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We analyze the 'roundness level' of bids-defined as the number of zeros at the end of the bid-in public procurement auctions for construction works in Okinawa Prefecture, Japan, where a bid-rigging case was filed. We hypothesize that bid rigging increases the roundness of bids through the bid coordination process. Specifically, winners choose round numbers to avoid any miscommunication when they announce their planned bids to other ring members, and losers prefer round numbers when they arbitrarily bid above the winning bid. We find that (1) there is a positive relationship between the roundness of a bid and its relative value as a fraction of the reserve price, (2) the roundness of bids is higher when collusion is active than when it is inactive, (3) among the ring bids, the roundness of the lowest bids is even higher than that of the other bids, and (4) bids by non-ring members are also round when collusion is active
