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# Insurance Market with Asymmetric Information

(The contents of this page are provided by the Finance and Economics Experimental Laboratory at the University of Exeter.)

You may find the example subject instructions helpful.

• Pre-requisite knowledge: ?
• Suitable modules: ?

### Abstract

Students play together in pairs as a consumer and an insurance company. The consumer has to decide whether or not to buy insurance and the company has to decide whether or not to sell insurance. The two decisions are made simultaneously. There is a 50% risk of a 'bad' outcome (from the consumer's point of view), when the consumer would benefit from buying insurance. The payoff matrices for the good and bad outcomes are as follows.

GOOD   Company Sells Insurance
Yes No
Consumer Buys Insurance Yes 0.6, 0.6 1, 0
No 1, 0 1, 0

Yes No
Consumer Buys Insurance Yes 0.6, -0.4 0, 0
No 0, 0 0, 0

The bad outcome costs the consumer 1 if he/she does not have insurance. The good or bad outcomes only affect the insurance company if it sells insurance and the consumer buys it. The insurance costs 0.6 to fully cover the loss of 1, so the payoff to the company is 0.6 for the good outcome and -0.4 for the bad outcome. The consumer is risk averse and has extra utility of 0.2 for the security of being insured, so the consumer's payoff when insured is 0.6 for both the good and bad outcomes.

The instructor can configure two versions of the game, one where neither player knows whether the outcome is good or bad and another where only one player is informed - in this case the consumer. Neutral terminology is used whereby the consumer and insurance company are referred to as the row player and column player respectively.

### Intended Learning Outcomes

2. It is not always good for the consumer to be better informed.

3. Characteristics of insurance markets in general.

### Discussion of Likely Results

If neither player knows whether the outcome is good or bad (and the two outcomes are equally likely), the consumer is better off buying insurance and the company is better off selling it. The consumer has an expected payoff of 0.6 when insured and 0.5 when uninsured. The company has an expected payoff of 0.1 when the consumer is insured and 0 when the consumer is uninsured. So there is profit in the market for both players

If, however, the consumer knows whether the outcome is good or bad, the company is better off not selling insurance. The consumer is better off only buying insurance when the outcome is bad, so the company can only sell to those consumers who are a bad risk. The company now has an expected payoff of -0.4 when the consumer is insured and 0 when the consumer is uninsured, so it cannot make a profit and the market for insurance collapses. Since insurance also benefits the consumer, this outcome is bad for both players.

For insurance to be profitable, the company needs to balance the risk across a large random sample of consumers. Adverse selection disrupts this by leaving the company with a disproportionately large number of consumers who are a bad risk, similar to a lemon market where the bad business drives out the good. (Alongside this is moral hazard, the tendency of consumers who are insured to act more recklessly.) To counter this, insurance companies require consumers to disclose factors that make them a bad risk, e.g. smokers have to pay more for health insurance. Insurance may then become prohibitively expensive for certain groups of consumers.