Design of Multidimensional Franchise Auctions by an Ignorant Principal

Abstract

The paper’s main aim is to identify under which conditions the criterion of prior-independent optimality is applicable in the design of multidimensional franchise auctions. We first establish an impossibility result for second-score auctions by showing that in single-crossing environments necessary and sufficient condition for score functions to be optimal in this sense is that bidders have equal variable cost functions. Then we show that the result is not confined to the second-score format but holds for any scoring auction under stochastic independence. Therefore, a regulator who has no information at all about firms’ costs cannot in such circumstances avail himself of prior-independent optimality as choice criterion. Conversely, if variable cost functions are equal across potential contractors, as is likely in certain public services markets, and the regulator knows it, it is possible for him to implement a prior-independent optimum by scoring bids according to the social welfare function under various auction formats, including first- and second-score auctions. This simple prescription however no longer applies if the regulator is ignorant about market demand too. In this case a fully rational choice of the score function is precluded, though it may be possible to make a reasonable one: a brief discussion of this point closes the paper.