Second-Price Sealed-Bid Auction
Truthful bidding as a dominant strategy, visualized
N bidders with private values drawn from your choice of distribution. Run a thousand auctions. Compare the histogram of winning bids against winner values — in the Vickrey format the two overlap exactly, which is what dominant-strategy truthfulness looks like.
Dominant strategy:
In a second-price sealed-bid (Vickrey) auction the winner pays the second-highest bid. Truthful bidding weakly dominates every alternative. The experiment: one focal bidder deviates, 1000 times, while the rest bid truthfully — does deviating help?
Flat — every value equally likely.
The histograms ride on top of each other because winning bids equal winner values — bidders are telling the truth. Deviating never beats truthful bidding in expectation: that is the whole point of the Vickrey format.