Definition:Rational Decision-Maker

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 $C$ of consequences of the moves available to $P$.

Let $g: A \to C$ be the consequence function on $A$.

Let $B \subseteq A$ be a the set of moves which are feasible.

$P$ is a rational decision-maker $P$ chooses an element $a^* \in B$ such that:
 * $\forall a \in a^*: \map g {a^*} \succsim \map g a$

where $\succsim$ is the preference relation on $C$.

That is, that $P$ solves the problem:
 * $\ds \max_{a \mathop \in B} \map U {\map g a}$

where $U$ is the utility function on $C$.

It is assumed that $P$ uses the same preference relation for all $B \subseteq A$.