Definition:Profile/Less Player

Definition

Let $G$ be a game.

Let $N$ be the set of players of $G$.

Let $V$ be a variable defining some aspect of each of the players.

Let $x = \family {x_i}_{i \mathop \in N}$ be a profile of $V$.

Then $x_{-i}$ is used to denote $x$ for all players except for $i$:

$x_{-i} := \family {x_j}_{j \mathop \in N \setminus \set i}$

Thus the profile $x = \family {x_i}_{i \mathop \in N}$ can be denoted:

$\family {x_{-i}, x_i}$

for some $x_i$ for $i \in N$.

Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): Chapter $1$ Introduction: $1.7$: Terminology and Notation