Efficient and strategy-proof mechanisms for general concave user utilities

This paper introduces a novel methodology for designing efficient and strategy-proof direct mechanisms for a class of problems, where the user types are represented by smooth, concave, and increasing utility functions. Such mechanisms facilitate distributed control and allocation of resources. Hence, they are applicable to diverse problems ranging from those in communication networks to energy management. A three-step mechanism design process is presented for deriving the resource allocation and pricing functionals based on user bids in an auction setting. The properties of the resulting class of mechanisms are formally analysed using strategic (noncooperative) games. Although these mechanisms belong to the Groves class, they differ from the Vickrey-Clarke-Groves (VCG) mechanisms. The developed design process is illustrated with analytically tractable examples, which are motivated by network control problems and use scalar-parameterised logarithmic utility functions. It is shown that the resulting schemes are both efficient and truth-revealing (strategy proof) as expected.