Definition:Profile of Preference Relations

Definition
Let $G$ be a game.

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

Let $C$ be the set $C$ of consequences of the moves available to $P$.

The profile $\left\langle{\succsim_i^*}\right\rangle$ of preference relations over $C$ is defined as:
 * $\forall a, b \in A: \left({a \succsim_i b}\right) \iff \left({g \left({a}\right) \succsim_i^* g \left({b}\right)}\right)$