This lecture explains risk averse, risk neutral, and risk acceptant (risk loving) preferences in a game theoretical context.

**Takeaway Points**

- Someone with risk neutral preferences simply wants to maximize their expected value. For example, consider a lottery that gives $1 million 50% of the time and $0 50% of the time. A risk neutral person would be indifferent between that lottery and receiving $500,000 with certainty.
- Someone with risk averse preferences is willing to take an amount of money smaller than the expected value of a lottery. In the 50/50 lottery between $1 million and $0, a risk averse person would be indifferent at an amount strictly less than $500,000.
- Risk aversion means that an individual values each dollar less than the previous. These preferences explain why people buy insurance.
- Someone with risk accceptant preferences requires an amount of money greater than the expected value of a lottery to be bought out. In the 50/50 lottery between $1 million and $0, a risk averse person would be indifferent at an amount strictly greater than $500,000.
- Risk acceptance means that an individual values each dollar more than the previous. Someone with such preferences would exhibit behaviors similar to a compulsive gambler.
- We can use exponents to conveniently represent these preferences. Consider the utility function x
^{a}, where x is the amount of money an individual receives. a = 1 represents risk neutral preferences; a > 1 represents risk acceptant preferences; a < 1 represents risk averse preferences. - Nothing in expected utility theory prevents us from modeling risk preferences. However, those preferences should be directly built into the payoffs you enter into a game matrix.