How does bidder collusion impact the social welfare and revenue outcomes of different auction formats?

1 First-price sealed-bid auction

In a first-price sealed-bid auction, each bidder submits a single bid without knowing the bids of others, and the highest bidder wins and pays their bid. Bidder collusion in this format can reduce the revenue of the seller by lowering the bids of the colluders and discouraging other bidders from participating. However, the colluders also face a trade-off between lowering their bids and increasing their chances of winning. Moreover, the colluders need a credible mechanism to enforce their agreement and prevent defection or cheating. Therefore, the extent of the revenue loss and the social welfare loss depends on the degree of collusion, the number of colluders, the distribution of values, and the enforcement mechanism.

2 Second-price sealed-bid auction

In a second-price sealed-bid auction, also known as a Vickrey auction, each bidder submits a single bid without knowing the bids of others, and the highest bidder wins and pays the second-highest bid. Bidder collusion in this format can also reduce the revenue of the seller by lowering the bids of the colluders and discouraging other bidders from participating. However, the colluders face a different trade-off than in the first-price sealed-bid auction. In this case, lowering their bids does not affect their chances of winning, but only their payoff if they win. Therefore, the optimal strategy for the colluders is to bid their true values and split the surplus among themselves. This strategy eliminates the incentive to defect or cheat, but also reduces the social welfare loss compared to the first-price sealed-bid auction.

3 English auction

In an English auction, also known as an ascending-price auction, the price starts low and increases gradually until only one bidder remains. Bidder collusion in this format can also reduce the revenue of the seller by signaling or dropping out early to let one of the colluders win at a low price. However, the colluders face a higher risk of detection and intervention by the seller or other bidders in this format, as their behavior is more visible and suspicious. Moreover, the colluders need a way to select the winner among themselves and to compensate the losers for their forgone profits. Therefore, the effectiveness of collusion in this format depends on the size of the collusion group, the information available to the seller and other bidders, and the allocation and transfer rules among the colluders.

4 Dutch auction

In a Dutch auction, also known as a descending-price auction, the price starts high and decreases gradually until one bidder accepts it. Bidder collusion in this format can also reduce the revenue of the seller by delaying or refraining from accepting the price until it reaches a low level. However, the colluders face a similar trade-off as in the first-price sealed-bid auction, as lowering the price reduces their payoff but increases their chances of winning. Moreover, the colluders need a way to coordinate their actions and to prevent free-riding or jumping ahead by other bidders. Therefore, the impact of collusion in this format depends on the speed and transparency of the price decline, the number and distribution of bidders, and the enforcement and punishment mechanisms.