Need help with question (1.B)

1. Mixed Strategies and the Punic War. In the Second Punic War, 218-202 B.C.E., the Romans faced a powerful army, with elephants as shock troops, lead by one of the great strategic generals, Hannibal. For most of the war, the Romans followed the strategy of Fabius Cunctator, (i.e., "Fabius the Delayer"). They avoided combat with Hannibal's army in Italy while undermining his base of support in other parts of the Mediterranean. Below is an Escape-Evasion Game where Generals Hannibal and Fabius have to choose between two mountain passes. If they choose the same one, there will be a battle and Fabius, whose army is much weaker, will lose. The game is depicted below: Fabius q 1-q North Pass South Pass Hannibal p North Pass 5 , -5 0, 0 1-p South Pass 0, 0 3, -5 (1.A) Is there a NE in pure strategies? If so, what is it? (1.B) Is there a NE in mixed strategies? If so, what is the mixed strategy for Fabius? Note that q is the probability that Fabius will choose the North Pass and 1 - q is the probability that Fabius will nchoose the South Pass. Show your work to get full credit. Hint: to find q*, the player Hannibal has to be indifferent between choosing the north and south passes, i.e. he must get the same expected payoff from both