Consider a monopolist who sells a single unit of a product that may be of high or low quality. Both events occur with probability 1/2. There are at least two identical consumers. Consumers are willing to pay 1 for a functioning product and 0 for a product that breaks down. A high quality product breaks down with probability 1/4 whereas a low-quality product breaks down with probability 3/4. Consider the game in which the firm first observes its quality (but not its actual performance, which is only observed after consumption), then decides whether to enter the market or to choose the outside option. Afterwards consumers simultaneously bid for the product, e.g., in a second-price auction. Assume that consumers bid their true willingness-to-pay. (The product goes to the highest bidder at the price of the second highest bid. With equal bids the product is assigned with equal probability to each bidder.) The outside option gives profit 0.

1. Suppose that the monopolist has a cost of 0 to produce and sell the product independent of its quality. Determine the equilibria in the game in which consumers simultaneously bid for the product and in which consumers bid their true willingness-to-pay.

2. Suppose now that the firm incurs a cost of c > 0 for high quality (and 0 for low quality). This cost is incurred if the firm decides to produce the product and offer it in the market. If it decides not to offer the product, it makes zero profit. Determine equilibria for all values of c ∈ (0, 1). (Consider only equilibria in which high and low-quality firms choose pure strategies.)

3. Return to the case in which the firms’ costs are zero. Suppose now that, at the stage between entering and consumer bidding, the monopolist can commit to a money-back guarantee. This money-back guarantee has the feature that for each faulty unit that is returned the firm pays back the full price. In addition it incurs a transaction cost t ∈ (0, 3) per unit returned. Would the firm offer money-back guarantees in equilibrium? Characterize the equilibrium with money-back guarantee (depending on t).

4. The monopolist is considering to advertise its product by spending A after entering (instead of offering a money-back guarantee). Discuss the effect of such a strategy. Is advertising possibly profitable. Analyze the equilibria in this market. Discuss informally which equilibrium should be selected and what are the features of this equilibrium.