First Price Auctions with General Information Structures: Implications for Bidding and Revenue
summary
Derives tight worst‑case bounds on seller revenue in first‑price auctions when the information structure is unknown, proving a global lower bound and constructing an equilibrium that attains it (two bidders with common uniform value yield revenue = one sixth). Main tools are a relaxed optimization over winning‑bid marginals and a family of uniform upward deviations (Bayes‑correlated equilibrium view), generalized to N bidders and arbitrary correlations; also contrasts the sharper bounds that obtain under known‑values assumptions.
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chapters (22)
- 0:00Intro
- 3:02A (toy) model
- 4:46Filling in beliefs
- 5:45Lower revenue?
- 8:05How we model beliefs matters
- 9:08Our results
- 12:06Uniform example continued
- 13:27One more construction
- 15:41Verification: Downward deviations
- 17:01Verification: Upward deviations
- 18:05Towards a bound
- 19:44Uniform upward deviations
- 21:18Restrictions on 8
- 22:44A lower bound on revenue
- 25:02Beyond the example
- 25:39Generalized approach
- 28:53General bounds
- 33:38Revenue lower bound
- 34:45Main result
- 40:22Results under known values
- 41:45Welfare set
- 43:07Conclusion