3. Consider the simple payoff matrix below. The game represents payoffs for a manager and a worker where the worker must choose whether to work or to shirk, and the manager

must decide whether to monitor or not to monitor the worker's productivity. Work Monitor Don't monitor -1 1 1 -1 1 -1 Shirk -1 1 a. How do the payoffs above reflect the relative cost of effort to the employee and the cost of monitoring by the manager? (2 points) b. What is the Nash equilibrium of the game, if any? Explain. (Note: There is an equilibrium concept in game theory that allows players to engage in "mixed strategies" where each player chooses a probability of taking a particular action. Some of you who have had courses in game theory are probably familiar with that concept, but I'm not looking for an equilibrium in "mixed strategies" here.) (3 points)/nC. Is the game above an example of a prisoner's dilemma? Explain. (2 points) d. How could you change the cost of effort to the employee or the cost of monitoring by the manager to change the equilibrium of this game? Explain the real-world circumstances where the changes you suggest might be relevant. (3 points) e. Construct a new payoff matrix that would generate (Monitor, Work) as the unique Nash equilibrium of the game. In changing payoffs to generate the equilibrium, explain how you constructed the payoffs to reflect the costs and benefits of monitoring and shirking for the employer and employee. (4 points)