Reserve Pricing Preserves Competitive Efficiency

Hartline, Hoy & Taggart · 2023 · arXiv:2310.03702

Adding a reserve price (minimum bid) to VCG does not break its truthfulness or efficiency properties. The seller captures more surplus without distorting incentives, as long as the reserve is set below bidders' values.

What a reserve price does

A reserve price sets a floor: bids below it are rejected. This eliminates low-value allocations and guarantees minimum revenue. The key result is that reserve pricing composes cleanly with VCG: the mechanism stays truthful and efficient among participating bidders.

Scheme

; Reserve price in a second-price auction
; Bids below reserve are rejected

(define (auction-with-reserve bids reserve)
  (let* ((eligible (filter (lambda (b) (>= b reserve)) bids))
         (sorted (sort eligible >)))
    (if (null? sorted)
        (list 'no-sale 0 0)
        (let* ((winner (car sorted))
               ;; Payment = max(reserve, second-highest eligible bid)
               (payment (if (null? (cdr sorted))
                            reserve
                            (max reserve (cadr sorted)))))
          (list 'sold winner payment)))))

(define bids '(10 8 5 2 1))
(display "Bids: ") (display bids) (newline)

(display "\nNo reserve: ")
(display (auction-with-reserve bids 0)) (newline)

(display "Reserve $3: ")
(display (auction-with-reserve bids 3)) (newline)

(display "Reserve $6: ")
(display (auction-with-reserve bids 6)) (newline)

(display "Reserve $12 (no sale): ")
(display (auction-with-reserve bids 12))
; Reserve raises revenue without breaking truthfulness

Why it preserves efficiency

Among bidders who clear the reserve, the allocation is still efficient (highest value wins) and truthful (dominant strategy is still to bid your value). The only "inefficiency" is when the item goes unsold because no bidder values it above the reserve. The seller gains because the payment floor is higher. Reserve pricing is one of the three levers a platform can pull: it sets the minimum quality bar without distorting which ad wins among qualified candidates.

Neighbors

june.kim/three-levers — reserve price as a revenue lever
💎 VCG 1973 — the mechanism reserve pricing augments
💎 Milgrom & Weber 1982 — revenue ranking of auction formats

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