# Economic Classroom Experiments/Insurance
## The Insurance Experiment: Introduction

This experiment illustrates how additional information can damage insurance markets making all parties worse off. This possibility was first mentioned by Hirschleifer (1971).
It demonstrates how undergraduate students’ own decisions when they act either as company or as consumer (player) do depend on the information they have. This asymmetric information leads to adverse selection in an insurance market. When companies realise this problem they stop supplying insurance policies and the insurance market will break down. In this experiment the consumers have the chance to receive information about their risk type. We want to explain how this additional information influences the decision of whether to buy or not an insurance contract.

## Description of the Experiment

At the beginning of the lesson every student receives one sheet of paper. More specifically 50% receive an information sheet to act as a company and the remaining to act as a player (consumer). The instructions for companies and players are slightly different. The student who has to act as a company has to decide whether or not she/he wants to supply an insurance contract over a fixed payment. And then the player has to decide if it worth of buying an insurance or not. This is the decision problem in the first round.
In the second step a program for testing the risk type of the player is available. Both, companies and players know that this software is available. The player will definitely undergo the testing of his risk type. Again the company-player has to decide if he/she is willing to supply the insurance. The players are asked to decide whether or not to buy the policy in both cases. Their final decision depends whether the people are a risk type and suffer from an illness or not.
The students have five minutes to read through the instructions and afterwards the experiment instructor/teacher will repeat the most important things. Here are the two sheets which are distributed to players and companies:

### Decision Problem: Player

You have a fantastic job as a professional video-game player that pays £100,000 per year. The group Parents against Violence of Videogames PAVLOV secretly put subliminal messages in the video game Halo2. These messages will cause a condition in people that have played Halo2 at the start of the year 2007. This will cause players to start drooling whenever they shoot people in video games. Such drooling is detrimental to playing the game at a world-class level. Fortunately, this condition is only triggered in roughly half the population that played Halo2. Also fortunately, several expensive sessions with a renowned psychologist can cure the condition. The cure is worth it and costs £100,000. There is an insurance company that may offer you insurance for a price of £60,000.
You have to decide on whether or not to buy the insurance if it is made available. (Assuming that you purchase the cure whether or not you have insurance.) At the same time, the insurance company has to decide whether or not to offer the insurance.
The payoffs for both the company and the video game player are displayed in the following table. The payoffs depend upon whether the player tries to buy insurance, whether the company is willing to sell insurance, and upon whether the player is not susceptible (Good) or susceptible (Bad) to the messages. Note that the payoffs are in utility and the player is risk-averse. This causes having 40k to be utility 60 while having a 100k to be utility 100 and 0k to be utility 0.
Please make the decision whether to try to buy insurance by circling your choice: BUY or NOT BUY.
___________________________________________________________ Step 2
Suddenly Microsoft announces that it has a downloadable program that will present a test that will tell you for certain whether you were susceptible to the subliminal messages. The insurance company does not know this information.
We ask you to make the decision to buy the insurance contingent on the outcome of the test. Do so by circling your choice.
If you ARE susceptible, will you BUY or NOT BUY.
If you ARE NOT susceptible, will you BUY or NOT BUY.

### Decision Problem: Company

You are the CEO of an insurance company. There is a professional video-game player that earns £100,000 per year. The group Parents against Violence of Videogames PAVLOV secretly put subliminal messages in the video game Halo2. These messages will cause a condition in people that have played Halo2 at the start of the year 2007. This will cause players to start drooling whenever they shoot people in video games. Such drooling is detrimental to playing the game at a world-class level. Fortunately, this condition is only triggered in roughly half the population that played Halo2. Also fortunately, several expensive sessions with a renowned psychologist can cure the condition. The cure is well worth it and costs £100,000.
You have to decide to offer this player insurance at a rate of £60,000. (Assume that this is the only possible price.) At the same time the player has to decide whether or not to buy the insurance.
The payoffs for both the company and the video game player are displayed in the following table. The payoffs depend upon whether the player tries to buy insurance, whether the company is willing to sell insurance, and upon whether the player is not susceptible (Good) or susceptible (Bad) to the messages. Note that the payoffs are in utility and the player is risk-averse. This causes having 40k to be utility 60 while having a 100k to be utility 100 and 0k to be utility 0
Please make the decision whether to offer insurance assuming that there is no way the player can know she/he is susceptible by circling your choice: SELL or NOT SELL.
___________________________________________________________ Step 2
Suddenly Microsoft announces that it has a downloadable program that will present a test that will tell the player for certain whether or not she/he is susceptible to the subliminal messages.
Please make the decision whether to offer insurance knowing that this test is available by circling your choice: SELL or NOT SELL.

## Procedure

* Distribution of the sheets to the students
* Students have 5 minutes to read the instructions
* Instructor/Teacher repeats the main information
* People make their decisions and hand their answer-sheets in
* The sheets are divided into ‘Company’ and ‘Player’ and the decisions in step one and step two are calculated
* The results of the whole class are filled into an Excel Spreadsheet which is projected on the Blackboard via a beamer
* The teacher interprets the results of the experiment together with the students
Hint: when the group is very large, it is probably better only to calculate some of the answer sheets. Otherwise this calculation can last too long and it is boring for the students.

## Theoretical Background

The aggregated payoff table has two Nash Equilibria, where the players are weakly better off by buying insurance and the companies supply insurance. The two actions buying and selling are weakly dominant. But besides this Pareto optimal Nash equilibrium, we have a second Nash equilibrium too, when players do not buy insurance then companies should not even supply them. In the two equilibria (shadowed payoffs) both parties choose the best reply to the behaviour of the other party. (Note that only the Pareto optimal Nash equilibrium is perfect.)

## Results of the Experiment

In the first round we can conclude that most of the companies and the players are willing to sell and pay for the insurance. About 70% of players are willing to buy insurance because of uncertainty about their type. In the beginning the players know that the probability to be a risk type is 50%. That means that about 50% of the players will be drooling when they are shooting people in this special computer game. As a result the players feel insecure and the majority is willing to buy the insurance from the companies.
Because of the uncertainty which is faced by the players, companies have a large profit opportunity. Most of the companies wanted to benefit from the situation, and as a result 88% of the companies were willing to sell insurance. Thus the large majority of companies choose the best reply against the average behaviour of the players, which is selling insurance. This means that the theoretical predicted equilibrium will be reached by the majority of 61% (88% times 69%) of the decisions made. We can conclude that the insurance market works quite efficient in the first round.
In the second round, however, the conditions are changing dramatically because of the announcement of the existence of a downloadable software program which presents a test that will tell whether or not you are susceptible to suffer from drooling during the game.
The players have to make the decision whether to buy insurance or not in accordance to the degree of susceptibility towards the disease. We expected that players would not buy insurance when they are informed that are not susceptible. 97% of the students did not buy insurance when they knew that they will not suffer from drooling. The opposite happened when people were acting as susceptible person, 93% of students bought insurance. Obviously the different kinds of information led to two totally different ways of behaviour from the players. The testing software leads to adverse selections! When they know that they will definitely have to suffer from drooling their willingness to buy insurance is much higher. However, when they are informed that they are not in a risk then the players are not willing to pay for insurance.
For the companies we can see that after the results they are not willing to sell insurance because they are realised the problem of adverse selection and therefore they stop supplying insurance policies. Because of risk adversity, companies are in apposition to realise that only ‘bad’ people will be willing to buy insurance. Thus the company in the future will be obliged to pay the insurance back. Thus the companies can not make any profits with their clients and therefore have no incentive to supply policies. Only 13% of companies supplied insurance in the second round of the experiment. These companies would face a loss because 57 out of 59 customers are from the ‘bad’ type. They are definitely looking forward to receive payments from the companies because they suffer from the game.
The insurance market will collapse because of the operating loss of the companies. The loss is a direct consequence of the adverse selection which is caused from the type testing software. In reality people who are really suffering would have no possibility to insure their selves against this ‘disease’. Also the companies are not able to make a profit in this environment. In general adverse selection leads to inefficiencies and especially in the insurance market it leads to a breakdown of the markets.

### Interpretation

The experiment shows that people are using the information to maximise their payments. We observed the behaviour was very close to the ex-ante efficient outcome (which was buying and selling insurance) in the first round. Additional information for buyers, however, destroys the ex-ante efficient outcome. Ex-post it is efficient not to buy insurance at all when you are a ‘good’ player and to buy insurance when you are a ‘bad’ player. Also in the second round we can observe a strong tendency of the participants of the experiment to choose the best reply and this leads to a quite efficient outcome of 84% and 81%. The derived conclusions of the model are limited because of the simplicity of the setup and the fixed amount of insurance. In reality companies would probably charge flexible prices for example.
But we can say when information is only attainable for consumers in the insurance market it leads to adverse selection. Only people who definitely know that they will become ill or will be suffering from something are willing to buy insurance. Whilst ‘healthy’ people with the same information are not willing to buy any insurance any longer. Therefore the market becomes for insurance companies uninteresting, because the possibility of making profits is decreasing. Especially if the payment of the policy is fixed, like in this particular case.
When we relate this result to reality we can say that adverse selection leads not only to inefficient markets but it also reduces the possibility for risk suffering people to buy cheap insurances.

### More details about the Results

About 121 undergraduate students took part at the experiment in March 2006. These were students at the University of Exeter taking Economics of Social Policy taught by Alison Wride. The procedure was supervised by Dieter Balkenborg and Todd Kaplan. The procedure was exactly as described above and the setup of the experiment was identical to the way described in the beginning. These are the results of the two rounds where we divided the students in two groups (Company and Players). Answers which did not fit the instructions where not taken into account.

#### First Round

About 53 companies out of 60 (88%) decided to sell insurance while only 7 companies (12%) take the decision not to sell insurance. 42 players out of 61 (69%) decided to buy insurance, while 19 players (31%) decided not to buy insurance.
If we multiply the percentage of the players who wanted to buy insurance (69%) with the percentage of the companies which wanted to sell insurance (88%) we get 61% of players who can sign a contract with a company. With the same procedure you can calculate the other percentages in the table above.
As in the information text mentioned an income of £40.000 gives the player a utility level of 60. When the player is insured he will always have an income of £40.000. In all other ways there is a 50% chance to suffer from drooling and the expected income is thus only £50.000, because of uncertainty. The possible utility level is therefore 50.
The next step was to measure the expected utility-payoffs of the players and the companies according to the decisions they made in the first round when they have not been supplied with the testing software yet. (All the numbers are measured in utility)
The utility-payoff for the players who bought insurance is 60. All the other payoffs will be 50 because of the 50% chance to suffer from the illness during the game. To calculate the subtotal payoffs in the experiment we multiplied the payoffs in the table with the percentages of the companies whether or not they wanted to sell insurances. (60*88% + 50*12% = 58.8). The total payoff of the players is the weighted sum of people who wanted to buy or not to buy insurance and equals 56.1 which can be seen as social welfare level. (58.8*69% + 50*21% = 56.1)
We followed a similar procedure for the companies to calculate the expected utility-payoffs. The expected payoff for a company which runs a contract is 10, because the firm has a 50% chance to either earn £60.000 or to lose £40.000. Then we multiplied the payoffs of the companies with the percentages of the players who wanted to buy insurance (10*69% = 6.9). We compute the total expected payoff (6.1) of firms by multiplying 6.9 with the percentage of companies (88%) which were willing to supply insurance. Hence also companies make profits in the insurance market even when the probability of customers who occupy payments in the future is 50%.
The overall utility-payoff of the society would be the sum of player’s payoffs (56.1) and companies’ payoffs (6.1) which equals 62.2.

#### Second Round

After the decisions in the first round all participants of the experiment were informed that a downloadable test is available which shows whether or not the player is susceptible. If a player is susceptible she/he would be seen as ‘bad’ person, if not susceptible she/he would be seen as ‘good’ person. The players were asked to act once as ‘bad’ and once as ‘good’ person. However the companies could only decide once whether or not supply insurance. As a consequence the decisions changed dramatically in comparison to the result of the first round. 93% of the players bought insurance when they were acting as ‘bad’ person whilst only 3% bought insurance when they were a ‘good’ person.
We can conclude that the test influenced the decisions of players and companies. Only 8 companies out of 60 (13%) decided to sell insurance and 52 companies (87%) decided not to sell insurance. The following table shows how we derived the different percentages we need to estimate the payoffs.
We followed the procedure of the first round and calculated the expected payoffs. All numbers in the table above are measured in utility level. The payments for the ‘good’ players would be very high because nobody has the danger of becoming ill and thus only few people sign an insurance contract. Thus the players save their whole wage and have a high utility. However the payments of the ‘bad’ players are very low, because everybody faces the possibility of the illness and even if people want to sign insurance, the supply of insurances is too low. The average payoff would be 53.7 and is lower than in the first round (56.1).
Obviously players are not buying insurance when they have the information that they are not susceptible of becoming ill. Hence the companies can make hardly any profits, the total utility-payoffs for companies equals 0.3 in the experiment. This outcome becomes even worse when people are informed that they are susceptible (‘bad’). Only ‘bad’ people, who would be receiving payments from the insurance in the future, are now willing to buy insurance. Hence the companies would even make a loss of –5 on average.
Also the overall average payoff with the same likelihood of ‘good’ and ‘bad’ players is negative (-2.4). Thus the insurance market will break down, because of the unwillingness of companies to supply insurance. The reason for the collapse is the adverse selection which gives players a huge advantage in decision making and leads to inefficiencies in the insurance market.

## Computerized Version

There is a computerized version of this experiment available on the Exeter games site.
You may find the sample instructions helpful.

## Conclusion

The Insurance Experiment shows students in an easy way how asymmetric information can lead to inefficient outcomes. Especially in the insurance market adverse selection can lead to a collapse of the whole market. Only ‘bad’ people will try to buy insurance and no company is willing to insure people because of the asymmetric information. As consequence people who are willing to buy insurance are not able to do so.
However, the simplification that the rate of payment is fixed did not allow the charge higher payments from the consumers when the company knows that only ill people are buying insurance. The overall statement stays the same, perfect adverse selection can lead to a break down of insurance markets. The experiment is very suitable for application in class and is a good basis for further discussions about asymmetric information and its consequences.

## Hints for the use of the spreadsheet

The spreadsheet with all the tables and already programmed formulas needed is provided at the homepage as well. Thus it is quite easy and not time consuming to cheek the answer-sheets after the experiment and sort it for buyers and sellers. For the first round you have to fill in only the number of companies which are either 'do sell' or 'do not sell' insurance in the provided table which you can see below.
After you have done this calculation for the players as well the table will calculate the different percentages automatically.
Then we have to measure the expected payoffs. The utility-payoff for the players who bought insurance is 60. All the other payoffs will be 50 because of the 50% chance to suffer from the illness during the game. To calculate the subtotal payoffs in the experiment we multiplied the payoffs in the table with the percentages of the companies whether or not they wanted to sell insurances. (60*88% + 50*12% = 58.8). The total payoff of the players is the weighted sum of people who wanted to buy or not to buy insurance and equals 56.1 which can be seen as social welfare level. (58.8*69% + 50*21% = 56.1) Again, the different values will be calculated automatically when you fill in the first table.
With the same procedure we are calculating the expected payoffs of the companies.
In the second round we have to distinguish the players to ‘good’ and ‘bad’ which depends on the condition they are. Again we have the number of the companies that have decided to sell or not to sell insurance. Then we are calculating the percentages of the numbers, and we are doing the same procedure for the number of the ‘good’ players that decided to buy or not to buy insurance. You have only to fill in the numbers of the decisions in the provided table below. The values of the percentages will then be calculated by the table. With the same procedure you can easily measure the results for the ‘bad’ players.
All other tables you have seen in the interpretation above are calculated automatically and thus need no further description.

### Footnotes

* ↑ Hirshleifer, J. (1971): “The Private and Social Value of Information and the Reward to Incentive Activity,” American Economic Review, 61, 561–574