Computing a revenue for VCG auction I would like your help with the following question regarding computing a revenue for a seller of an VCG (vickrey clarke groves) auction, I'm really new to this auctions\game theory so I'd really appreciate an explanation. The auction is as follows: Three bidders,one item. each bidder has a valuation out of a uniform distribution $[0,1]$. How do I calculate the revenue of such auction?

With a single item, the VCG payment rule is just that the winner pays the second-highest bid*. So the expected revenue is the expected second-highest bid. As noted at , for $3$ bidders distributed uniformly and independently on $[0,1]$, this is $0.5$.

* (Edit) perhaps it is helpful to explain this. If the winner were not in the auction, the total utility of the remaining bidders would be the second-highest bid, since that bidder would get the item and gain that utility. If the winner _is_ in the auction, the total utility of the remaining bidders would be zero because the item goes to the winner. So the difference in welfare is the second-highest bid, so this is what the winner must pay.