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

Expert Answers

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At its core, this is a question about the prisoner's dilemma (see source), but at a high level, the prisoner's dilemma is an illustrative example of a decision in which the outcome is sub-optimal (see screenshot for payoff matrix) if the parties involved act in a self-interested manner (i.e., "monopolize the offense"). The optimal solution is for both Barbara and Juanita to cooperate (total payoff of 24 points). If we work under the assumption that the overarching goal (to which the payoff of Barbara and Juanita's respective decisions contribute) is to win the game, then the expectation would be that they would always cooperate and thus contribute the greatest collective points total to the team.

However, there may be competing interests at play. If either Barbara or Juanita (or both) have aspirations to play college / professional basketball, and we employ the assumption that the college / professional teams are most interested in scoring prowess, it becomes less clear what the overarching goal is (i.e., winning games versus being the leading scorer). An important consideration when performing decision analysis is to ensure that it is clear what the end goal is, because, as evidenced in this example, there may be competing interests and multiple interpretations of the "optimal" solution, irrespective of the output of the payoff matrix.

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