Mechanism design with incomplete languages

A major achievement of mechanism design theory is the family of truthful mechanisms often called VCG (named after Vickrey, Clarke and Groves). Although these mechanisms have many appealing properties, their essential intractability prevents them from being applied to complex problems like combinatorial auctions. In particular, VCG mechanisms require the agents to fully describe their valuation functions to the mechanism. Such a description may require exponential size and thus be infeasible for the agents.A natural approach for this problem is to introduce an intermediate language for the description of the valuations. Such a language must be succinct to both the agents and the mechanism. Unfortunately, the resulting mechanisms are neither truthful nor do they satisfy individual rationality.This paper suggests a general method for overcoming this difficulty. Given an intermediate language and an algorithm for computing the results, we propose three different mechanisms, each more powerful than its predecessor, but also more time consuming. Under reasonable assumptions, the results of our mechanisms are at least as good as the results of the algorithm on the actual valuations. All of our mechanisms have polynomial computational time and satisfy individual rationality.