I want to know how to solve this exercise:

lilT Diluted Happiness: Consider a relationship between a bartender and a cus- tomer. The bartender serves bourbon to the customer and chooses x E ID. 1], which is the proportion of bourbon in the drink served, while 1 x is the pro- portion of water. The cost of supplying such a drink [standard 4-ourtce glass) is era. where c 2:- D. The customer, without knowing it, decides on whether or not to buy the drink at the market price p. If he buys the drink his payoff is tor p, and the bartender's payoff is p ch. Assume that u r:- c and all pay- offs are common knowledge. If the customer does not buy the drink he gets all and the bartender gets ch. Because the customer has some experience, once the drink is bought and he tastes it, he learns the value of x, but this is only after he pays for the drink. apter l Repeated Games a. Find all the Nash equilibria of this game. b. Now assume that the customer is visiting town for ll] days. and this \"bar game" will be played on each of the It) evenings that the cus- tomer is in town. Assume Lhat each player ies to maxinze Lhe {non- discounted) sum of his stage payoffs. Find all the subgame-perfect equilibria of this game. c. Now assume that the customer is a local. and the players perceive the game as repeated innitely many times. As sume that each player tries to maximize the discounted sum of his stage payoffs. where the discount rate is 3 E (D, 1). What is the range of prices p (expressed in the parameters of the problem] for which there exists a subgame perfect equilibrium in which every day the bartender chooses x = l and the customer buys at the price p? d. For which values of 5 [expressed in the parameters of the problem} cart the price range that you found in (c) exist