Auction Revenue Equivalence, explained.
Revenue equivalence gives conditions under which different auction mechanisms have the same expected payments despite different bidding and realised prices.
Why it happens
Three risk-neutral bidders have independent uniform values on 0–100. In symmetric first-price equilibrium each bids 2v/3; in second-price auctions each bids value. The highest value wins, paying its own bid or the second-highest value. Compare one auction and 500 paired auctions against expected revenue 50.
Revenue equivalence gives conditions under which different auction mechanisms have the same expected payments despite different bidding and realised prices.
Read the result
Compare one auction's two revenues before the batch averages. Expectation-level equality allows substantial differences in any individual sale.
A worked example
Two payment rules for the same bidders
Draw a set of three values and observe that the first-price winner shades its bid while second-price bidding is truthful.
Compare the winning first-price bid with the second-highest value, noting that the realised payments usually differ.
Run five hundred auctions and compare means with fifty. Sampling fluctuation remains even under all of the stated assumptions.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Three risk-neutral bidders have independent uniform values on 0–100. In symmetric first-price equilibrium each bids 2v/3; in second-price auctions each bids value. The highest value wins, paying its own bid or the second-highest value. Compare one auction and 500 paired auctions against expected revenue 50.
Where this idea is useful
A practical use
A seller comparing auction formats should distinguish strategic bidding changes from the payment rule itself.
A common misconception
“Revenue equivalence means every auction format raises the same amount.”
It is a conditional expectation result. Different assumptions, reserve rules, risk attitudes or information structures can change expected revenue.
What this explanation leaves out
- The result depends on the stipulated independent private values, symmetry, risk neutrality, allocation and boundary-payment conditions. Reserves, asymmetric information, collusion and risk aversion are absent. One auction need not produce equal revenue.
Why not use truthful bids in both formats?
First-price bidders pay their own bids, so bidding value would erase surplus. The teaching model uses the symmetric equilibrium bid appropriate to three uniform bidders.
Which assumption about bidders would you test before transferring this comparison to a real auction?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.