Assignment Preferences and Combinatorial Auctions

The bipartite matching problem and the closely related assignment problem form a cornerstone of the Networks literature. In this paper we consider the problem of a firm whose valuation function for bundles of goods is determined by an optimal assignment of goods among several agents (or tasks,) each with independent valuations for each good. Though this model of preferences may be useful on its own for several particular markets, the underlying assignment network structure also leads us to an easy to use first approximation of preferences in more general settings. We show that because of its computational tractability and polynomial growth of user input, the resulting restricted bid language (which we call bid tables) is useful as a dynamic revelation phase in a multi-stage hybrid auction. We demonstrate that this representation is one for which linear price signals are appropriate, and show how lowest Walrasian equilibrium prices can be easily computed for preferences that can be represented as bid tables, generalizing the earlier work of Demange et al. (1986).