4 . 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 $3 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $100,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win four fths, or 0.8, of the time. Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To nd the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.) Management (M) No Lawyer Lawyer Lb L NoLawyer L:I$ I,M:I$ I L:I$ ,M:I$ I aor(] Lawyer L:I$ I,M:I$ I L:I$ ,M:I$ I The Nash equilibrium for this game is for Management to V a lawyer, and for Labor to V a lawyer