4th and Goal: Overtime (5 points total) Consider the following modified version of the 4th and Goal game that was discussed in class. In this version, we imagine that the offense has an additional pure strategy available: the run-pass option. The run-pass option (RPQO) is a hybrid formation in which the quarterback can choose to either run or pass based on what the defense does. We can incorporate this new strategy into our model by adding a row to our original payoff matrix corresponding to the new strategy, as seen below: Defense CP R | (50,50) (80,20) P | (90,10) (20,80) RPO | (70,30) (60, 40) Offense (a) (1 mark) Is the mixed strategy Nash equilibrium that we had found in class still a Nash equilibrium in the modified game? (b) (1 mark) Let's assume that the defense mixes according to the mixed strategy op = qCR + (1 q)CP. Calculate the offense's expected payoffs from each of their three pure strategies. () (1 mark) Each of the three expected payoffs that you found above can be thought of as a function of g. Setting 0