How to do these two questions. Please write steps for all parts.

Q1. There are ten customers and two cafes A and B. Customers want to purchase from the cafe with fewer customers. A customer's payoff when purchasing from cafe A is -mA, where mA is the number of customers excluding herself purchasing from A. A customer's payoff when purchasing from cafe B is -mg, where my is the number of customers excluding herself purchasing from B. a. Find a pure-strategy Nash equilibrium of this game. Prove that it is a Nash equilib rium. (3 marks) b. Suppose each player chooses cafe A with probability , and cafe B with probability ?. Show that this is a (mixed-strategy) Nash equilibrium. (5 marks) c. Compare the expected number of customers for each cafe in the pure-strategy and mixed-strategy Nash equilibria. (2 marks) ( Remember to show all working)Q4. Now consider collusion between n price-setting firms which produce a homogenous good. The monopoly profit in this industry is 100. The n firms collude by setting the monopoly price and dividing the monopoly profit evenly between them. a. When the game is played once, show that there is a profitable unilateral deviation for each firm from this collusive agreement. (2 marks) b. Now suppose that the firms interact repeatedly, with the probability of the game continuing each period being 6. Consider the following set of strategies: firms begin in a cooperative phase, colluding until there is a deviation. If there is a deviation, the firms enter a punishment phase, in which they price at marginal cost for T periods. After the punishment phase finishes, they revert to the cooperative phase. Show that these strategies constitute a Nash equilibrium of the repeated game if 1 - 87+1 > n(1 - 6). [Hint: recall that: x + or + 8'x + ... = =] (5 marks) c. Intuitively, why is a lower o required to support collusion in the repeated game when T is larger? (2 marks) (Remember to show all working)