Interactive modelAdvanced Microadvanced

Auction Theory

First-price, Vickrey, and common-value auctions, bidding strategy and the winner's curse.

Equilibrium: v* = 60.0, b* = 45.0

Current equations

First-price optimal bid: b = 0.75·vBid your value (second-price): b = 1·vYour value: v = 60

You value the item at the orange line. Bid that much and winning earns you nothing, so in a first-price auction you shade your bid below your value. The blue line shows the optimal shading: with three rivals, bid about three-quarters of what it is worth to you.

Shift the curves

Number of rival bidders0

More rivals force you to bid closer to your true value: shading shrinks toward zero.

How much the item is worth to you0

Slide your value and read your optimal first-price bid off the blue line.

The Auction Theory model, in writing

Definition

The design and strategy of selling under competition: first-price (bid your shaded value), second-price/Vickrey (bid your true value), and common-value auctions (beware the winner's curse).

Vickrey: truthful bidding is dominant; Revenue Equivalence: standard formats yield equal expected revenue

The intuition

In a second-price auction your bid only sets WHETHER you win, not what you pay, so honesty is free. In common-value settings, winning is bad news, you were the most optimistic estimator, so rational bidders shade down.

Exam tip

Say WHY truth-telling is dominant in Vickrey (your bid never affects your price), not just that it is.

Related models in Advanced Micro

Consumer Theory (Indifference Curves) →Producer Theory (Isoquants & Isocosts) →Cournot Competition →Adverse Selection (Lemons Problem) →