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 $1 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 lawyers or 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 three-quarters 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?