ECON7870 Chap.10 Auction Design and Bidding Strategy
Auction Design and Bidding Strategy
Read allocation and payment together
English, Dutch, first-price sealed-bid and second-price sealed-bid auctions differ in what bidders observe and how the winner pays. Strategic equivalences rely on information assumptions.
Open ascending bidding resembles a second-price rule under private values, while Dutch bidding resembles a first-price sealed decision.
Identify the value model before advising
Truthful bidding is weakly dominant for a single object under independent private values and a second-price payment. Common values make winning adverse information, producing the winner's curse.
Multiple advertising slots create another strategic environment where generalised second price is not generally truthful.
Prove strategy by deviations
Hold the highest rival bid fixed and compare it with value. In a second-price private-value auction, an upward deviation can create a loss but cannot improve a beneficial win, while a downward deviation can destroy a gain but cannot improve a desired loss.
In first price, shading changes payment and winning probability together, so beliefs about rivals matter.
Condition on winning
For a common-value object, the winner learns that every competing signal was lower. A naive estimate is therefore too optimistic conditional on winning. More bidders increase competition and can make the information in winning worse.
The rational bid uses conditional value rather than the bidder's unconditional signal estimate.
Evaluate the design objective
Efficiency, expected revenue, simplicity and robustness need not point to the same format. A reserve price can raise revenue while blocking trades that would create surplus. An additional bidder may raise revenue without that particular inefficiency.
State which objective is being assessed before calling one design better.
Audit an auction recommendation
Write four lines before comparing formats: what bidders know, whether values are private or common, how allocation is determined and how payment is calculated. Then test a proposed bid against upward and downward deviations while holding rival bids fixed.
In a common-value setting, replace the unconditional estimate with value conditional on winning. For multiple slots, calculate the price attached to each position rather than importing the single-object truthful-bidding result. Close by naming the seller's objective, because a design that raises expected revenue can reduce allocative efficiency or impose greater strategic complexity on participants.
What this chapter covers
- 01
English and Dutch auctions
- 02
First-price sealed bids
- 03
Second-price sealed bids
- 04
Dominant strategies
- 05
Bid shading
- 06
Reserve prices
- 07
Common values
- 08
Advertising slots
Worked example · free
Prove truthful bidding by cases
- 3Consider a highest rival bid below value.
- 3Consider a highest rival bid above value.
- 2Identify how each deviation can hurt and never help.
Key terms
- Allocation Rule
- The mapping from submitted bids to the identity or probability of the auction winner.
- Payment Rule
- The mapping from bids and allocation to the amount each participant pays.
- Bid Shading
- Submitting less than value to preserve surplus when the winner pays their own bid.
- Private Value
- A valuation known to the bidder that does not change when rivals' signals are revealed.
- Common Value
- A shared underlying value about which bidders receive different noisy signals.
- Winner's Curse
- The adverse information conveyed by winning when the highest estimate is systematically optimistic.
Auction Design and Bidding Strategy FAQ
Why do bidders shade in first-price auctions?
The winner pays their own bid, so bidding full value leaves zero surplus whenever the bid wins. A lower bid preserves surplus conditional on winning but reduces the chance of winning. The equilibrium balances those effects and depends on rivals' value distribution and risk assumptions.
Why is truth telling safe in a second-price auction?
Under independent private values for one object, the winner pays the highest rival bid. Bidding value wins exactly when that rival price is below value and loses when it is above value. An upward deviation can create a harmful win, while a downward deviation can destroy a beneficial win.
What changes under common values?
Winning reveals that the bidder had the highest signal, making the unconditional estimate too optimistic. A rational bidder values the object conditional on winning and shades further to avoid the winner's curse. More bidders can make winning stronger adverse news even as competition rises.
Exam move
For each auction, write four lines: information observed, allocation rule, payment rule and value environment. Then test one upward and one downward deviation. Add a reserve or common-value signal only after the private-value benchmark is clear, because each extension changes a different part of the logic.
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