Auctions & Mechanism Design

Auctions and Mechanism Design · Open board

The last lesson of the Game Theory track. Every earlier lesson took a game’s rules as fixed and asked how rational people would play it; this one asks the opposite question, and answers it with the best-known trick in the whole field: an auction.

Before you start. The last lesson showed how two strangers who must meet in New York without phoning end up at the same spot: noon at Grand Central, the obvious default everyone expects. The shape of the situation settled it, not persuasion. This lesson writes that shape on purpose: you set the rules so each player’s own self-interest builds the outcome you want.

The idea in 30 seconds

An auction is a rule for finding out who wants something most, without anyone having to volunteer the true number for free.
In a first-price auction you pay what you wrote, so you’re forced to guess how far below your real value to shade.
In a second-price (Vickrey) auction you pay the runner-up’s bid, which makes writing your true value the smart move no matter what anyone else does - a dominant strategy.
Writing the rules so people’s own self-interest produces the outcome you want, instead of asking them to behave, is mechanism design.
A rule under which telling the truth is each person’s best move is incentive-compatible: honesty costs nothing and can only help.
When a good is worth the same to everyone but its value is unknown, even honest bidding overpays on average - the winner’s curse.

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