This question is from " Networks, Crowds, and Markets: Reasoning about a Highly Connected World" textbook in chapter 6

In this question we will consider several two-player games. In each payo matrix below the rows correspond to player As strategies and the columns correspond to player Bs strategies. The rst entry in each box is player As payo and the second entry is player Bs payo. (a) Find all Nash equilibria for the game described by the payo matrix below. 6.11. EXERCISES 203 Player A Player B L R U 1,1 3,2 D 0,3 4,4 Player A Player B L R U 5,6 0,10 D 4,4 2,2 (b) Find all Nash equilibria for the game described by the payo matrix below (include an explanation for your answer). [Hint: This game has a mixed strategy equilibrium. To nd the equilibrium let the probability that player A uses strategy U be p and the probability that player B uses strategy L be q. As we learned in our analysis of matching pennies, if a player uses a mixed strategy (one that is not really just some pure strategy played with probability one) then the player must be indierent between two pure strategies. That is, the strategies must have equal expected payos. So, for example, if p is not 0 or 1 then it must be the case that 5q + 0(1q) = 4q + 2(1q) as these are the expected payos to player A from U and D when player B uses probability q.]