Perhaps I’m missing something, but it seems to me this doesn’t cover risk-aversion properly.
One great feature is that it implicitly accounts for risk aversion: not risking $100 for a 10% chance to win $1000 and 90% chance to win $0 just means that for you, utility($100) > 10%utility($1000) + 90%utility($0).
Suppose for me, utility($100) = 1, and utility($1000) = 100, and utility($0) = 0. Then, utility($100) < 10%utility($1000) + 90%utility($0); (1 < 10). Now suppose I am extremely risk-averse; I prefer to never wager any money I actually have and will practically always take a certain $100 over any uncertain $1000. It does not seem this configuration is impossible in an agent, but is not supported by your model of risk-aversion.
Does this merely mean that this type of risk-aversion is considered irrational and therefore not covered in the VNM model?
Does this merely mean that this type of risk-aversion is considered irrational and therefore not covered in the VNM model?
Yes. If you are risk-averse (or loss-averse) in terms of marginal changes in your money, then you’re not optimizing any consistent function of your total amount of money.
Perhaps I’m missing something, but it seems to me this doesn’t cover risk-aversion properly.
Suppose for me, utility($100) = 1, and utility($1000) = 100, and utility($0) = 0. Then, utility($100) < 10%utility($1000) + 90%utility($0); (1 < 10). Now suppose I am extremely risk-averse; I prefer to never wager any money I actually have and will practically always take a certain $100 over any uncertain $1000. It does not seem this configuration is impossible in an agent, but is not supported by your model of risk-aversion.
Does this merely mean that this type of risk-aversion is considered irrational and therefore not covered in the VNM model?
Yes. If you are risk-averse (or loss-averse) in terms of marginal changes in your money, then you’re not optimizing any consistent function of your total amount of money.