Proving the Mysterious Vickrey Auction

Image taken from google. Vickrey Auction can be extended to Real Time Bidding (RTB)

Vickrey auction is known for its “too good to be true” property. This type of auctions is designed in such a way that bidders will bid at their true valuations. In other words, they will not lie! How does that even work? Without further a do, let us use a simple game theory to prove that.