Definition:Consequence Function with Probability

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Definition

Let $G$ be a game.

Let $P$ be a player of $G$.

Let $A$ be the set of moves available to $P$.

Let $C$ be the set of consequences of those moves.

Let the consequences of those moves be affected by a random variable on a probability space $\Omega$ whose realization is not known to the players before they make their moves.


A consequence function for $P$ is a mapping from $A \times \Omega$ to $C$:

$g: A \times \Omega \to C$

interpreted as that $\map g a$ is the consequence when the move is $a \in A$ and the realization $\omega$ of the random variable is $\omega \in \Omega$.


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