1. Reputation for High Quality. A buyer must decide whether to buy (B) or not buy...

Transcribed Image Text:

1. Reputation for High Quality. A buyer must decide whether to buy (B) or not buy (DB) a good from a seller. The seller chooses whether to supply a good of high quality (H) or low quality (L). The surplus to each party from each action pair are summarized below. (The first number in each entry is the buyer's surplus.) Assume throughout that quality cannot be observed before the good is purchased: the buyer must simply decide whether or not to buy and can only observe quality after purchase. Both parties discount the future at rate 0 < 5 < 1. H Seller L B Buyer 2,1 0,-1 0,0 -1,2 Figure 1: Product quality stage game (a) Suppose that the game is played once. Identify any Nash equilibria and whether each of them is Pareto optimal. (b) Suppose the game is repeated infinitely often, with each party observing at each date the history of actions chosen up to that date. What is the lowest value of the discount factor & that supports the supplier providing high quality at each date as part of a subgame-perfect Nash equilibrium of the infinitely repeated game? Explain how you know the outcome is a subgame perfect Nash equilibrium outcome. 1. Reputation for High Quality. A buyer must decide whether to buy (B) or not buy (DB) a good from a seller. The seller chooses whether to supply a good of high quality (H) or low quality (L). The surplus to each party from each action pair are summarized below. (The first number in each entry is the buyer's surplus.) Assume throughout that quality cannot be observed before the good is purchased: the buyer must simply decide whether or not to buy and can only observe quality after purchase. Both parties discount the future at rate 0 < 5 < 1. H Seller L B Buyer 2,1 0,-1 0,0 -1,2 Figure 1: Product quality stage game (a) Suppose that the game is played once. Identify any Nash equilibria and whether each of them is Pareto optimal. (b) Suppose the game is repeated infinitely often, with each party observing at each date the history of actions chosen up to that date. What is the lowest value of the discount factor & that supports the supplier providing high quality at each date as part of a subgame-perfect Nash equilibrium of the infinitely repeated game? Explain how you know the outcome is a subgame perfect Nash equilibrium outcome.