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 $\sequence {\succsim_i^*}$ of preference relations over $C$ is defined as:

$\forall a, b \in A: \paren {a \succsim_i b} \iff \paren {\map g a \succsim_i^* \map g b}$

Sources

• 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