In many examples of competitive bidding (e.g., government construction contracting) the relevant object is either partially divisible or ill-defined, in contrast to much of the recent theoretical work on auctions. In this paper we consider a more general class of auctions, in which bidders name a “menu” of offers for various possible actions (allocations) available to the auctioneer. We focus upon “first-price” menu auctions under the assumption of complete information, and show that, for an attractive refinement of the set of Nash Equilibria, an efficient action always results. Our model also has application to situations of economic influence, in which interested parties independently attempt to influence a decision-maker's action.