Consider a monopoly platform which serves two sides of a market (e.g. an auction website which brings together buyers and sellers). Each side of the market consists of two agents.

By joining the platform each buyer gains a payoff of 5 if one seller joins the platform and 8 if two sellers join. Each seller gains 4 if one buyer joins and 7 if two buyers join.

Consider the following two-stage game: In the first stage, the platform announces an access price to each side of the market. Assume that the platform may charge different access prices to agents from different sides but cannot price discriminate between agents on the same side. In the second stage, each agent decides whether or not to pay the access price and join the platform. All agents move simultaneously.

What are the access prices that the platform will charge in the subgame perfect equilibrium which maximizes the platform’s profit? What will be the platform’s profit in this case?

Now assume that the utilities of each agent, given above, will decrease by 4 if the other agent of the same side joins the platform. What are the access prices that the platform will charge in the equilibrium which maximizes the platform’s profit? What will be the platform’s profit in this case?