Equilibrium and negotiation in multiple resource auctions

The application of economic ideas to control electronic technology is an emerging design paradigm. In network and computational settings, divisible auctions are a viable tool for regulation of services such as bandwidth and processing share. Often, the performance of an agent in the system depends simultaneously on the allocation received from several resources. In this paper, we investigate the extension of a proportionally fair divisible auction to the case where agents´ utilities have complementarities across multiple resources. We show the existence and uniqueness of a Nash equilibrium under various symmetry conditions. We propose a negotiation algorithm and prove that under relaxation, the scheme is locally stable for particular agent characterizations.