lottery (probability)

Definition

Suppose a decision maker is faced with a decision determining which of a finite number of possible outcomes, "prizes", he will receive. Denote the set of possible outcomes by $O = \{A_1, A_2,..., A_K \}$. Given the set of outcomes $O$, the relevant space for conducting analysis is the set of lotteries over the outcomes in $O$.

A lottery in which outcome $A_k$ has probability $p_k$ (where $p_1,...,p_K$ are nonnegative real numbers summing to $1$) is denoted by

and the set of all lotteries over $O$ is denoted by $\mathcal{L}$.

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 13.
2. https://en.wikipedia.org/wiki/Lottery_(probability)