References: FrankA.Cowell(2018).Microeconomics:PrinciplesandAnalysis.OxfordUniversityPress.

1. Find one Nash Equilibrium. You need to show your work.

2. Other than the one you showed in 1, is there any other Nash Equilibrium?

Question 5 [25 marks] Consider the following three-player simultaneous-move game where (i) each player 2' E {1, 2, 3} has two pure strategies 3, = {s,,t,~} and (ii) the -th element in each cell is player 's payoff for each 3' E {1, 2,3}. For each player's,C E {1, 2,3}, let (p,,1 pi) be player is mixed strategy where p, 6 [0,1] is the probability assigned to s, (and thus 1 p, is assigned to 23,). Player 3 33 t3 Player 2 32 t2 31 31 Player 1 Player 1 $1 1'21 (a) Find one Nash equilibrium. You need to show your work. [15 marks] (b) Other than the one you showed in (a), is there any other Nash equilibrium? Dis- cuss. [10 marks]