Definition:Lottery

Definition

A lottery is a game in which the consequence of each move is determined by the realization of a random variable.

Let $X$ denote the set of prizes which a player may receive.

Let $\Omega$ denote the set of possible states.

A lottery is a mapping $f: X \times \Omega \to \R_{\ge 0}$ such that:

$\forall t \in \Omega: \ds \sum_{x \mathop \in X} \map f {x, t} = 1$

Probability Model

In a probability model, a lottery is a probability distribution over a set of prizes.

State-Variable Model

In a state-variable model, a lottery is defined as a mapping from a set of possible states into a set of prizes.

Sources

• 1991: Roger B. Myerson: Game Theory ... (previous) ... (next): $1.2$ Basic Concepts of Decision Theory
• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $\text I$ Strategic Games: Chapter $2$ Nash Equilibrium: $2.1$: Strategic Games