Exercise 1. Finding Nash equilibria Find all pure and mixed strategy Nash equilibria of the following games (i) L R 0,0 1,3 B 3, 1 0,0 (ii) L R T 9, -9 7, -7 B 6, -6 8, -8 (iii ) L C R T 4, 3 2, 7 0 , 4 B 5,5 5, - 1 -4,-2 Exercise 2. Voting Voters in Suburbia are choosing between two candidates, L and R. L is proposing new infras- tructure funded with new taxes. Candidate R is in favour of preserving the status quo, i.e., no new taxes and no new spending. Consider three voters - Alison, Beth, and Chandra - whose preferences and payo ff are as follows. . Alison strictly prefers L to R. She gets a payoff of 2 if L wins but 0 otherwise. . Beth strictly prefers R to L. She gets a payoff of 2 if R wins but 0 otherwise. Chandra is not interested in electoral politics . Nonetheless voting is compulsory in Suburbia so he always votes. He gets 0 if the candidate he votes for wins. Otherwise, his payo ff is - 1. All three individuals - Alison , Beth , and Chandra - vote . Candidates receiving majority of the votes wins. (i) Write down the 3-person normal form game where Alison , Beth , and Chandra are three players and each of them has two strategies - vote for L or vote for R. As described above, their payoffs depend on the outcome of the election