\begin{definition}[Definition:Rational Decision-Maker]
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''' {{iff}} $P$ 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 $B \subseteq A$.
\end{definition}