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Game Theory: Payoff matrix, strategy

Two basketball players, Barbara and Juanita, are the best offensive players on the school's team. They know if they "cooperate" and work together offensively-feeding the ball to each other, providing screens for the other player, and the like- they can each score 12 points. If one player "monopolizes" the offensive game, while the other player "cooperates," however, the player who monopolizes the offensive game can score 18 points, while the other player can only score 2 points. If both players try to monopolize the offensive game, they each score 8 points. Construct a payoff matrix for the players that captures the essence of the decision of Barbara and Juanita to cooperate or monopolize the offensive game.

a. If the players play only once, what strategy do you expect the players to adopt?

b. If the players expect to play in many games together, what strategy do you expect the players to adopt? Explain.

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