Question 1 - Nash Equilibria a) Suppose that we have the following game with 2 players: Player 2 A B C Player 1 X 4, 2 3, 4 3, 5 Y 3, 2 4, 5 2, 1 Z 2, 4 6, 1 5, 2 Find the mixed nash equilibrium in this game. (hint 1: do not start by assigning a probability to every pure strategy and then use EV, [X, o] = EU2 [Y, o] = EU, [Z, o] to find the value of each probability... you will get into trouble and waste a lot of time in your calculations leading you nowhere; hint 2: start by showing that player I can create a mixed strategy that will strictly dominate Y... then as Y is strictly dominated it will never be played and you can eliminate it... in the end you only need to work with a 2 x 2 game) b) Now suppose that we have a game with three players. A is a girl and B is a boy who like each other and like to spend time together. C is a good friend of A and B and likes spending time with both of them. A and B like spending time with C but they prefer to spend time with each other, alone. Each one of them has to decide between going to the opera or to a football game. A prefers to go to the opera over football, B prefers to go to a football game over opera and C doesn't like either activity and just wants to spend time with A and/or B (in particular, C prefers to spend time with both of them at the same time). We cannot draw a 3/ table with payoffs but we can use two tables to represent the whole game (assume that the payoffs are represented as (UA = UB = UC)): If C chooses O If C chooses F Opera Football Opera Football Opera 6,2,2 1,0,1 Opera 8,4,0 0,1,1 Football 0,1,1 4.8,0 Football 1,0,1 2,6.2 What are the two Nash equilibria where all three players only use pure strategies. (please be careful in your explanation)