Definition:Payoff Function

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Definition

Let $G$ be a game.

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

Let $A$ be the set of moves available to player $i \in N$.


A payoff function on $A$ is a mapping $u_i$ from $A$ to the real numbers $\R$:

$u_i: A \to \R$

defined by the condition:

$\forall a, b \in A: a \succsim_i b \iff \map {u_i} a \ge \map {u_i} b$

where $\succsim_i$ denotes the preference relation for player $i$.


Also known as

This is also known as a utility function, but the latter has also been defined as a mapping from the set of consequences $C$ to $\R$.

It can also be referred to informally as a utility scale.


Also see


Sources