‘collusive-seeming Equilibria’ in the Uniform-price Auction

The fixed-supply uniform-price auction suffers from existence of “collusive-seeming equilibria” in which all bidders dramatically shade their bids and very low prices may be realized. Our main result is that such equilibria do not exist in a family of “money-prize perturbations” of the uniform-price auction, in which a small payment discount is split among all rationed bidders. To shed light on what drives this result, we also examine three natural variations with endogenous supply – called “adjustable-supply”, “increasable-supply”, and “decreasable-supply” auctions – in an illustrative degenerate model. Collusive-seeming equilibria exist in the decreasablebut not in the adjustablenor increasable-supply auctions. Finally, we apply McAdams (2000) to prove existence of a pure strategy “competitive equilibrium” in the uniform-price auction as well as in all of its money-prize perturbations, under assumptions which guarantee that an appropriate single-crossing property is satisfied.