Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor above which the perfectly collusive outcome with equal sharing is sustainable on a stationary path. Under the Market Clearing Price rule, only one step is required. That is, within the class of step bidding functions with a finite number of steps, maximal collusion is attained with simple price-quantity strategies exhibiting capacity withholding.