Below are a few basic terms used in game theory.

Player: Usually a firm, but sometimes a consumer or any other economic entity for which we want to analyize strategic behavior.
Payoff: The profit a firm earns or the utility a consumer receives or the benefit of interest obtained by a player. Maximizing payoffs is what motivates the player and helps us understand her behavior.
Strategy: An action that a firm or consumer or the player can engage in as one of its possible plays in the game.
Payoff matrix: A simple method of displaying payoff information.