Lotteries and expected utility A lottery:L=(P,…,)P≥0∑P=1 A compound lottery: L=(L 1k:1 va20∑P=1andL=(P…,P) A simplified lottery of(L, . Lk;a, ak) 1sL=ax1L1+…+ a,l or l=(P;…P) P=a,P1+…+a,PR See the figLotteries and expected utility • A lottery: • A compound lottery: and . • A simplified lottery of is or See the fig 1 ( , , ) L P P = N 1 , 0 1 N i i i i P P =   =  1 ( , , ) k k L P P k N = 1 1 ( , , ; , ) L L L = k k   1 , 0 1 N k i i k P  =   =  1 1 ( , , ; , ) L Lk k   L L L = + +   1 1 k k 1 ( , ) L P P = k 1 1 k P P P n n k n = + +  