Auctions for Divisible Resources: Price Functions, Nash Equilibrium, and Decentralized Update Schemes

One of the many emerging applications for software agents are their ability to serve as proxies for trade and bartering. This has led to the analysis and development of auction protocols for various goods. We consider agent-mediated allocation of computational and network resources through market mechanisms. Single-good and combinatorial auctions do not apply readily to these products, thus we propose a divisible auction that is proportionally fair and has low signaling and computational costs. The structure of the auction enables us to represent optimal responses as price functions. From this we are able to characterize agent valuations and prove the existence of a unique Nash equilibrium. We further develop a decentralized algorithm that allows the agents to converge to the operating point without sharing private information.