Tensions in Practice: Truthful alone does not rule out a bidding coalition¶
A finite second-price auction with a fixed reserve option
An invented auction sells one item to the highest bidder, who pays the larger of the second bid and a declared reserve; it does not sell if both bids are below the reserve. A and B have private values 10 and 8 in the high-value case. Honest bids make A pay 8. If B jointly agrees to bid 0 while A bids 10, A still wins but pays less; B still loses. Compare reserve 0 with reserve 3, and also inspect a separate low-value case with honest bids 2 and 1.
Allow lower-value trades
Sell even when both valuations fall below a positive reserve.
Keep a minimum sale payment
Limit how far a reduced losing bid can lower the winner’s payment.
Why these aims pull against each other
Individual truth-telling incentives do not rule out a deviation that benefits the winner while leaving the losing bidder’s own allocation unchanged. A reserve bounds this payment channel while excluding some trades; it does not eliminate the coalition incentive.
Choose an arrangement to see what changes and what remains difficult.
Bids A/B lists the two reported bids. Pays is the winner’s payment to the seller; None means the item is not sold. The high and low valuation cases are separate stipulated scenarios, not changes caused by the reserve.
What this choice protects
What it costs
When it fits
Compare the arrangements
No positive reserve
Use reserve 0. In the high-value case, changing only B’s bid from 8 to 0 lowers A’s payment from 8 to 0. In the low-value case, A wins and pays 1.
| Bids A/B | Winner | Pays | |
|---|---|---|---|
| Honest high | 10 / 8 | A | 8 |
| Joint low bid | 10 / 0 | A | 0 |
| Honest low | 2 / 1 | A | 1 |
- What it protects
- The item is sold in the low-value case, where the winning value 2 exceeds the assumed item cost of 0.
- What it costs
- The high-value coalition can suppress the payment to 0 through the specified losing-bid channel.
- When it fits
- Plausible when enabling lower-value allocation is important and this revenue exposure is acceptable or managed separately.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
Reserve of 3
Use the same allocation and payment rules with reserve 3. The joint lower bid now leaves A paying 3; honest bids 2 and 1 produce no sale.
| Bids A/B | Winner | Pays | |
|---|---|---|---|
| Honest high | 10 / 8 | A | 8 |
| Joint low bid | 10 / 0 | A | 3 |
| Honest low | 2 / 1 | None | 0 |
- What it protects
- The specified coalition cannot reduce a sale payment below 3 by lowering the losing bid alone.
- What it costs
- The coalition still reduces payment from 8 to 3, and the low-value case leaves the item unsold despite a positive value above cost.
- When it fits
- Plausible when a minimum payment is worth losing those lower-value sales and the reserve is credible and applied consistently.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
What this illustration does—and does not—establish
The source establishes the structural tension; the concrete alternatives and their conditional costs are editorial synthesis. No arrangement is a universal recommendation.
- Values, bids, reserve and zero item cost are invented. No optimal-reserve estimate, participation forecast or real auction recommendation is supplied.
- The ordinary single-bidder private-value guarantee is weak dominance: losing B can be indifferent among bids that lose. This joint deviation weakly benefits both and strictly benefits A; no claim that B benefits strictly without a side payment is made.
- A fixed reserve does not make the auction coalition-proof. Common values, risk preferences, other bidders, repeated play and side payments require additional analysis.
Source entries
Incentive Compatibility
Incentive compatibility Mechanism-Internal IC vs Off-Mechanism Gaming supplies the local tension. The setting, alternative arrangements, and stipulated consequences are editorial applications.
Mechanism-Internal IC vs Off-Mechanism Gaming
Real agents can coordinate through side channels, collude across auction rounds, form bidding coalitions, exchange side payments, or strategically abstain — moves the formal model may not describe and IC therefore does not constrain.
Auction Theory
Auction Theory: Efficient Allocation vs Revenue Maximization supplies the reserve’s allocation-versus-payment tradeoff. The finite reserve is illustrative and is not claimed optimal.
Efficient Allocation vs Revenue Maximization
Myerson's optimal auction uses a reserve price that deliberately *withholds* the item from some bidders who would have valued it above marginal cost — a strictly inefficient outcome — in order to extract more surplus from the bidders who remain.