Barry has a company that makes tea. His only customer is Andrew. Barry has to decide whether to make his tea good or bad quality. Good tea is more expensive to make. Andrew has to decide whether to buy one or two bottles. All the bottles in a given production run are of the same quality, and Barry decides on the quality of the tea without knowing how many bottles Andrew will buy. Andrew cannot tell the quality of the tea when he decides how many bottles to buy, but he does discover the quality later, once he drinks it.

Andrew's payoffs are as follows: 3 if he buys two bottles of tea and it is good quality; 2 if he buysone bottle and it is good quality; 1 if he buys one bottle and it is bad quality; and 0 if he buys two bottles and it is bad quality.Barry's payoffs are: 3 if he makes bad quality tea and sells two bottles; 2 if he makesgood quality tea and sells two bottles; 1 if he makes bad quality tea and sells one bottle; and 0 if he makes good quality tea and sells one bottle.

a. Write down the payoff matrix for this one-shot game and find the Nash equilibrium.

b.Suppose this game is repeated for two periods. Find the subgame-perfect equilibrium of this game. You do not need to draw the game tree but be careful to write down a complete strategy for eachplayer and explain your answer. (Assume that people are patient enough that you don't have to discountthe payoffs to be received in the second periodnote that this is the assumption that we worked with in class)

c. Suppose this game is repeated for two periods. Suppose that instead of choosing the quality of his tea afresh in each period, Barry must set the quality once and for all before period 1. That is, whatever the quality Barry chooses for the first period is then fixed for the rest of the game. Andrew, as before, makes a fresh choice of one or two bottles each period between buying one bottle or two bottles.Andrew knows that Barry's tea quality is fixed, but he does not observe it until he drinks (at the end of the first period). The payoffs in each period are the same as before, except that, if Barry fixes his tea qualityas good, then Barry's payoff if Andrew buys two bottles in a period is reduced from 2 to 1.9. (E.g. ifAndrew buys two bottles of good quality milk in both periods, Barry's final total payoff from the twoperiods would be 1.9+1.9=3.8.) Write down the game tree and find the subgame-perfect equilibrium.