This question from Network,crowd and Market, question 24.2

Consider an airport that is trying to sell exclusive rights to operate a wireless access network in its terminals. Depending on what proportion of all trav- elers use the network, it can become congested and result in a low-quality experience for everyone. Specially, suppose for simplicity that there are N travelers at any given time during normal hours in the airport, and if a fraction x of them attempt to use the network concurrently, then the payoff to each of them will be 1/2 - x. (We can view this payoff as the amount theyd be willing to pay for the service.) (a) When the airport sells the rights to operate the network to a third-party access provider, this provider will make back what it pays for the rights by charging travelers in the airport a fee to connect to the networks. How much should the airport expect to be able to sell the rights for, how much will the third-party access provider in turn charge to travelers, and what will be the resulting sum of payoffs to all travelers? Explain. (b) Suppose instead that the airport were to let people use the service for free. What would be the sum of payoffs to all travelers in this case? Explain.