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Problem 2. Consider the following two player game (or more accurately, family of games) Player 2 L R T 7.3 0.2 Player 1 2,0 C. 7 (1) Suppose that a can take on any value between -3 and 3. Find regions in which the equilibria are qualitatively the same as in the first problem and regions in which they qualitatively differ. Characterise the equilibria and the equilibrium payoffs in those regions. [20 Marks] (2) Find, as a function of , the (mixed) strategies of the players in the equi- libria in the various regions and graph those mixed strategies as a function of r. In two dimensions, you will not want (or be able) to graph the entire mixed strategy profile, which will involve four numbers. You don't really need to graph all four numbers, but be very explicit about what you are graphing.] [20 Marks] (3) What is the payoff, as a function of a, to Player 1 in each of the equilibria? Graph each of these payoffs as a function of z. That is, make sure that you don't show a payoff for an equilibrium that doesn't exist. If for some value r' there are three equilibria then you should show three values of the payoffs "above" that value of r. If for some other value a" there is only one equilibrium then you should show only one value of the payoff above that value of a.] [10 Marks]