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EC 401001 - FINAL EXAM (1) (10 I 20 = 30 points in total) Consider the following game theoretic scenario: Two army generals A and B are engaged in a battle. The battle is being fought in two geographic fronts, north and south. Each general has exactly two battalions of soldiers. Both generals decide simultaneously how to deploy the two battalions in the two fronts. A battalion of soldiers cannot be broken up in smaller groups during deployment. So, the option available to a general is limited to deploying both battalions in the northern front while leaving the southern front vulnerable, deploying both battalions in the southern front while leaving the northern front vulnerable, and sending one battalion in each of the two fronts. In any war front, the general who has deployed more battalions wins the battle in that front. If both generals deploy same number of battalions in a given front, no one wins, and it is classed a \"deadlock\". Each general gets a payoff of 10 from Winning the northern front and 5 from winning the southern front, and only 1 if the war ends in a deadlock. (a) Write down this game in normal form using the payoff table given below (i.e., list the strategies and payoffs). General B General A (b) Find all NE of this gameiboth in pure and mixec strategies. What are the players' payoffs in each of these Nash Equilibria