apply game theory to various sports and consider how players, teams and individuals can think strategically. One of the big debates in tennis is ‘who is the best ever’ and I argue that Nadal is the greatest, based on a huge range of metrics.

I saw this article in the Economist, providing analysis and comparison between some of the best tennis players. It shows how we can use economic thinking, probability, game theory and analysis to come to something of an answer about who is the greatest, considering the various players’ runs to the title in the Grand Slams. Of course the reason I’m posting this is because according to the Economist, Rafa is the best! And the reasoning is very sound. Enjoy. I certainly did.

Sorry Roger: Rafael Nadal is not just the King of Clay The Economist (13/09/17)


  1. What is game theory and why is it useful?
  2. How does the rating system aim to measure the skill of a tennis champion?
  3. In this particular scenario, why is it important to use probabilities?
  4. We can use game theory to think about penalty shoot outs and whether footballers play to the Nash equilibrium. Can we also use the Nash equilibrium when thinking about tennis? (Think about the serve!)
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A flood of insurance concerns

Next year a government agreement with insurance companies is set to end. This agreement requires insurance companies to provide cover for homes at a high risk of flooding.

However, in June 2013, this agreement will no longer be in place and this has led to mounting concerns that it will leave thousands of home-owners with the inability either to find or afford home insurance.

The key thing with insurance is that in order for it to be provided privately, certain conditions must hold. The probability of the event occurring must be less than 1 – insurance companies will not insure against certainty. The probability of the event must be known on aggregate to allow insurance companies to calculate premiums. Probabilities must be independent – if one person makes a claim, it should not increase the likelihood of others making claims.

Finally, there should be no adverse selection or moral hazard, both of which derive from asymmetric information. The former occurs where the person taking out the insurance can hide information from the company (i.e. that they are a bad risk) and the latter occurs when the person taking out insurance changes their behaviour once they are insured. Only if these conditions hold or there are easy solutions will the private market provide insurance.

On the demand-side, consumers must be willing to pay for insurance, which provides them with protection against certain contingencies: in this case against the cost of flood damage. Given the choice, rational consumers will only take out an insurance policy if they believe that the value they get from the certainty of knowing they are covered exceeds the cost of paying the insurance premium. However, if the private market fails to offer insurance, because of failures on the supply-side, there will be major gaps in coverage.

Furthermore, even if insurance policies are offered to those at most risk of flooding, the premiums charged by the insurance companies must be high enough to cover the cost of flood damage. For some homeowners, these premiums may be unaffordable, again leading to gaps in coverage.

In light of the agreement coming to an end next year, there is pressure on the government firstly to ensure that insurance cover is available to everyone at affordable prices and secondly to continue to build up flood defences in the most affected areas. Not an easy task given the budget cuts. The following articles provide some of the coverage of the problems of insuring against flood damage.

200,000 homes ‘at flooding risk’ BBC News (3/1/12)
MPs slam government flood defences Post Online, Chris Wheal (31/1/12)
Flooding: 200,000 houses at risk of being uninsurable The Telegraph (31/1/12)
Flood defences hit by government cuts ‘mismatch’, says MP Guardian, Damian Carrington (31/1/12)
Fears over cash for flood defences The Press Association (31/1/12)
ABI refuses to renew statement of principles for flood insurance Insurance Age, Emmanuel Kenning (31/1/12)


  1. Consider the market for insurance against flood damage. Are risks less than one? Explain your answer
  2. Explain whether or not the risk of flooding is independent.
  3. Are the problems of moral hazard and adverse selection relevant in the case of home insurance against flood damage?
  4. If ABI doesn’t put in place another agreement to provide insurance to homeowners at most risk of flooding, what could be the adverse economic consequences?
  5. Is there an argument for the government stepping in to provide insurance itself?
  6. Explain why insurance premiums are so much higher for those at most risk of flooding. Is it equitable?
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Should cyclists have insurance?

Most people are risk-averse: we like certainty and are generally prepared to pay a premium for it. The reason is that certainty gives us positive marginal utility and so as long as the price of insurance (which gives us certainty) is less than the price we place on certainty, we will be willing to pay a positive premium. By having insurance, we know that should the unexpected happen, someone else will cover the risk. As long as there are some risk-averse people, there will always be a demand for insurance.

However, will private companies will be willing to supply it? For private market insurance to be efficient, 5 conditions must hold:

1. Probabilities must be independent
2. Probabilities must be less than one
3. Probabilities must be known or estimable
4. There must be no adverse selection
5. There must be no moral hazard

If these conditions hold or if there are simple solutions, then insurance companies will be willing and able to provide insurance at a price consumers are willing to pay.

There are many markets where we take out insurance – some of them where insurance is compulsory, including home and car insurance. However, one type of insurance that is not compulsory is that for cyclists. No insurance is needed to cycle on the road, but with cycle use increasing and with that the number of accidents involving cyclists also increasing, the calls for cyclists to have some type of insurance is growing. If they are hit by someone without insurance and perhaps suffer from a loss of income; or if they cause vehicle damage, they will receive no compensation. However, whilst the risk of accident is increasing for cyclists, they are still statistically less likely to cause an accident than motorists. Perhaps a mere £30 or £40 per year for a policy is a price worth paying to give cyclists certainty. At least, this is what the Association of British Insurers (ABI) is claiming – hardly surprising when their members made a combined loss of £1.2 billion!

Cyclists ‘urged to get insurance’ BBC News, Maleen Saeed (26/11/11)
Cyclists urged to get more insurance by … insurance companies Road.CC, Tony Farrelly (26/11/11)
The future of cycle insurance Environmental Transport Assocaition (24/11/11)


  1. With each of the above conditions required for private insurance to be possible, explain why each must hold.
  2. What do we mean by no moral hazard and no adverse selection? Why would their existence prevent a private company from providing insurance?
  3. Using the concept of marginal utility theory, explain why there is a positive demand insurance.
  4. What might explain why cyclists are less likely to take out insurance given your answer to the above question?
  5. Do you think cyclist insurance should be compulsory? If governments are trying to encourage more sustainable transport policy, do you think this is a viable policy?
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