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 $3 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $300,000) 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 fit in the expected payoff, in dollars, for each cell in the matrix.
Management (M)
No Lawyer Lawyer
No Lawyer L: M: S L: S M: S
Labor (L) Lawyer L: M: S L: S M: S
The Nash equilibrium for this game is for Management to_a lawyer, and for Labor to_a lawyer.

At the Nash Equilibrium, there is no incentive for either player to deviate from the strategy they are pursuing as it is the best(most beneficial) one given the strategy of the other player and a situation where there is no cooperation.

If management decides not to hire a lawyer and labor does, management will lose 0.9 of the time, this applies to labor as well. Neither of them will agree to having no lawyer as there is no cooperation and if one does so, the other will seize the opportunity to hire a lawyer and make more.