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This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity-constrained firms. Under two popular definitions of the uniform price, when each firm sets a price-quantity pair, perfect collusion with equal sharing of profit is easier to sustain in the uniform price auction than in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. Even when firms may set bids that are arbitrary finite step functions of price-quantity pairs, in repeated uniform price auctions maximal collusion is attained with simple price-quantity strategies exhibiting capacity withholding.