Monotone Equilibrium in Multi-Unit Auctions

Existence of monotone pure strategy equilibrium is established in the discriminatory and uniform S + a-th price (a in [0, 1]) auctions of S identical objects when bidders are risk-neutral with independent signals. The model requires discrete price / quantity grids and allows for multi-dimensional signals, interdependent values, increasing marginal values, allocative externalities, and two-sided trading. Given no externalities, further, all mixed-strategy equilibria in these auctions must be ex post allocation- and interim expected payment equivalent to some monotone pure strategy equilibrium. Thus, for standard expected surplus / revenue analysis, there is no loss in restricting attention to monotone strategies