Competing mechanisms with multi-unit consumer demand

The competing mechanisms literature is extended to a market setting in which firms have fixed capacity, and there is a continuum of consumers who desire multiple units and can only purchase from one firm. Firms choose incentive compatible mechanisms in which consumers report their utility types; consumption of the good and payments of the numeraire are continuous functions of the reports. Uniform price auctions with reserve prices, reinterpreted as direct mechanisms, are not consistent with equilibrium. However, modified auctions without reserve prices but with type-specific entry fees do constitute an equilibrium of the competing mechanisms game under additional regularity assumptions. When all firms announce fixed prices at the perfectly competitive level, this profile also constitutes an equilibrium of the competing mechanisms game.