Expected utility V N-M expected utility function U(D)=4P+…+RN Proposition 1: a utility function U: @->R is an expected utility function if and only if it's liner, that is vk L∈and(a,…a)>0.∑ar=1 We have:UC∑aL)=∑AaU(L)Expected utility • v.N-M expected utility function: • Proposition1: a utility function is an expected utility function if and only if it’s liner, that is we have: 1 1 ( ) U L u P u P = + + N N U :L →  1 ( , ) 0, 1 k k i    = k L and L     1 1 ( ) ( ) K K k k k k k k U L U L   = =  =