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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.
1. Diagram this simultaneous move game.
2. What is the Nash Equilibrium of the game?
3. Would the sides want to ban lawyers?

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Answer:

1. Please find it attached.

If both of them don't get lawyers they will each make half of the $5 million being $2.5 million a piece.

If one side hires a lawyer and the other doesn't, the side with the lawyer will win 0.9 of $5 million which is $4,500,000. However they would have paid the lawyer $200,000 so that payout drops to $4,500,000. The other would make 0.1 which is $500,000.

If they both get a lawyer they will each get half which is $2,500,000 but they would both have paid their lawyers $200,000 a piece so the net payout would be $2,300,000.

2. The Nash Equilibrium is the alternative that it would not serve either party to deviate from as it serves them both well. The Nash Equilibriums would be If both don't get a lawyer or if both get a lawyer.

3. Yes they would because without lawyers they would make more money as they would not have to pay the $200,000 in fees.

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If neither team hires a lawyer, they have a 50% probability of winning, hence the projected pay out is $1 million divided by two equals $500,000.

Computation Table;

                                                     Management

                                           No-lawyer                  Lawyer

Labor        No-lawyer      500,000;500,000     250,000;550,000

                   Lawyer         550,000;250,000     300,000;300,000

If they both employ a lawyer, their odds of winning are still 50%, but they'll have to pay money of $200,000, therefore the projected compensation will be $500,000 - $200,000 = $300,000.

Answer 2:

If both employ a lawyer or neither hires a lawyer, there is a Rational Function.

Answer 3:

Yes, both sides would prohibit the use of a lawyer because no lawyer results in more earnings.

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