I'd like help with (1.B)

powerinl army, with elephants as shock troops, load by one of the great strategic generals, Hannibal. For most of the war, the Romans followed the strategy of Fabius Comctator, (Le, "Fabius the Delayer"). They avoided combat Flammill's areby in Italy while undermining his base of support in other parts of the Mediterranean. Below is an Escape Everion 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 North Pass South Pass Hannibal p North Pam 5, -5 0.0 1-p South Pass O.0 3, -5 (I A) 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 nchopes 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, Le, he must get the same expected peyoff from both. (1.B) Trace out the expected payoffs for Hannibal for each of his strategies given levels of q chosen by Fabius. Hint: If q =0, what is the payoff to Hannibal from choosing the North Pass? If q = 1, what is the payoff to Hannibal from the North Pass? Now do the same for the other strategy, for the South Pass. Where these curves intersect is the q" for Fabius. The height of the curve at this point also gives the expected payoff to Hannibal. What is the expected equilibrium payoff for Hannibal? Do the calculation. Payoff Hannibal T 10 g