Abstract

We consider a weighted proportional allocation of resources that allows providers to discriminate usage of resources by users. This framework is a generalization of well-known proportional allocation accommodating allocation of resources proportional to weighted bids or proportional to submitted bids but with weighted payments.

We study a competition game where everyone is selfish: providers choose discrimination weights aiming at maximizing their individual revenues while users choose their bids aiming at maximizing their individual payoffs. We analyse revenue and social welfare of this game. We find that the revenue under so called price anticipating users is lower bounded by k/(k+1) times the revenue under standard third-degree price discrimination with a set of k users excluded. Under price anticipating users with linear utility functions, we find that the social welfare is at least 1/(1+2/\sqrt{3}) of the maximum social welfare (approx. 46%), and show that this bound is tight. We extend the latter result to a broad class of utility functions, which accommodates many utility functions found in literature and to an oligopoly of multiple competing providers. Our results suggest that the weighted proportional allocation achieves competitive revenue and social welfare despite the fact that everyone is selfish.

The mechanism allows for resource constraints described by general polyhedrons that accommodate a variety of resources, including networks of communication links, systems of computing resources, and sponsored search ad slots.

Joint work with Thanh Nguyen.