S-shaped utility of knowledge in a winner-take-all environment
Principle that the utility function for the amount of knowledge becomes S-curve in a winner-take-all environment.
Assume the following model
The distribution of a person's amount of knowledge follows a unimodal probability distribution
When two people encounter an opportunity to use their knowledge to create utility, the one with the greater amount of knowledge gains utility and the one with the lesser amount gains nothing
Opportunities to use knowledge come with equal probability and the utility gained is constant
The expected value of the utility gained is proportional to the probability that no one else has more knowledge than you
That is, CDF (Cumulative distribution function - Wikipedia)
https://gyazo.com/eb94e3c5c1548d94af7f7ff0e9cd4bca
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