4 . Individual Problems 15-5Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one si

4 . Individual Problems 15-5Every 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. 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 not hire or hire a lawyer, and for Labor to hire or not hire a lawyer.