Question

5. Individual Problems 15-5 Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win nine tenths, or 0.9, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer No Lawyer L: ,M:$ M: $ Labor (L) L: $ Lawyer M: L: $ M: $ a lawyer The Nash equilibrium for this game is for Management to a lawyer, and for Labor to

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Answer 1

In this game, let's go through each scenario to get their expected payoffs for the same. First, let's take the case when Labor as well as management doesn't hire lawyer. In this case, each side is expected to win half the time, such that the expected payoff would be same for both and would be, [C)* ($5 million)] $2.5 million. Now, let's take the case when both sides hire a lawyer, such that along with the profit of $5 million, there would be a cost of lawyer as well if they win, while there would be cost of lawyer only if they lose, though both will have the same expected payoff, which would be, [(%)* (S5 million - $0.2 million)] + [(%) * (- $0.2 million)] $2.3 million If Labor chooses to hire a lawyer, while management chooses not to, then Labor can expect to win nine tenths of the time, such that labor's expected payoff would be, [(0.9) * ($5 million $0.2 million)] [(0.1)* (-$0.2 million)] $4.3 million. The expected payoff for management would be, [(0.1)* (S5 million)] [(0.9)* (0)] = $0.5 million Now, if management chooses to hire lawyer, while Labor chooses not to, then similar to the previous case, the expected payoff of management, in this case, would be $4.3 million. While that of labor would be, $0.5 million The payoff matrix would be, Management (M) Lawyer No Lawyer No Lawyer L: S2.5million M:2.5million L: 0.5million M:4.3million Labor (L) Lawyer L: 5 4.3 million M:0.5million L: 2.3million M2.3million The Nash Equilibrium in this game is for management to hire a lawyer, and for labor to hire a lawyer as well

This is computed by finding the dominant strategy for both the players, which would be to hire a lawyer no matter what the other chooses. In case of management, if Labor chooses not to hire a lawyer, then management would have the highest payoff if it chooses to hire a lawyer as well, which would be $4.3 million. If Labor chooses to hire a lawyer, then also, management would be better off by choosing to hire a lawyer, with the expected payoff of $2.3 million. Similar is the case for labor as well