Definition:Game

Definition
A game is a problem of strategy between two or more parties in which all parties involved seek to maximise their outcome.

A game $G$ can be specified by:
 * its players
 * the moves available to each player
 * the preference relation for each player:

that is:
 * $G = \left\langle{N, \left\langle{A_i}\right\rangle, \left\langle{\succsim_i}\right\rangle}\right\rangle$

$G$ can also be specified by:
 * its players
 * the moves available to each player
 * the payoff function for each player:

that is:
 * $G = \left\langle{N, \left\langle{A_i}\right\rangle, \left\langle{u_i}\right\rangle}\right\rangle$

Also see

 * Examples of games can be found here.