1. Below we solve, in several steps, for a Nash equilibrium of the following game: 2 L R T 7, 2 2, 7 3,6 B 2, 7 7, 2 4,5 Let p ( [0, 1] be the probability that player 1 plays T. Let q c [0, 1] be the probability that player 2 plays L and r ( [0, 1] the probability that player 2 plays C. Then a mixed strategy profile is represented by (p, q, r), where q t r 0}. Show that in each Nash equilibrium of the game, each player receives the same (and maximum) payoff from any two strategies that are played with positive probabilities (under, of course, the assumption that his opponents play the Nash equilibrium strategies); i.e., for each Nash equilibrium o E E of I and each i ( N, if s;, $; E supp(o;), then u, (s;; 0 ;) = u;(s;,0_;). 3. In class and in Problem 1, we saw how to solve games for which Nash equilibria are visually represented as intersections of best responses. A drawback of this approach is that it is applicable only when strategies are represented by at most three parameters (can you visualize a graph in a four- or higher- dimensional space?). For games with multiple players and multiple strategies