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 fifths, 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 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 labor (l) no lawyer l: $ , m: $ l: $ , m: $ lawyer l: $ , m: $ l: $ , m: $ the nash equilibrium for this game is for management to a lawyer, and for labor to a lawyer.