Question - Consider a market with two platforms, "old" and "new", that connect between a buyer and a seller. Suppose that if the buyer and the seller join the same platform, the buyer's payoff is 10 and the seller's payoff is 15. The buyer and the seller cannot interact without joining a platform, and if they join different platforms their payoffs are 0. The old platform cannot charge access prices and is not a strategic player. The new platform is a strategic player that can charge access prices, pB from the buyer and pS from the seller, which can be positive or negative. The platform cannot charge transaction fees. In the first stage, the new platform sets the two access prices. In the second stage, the buyer and the seller observe the two access prices and choose simultaneously to which platform to join. The new platform suffers from "unfavorable beliefs" according to our definition in class: if there is an outcome in which each side expects that the other side will join the old platform, the two sides join the old platform.
(a) Solve for the optimal divide-and-conquer strategy for the new platform. Can the new platform earn positive profits?
(b) Repeat your answer to (a) when the new platform can also charge transaction fees.
(c) Suppose now that the market includes two buyers, buyer 1 and buyer 2, and one seller. The payoff of buyer 1 from meeting the seller is 10 and the payoff of buyer 2 from meeting the seller is 5. The seller has a payoff of 15 from meeting buyer 1 and no payoff from meeting buyer 2. The new platform charges an access price to the seller, pS, and an access price to the two buyers, pB (the platform cannot charge a different access price from each buyer and cannot charge transaction fees). Solve for the optimal divide-and-conquer strategy for the new platform. Can the new platform earn positive profits?