Network Pricing and The Price of Anarchy

We consider a network in which products consist of combinations of connecting edges and each edge corresponds to a perishable resource. In our model, different revenue-maximizing “controllers” determine the prices associated with different resources and the price of the product is the sum of the prices of the constituent resources. At one extreme, a single controller might set all resource prices – at the other extreme there would be a different controller associated with each resource. We show that decentralized pricing always leads to lower total revenue relative to centralized pricing. For the uncapacitated networks, we develop bounds on the “price of anarchy” – the loss from totally decentralized control versus centralized control – as the number of controllers increases. We present provably convergent algorithms for calculating Nash equilibrium prices for both the uncapacitated and capacitated cases. We present numerical analyses to illustrate the effect on producer and consumer surplus of decentralization. While we develop our model in the context of airline pricing, it is applicable to any service network such as freight transportation, pipelines, and toll roads as well as to the more general case of supply chain networks. ∗Columbia Business School and Nomis Solutions, e-mail: [email protected] †Columbia Business School, e-mail: [email protected]