Lottery

utility-theory

Definition

Lottery

A lottery $L$ with possible outcomes $S_1,\dots ,S_n$ that occur with probabilities $p_1,\dots ,p_n$ is written as:

$$L=[p_1,S_1;p_2,S_2\dots ;p_n,S_n]$$

where $S_i$ is either an atomic state or another lottery.

Expected Utility

The utility of a lottery is the sum of the probability of each outcome times the utility of that outcome:

$$U([p_1,S_1;\dots ;p_n,S_n])=\sum _{i=1}^n{p}_i\cdot U(S_i)$$