(Inspired by the HBS case The Toy Game.) There are two primary sellers of toy cars, Matchbox and Hot Wheels. Suppose there are 100 consumers, each of whom wishes to buy at most one car: a toy car is worth $5 to a consumer. Half of the consumers are Matchbox fans; the other half are Hot Wheels fans. However, fandom is fickle: a consumer will buy the cheapest car unless both cars are equally costly to the consumer, in which case the consumer buys according to his fandom. The marginal cost of producing a car is $1 for both firms. Matchbox chooses its price, and then Hot Wheels chooses its price; afterwards, each consumer decides which car to buy, if any. Note that no calculus is required to understand the strategies in this case.

a) Predict Matchbox's profits. Be sure to explain your reasoning.

b) Suppose now that Matchbox can issue coupons for a $1 rebate on its toys to its fans (and only its fans). Determine an optimal pricing strategy for Matchbox. What are your expected profits?

c) Suppose now that Hot Wheels can issue coupons for a $1 rebate to its fans after Matchbox issues its own coupon (but before pricing decisions are made). Will Hot Wheels wish to issue the coupon? Will Matchbox, anticipating Hot Wheels' action, decide to issue a coupon? What are the final expected profits and prices?

d) Explain intuitively how Matchbox and Hot Wheels are "differentiating" their product by issuing these coupons.