Question 3 (Problem 7U6 - 15 points ] Recall the game of chicken we discussed in class. DEAN Swerve Straight Swerve 0, 0 1, 1 JAMES . Straight 1, -1 2, -2 (a) Find the mixed strategy Nash equilibrium in this game , including the expected pay - offs for James and Dean . (b) Now suppose that the payoff of James from being "tough" when Dean is "chicken" is 2, rather than 1. Find the mixed strategy Nash equilibrium in this variant of the game . Is Dean's probability of playing Straight higher now than before ? What about James's probability of playing Straight? (c) How have the two players' expected payoffs changed? Are these differences between the two versions' equilibrium outcomes paradoxical in light of the new payoff structure? Explain how your ndings can be understood in light of the opponents indifference principle Question 4 (MBTA FreeRiding - 30 points) Consider a toy model of interaction between the MBTA Transit Police and riders. There is a ne f > 0 for being caught free -riding , so riders prefer to pay $3 for the ride if they are checked. Otherwise , they prefer to free -ride and keep the $3. Checking is costly, so the Transit Police incur a cost of $1 if they check, irrespective of whether the rider has paid the fare or is freeriding. However, when they do catch a free-rider, the moral satisfaction offsets the cost of checking, so they get the payoff of $3+f in this case . The game can be represented in the following normal form RIDER Pay FreeRide Check -1,3 3+f,i3if MBTA P OLICE Don't Check 0, 3 0, 3 (a) Find the mixed -strategy Nash equilibrium of the game as a function of ne f . What is the optimal rate of screening and fare compliance ? (b) How do the optimal rate of screening and fare compliance change with f ? (c) Could the law-makers set a value of fine f to deliver perfect fare compliance in equi - librium ? If so, what is it