Definition:Game/Payoff

Definition

The payoff of a game is the reward or punishment made to a player at the end of the game as a result of combination of the various strategies employed.

Let $G$ be a game.

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

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

Let $u_i: A \to \R$ be a the payoff function on $A$.

A payoff is the value of $u_i$ for a given $a \in A$.

Also known as

Some sources hyphenate: pay-off.

Sources

• 1983: Morton D. Davis: Game Theory (revised ed.) ... (previous) ... (next): $\S 1$: An Overview
• 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
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): payoff