Investor Presentaiton
Bernoulli's resolution relies on expected "utility"
He thought it unrealistic that players value all winnings equally.
▷ In practice, the first million is more valuable than the second million.
(Even though two million dollars is more valuable than one million.)
▷ But all winnings have same weight in an expected value calculation.
Let utility, u(w), denote the value derived from winning w.
▷ Bernoulli believed the increase in utility of the winnings should be
inversely proportional to total wealth.
▷ This implies utility should be a logarithmic function of winnings:
Suppose
du
C1
dw w+C₂
where w is the amount won, c₁ is the
relative (marginal) value of wealth, and c₂ is the player's wealth
before playing.
Integrating yields u(w) = Co+c₁ log (w + c₂).
To make calculations in this lecture easier, we assume that
Coc₂ = 0 and c₁
=
= log2(e). In this case, u(w) = log(w).View entire presentation