Source-linked AI summary
Marginal Expected Revenue for Jointly Ranking Auction and Fixed-Price Listings in E-Commerce Sponsored Search
Greg Kocher, Sanjana Arun
TL;DR
Mixed-format sponsored-search ranking must estimate revenue when auction prices evolve and final transaction values are unknown. The paper extends eCPM with marginal eCPM for fixed-price, auction, and ABIN listings, then implements an approximation for cold-start deployment. Online tests showed positive revenue gains and statistically significant user-metric improvements, and the system was deployed to production.
Problem
Revenue estimation is well understood for fixed-price listings but difficult for auction and ABIN listings because prices evolve and final transaction values are unknown at ranking time.
Method
The paper derives a marginal eCPM framework for fixed-price, pure auction, and ABIN listings and implements a simplified approximation for cold-start conditions.
Results
Online A/B tests showed positive revenue gains and statistically significant improvements in user metrics, and a version of the system was deployed to production.
Takeaways & Limitations
Mixed fixed-price and auction listings can be integrated into expected-value ranking under a unified marginal-revenue formulation.
Takeaways & Limitations
The full meCPM formulation remained future work because valid-bid-through-rate and conditional bid-value estimators were unavailable in the initial cold-start setting.
Abstract
from arXiv · showhide
E-commerce search ranking must balance multiple objectives--relevance, user engagement, and platform revenue--when allocating impression slots to competing listings. Estimating the expected revenue component is well understood for fixed-price items, but becomes challenging when marketplace inventory includes mixed listing formats such as pure auctions and hybrid "Auction with Buy It Now" (ABIN) items, where prices evolve dynamically and the final transaction value is unknown at ranking time. Yet auction and ABIN listings account for a meaningful share of inventory and transaction volume on platforms such as eBay, and are a popular format for individual sellers and for unique items with unclear value. We extend the standard Expected Cost-per-Mille (eCPM) framework to auction and ABIN listings by deriving a marginal eCPM (meCPM) that captures the incremental value of showing one more impression of an item whose price is still evolving. The resulting formulation extends the familiar fixed-price eCPM--which is already inherently marginal--to auction dynamics, allowing unified ranking of fixed-price, auction, and ABIN listings under a single objective. We then describe a practical production implementation that approximates this objective, addressing cold-start challenges by bootstrapping from existing engagement models. Online A/B tests at a large e-commerce platform showed positive revenue gains and statistically significant improvements to user metrics, and the system was deployed to production.
1. Introduction
The section frames sponsored-search ranking as a multi-objective allocation problem and identifies auction listings as difficult to monetize because their prices and final values evolve. It introduces meCPM as a unified revenue-ranking framework for fixed-price, auction, and ABIN listings, with production validation.
- Sponsored search allocates limited impression slots across listings while balancing buyer engagement, relevance, seller outcomes, and platform revenue.
- Fixed-price eCPM is well understood, but auction listings introduce uncertainty in both buyer engagement and final transaction value.
- The paper introduces marginal eCPM to account for stochastic, evolving auction prices and derives expressions covering fixed-price, pure auction, and ABIN listings.
- A simplified implementation addresses cold-start constraints, achieves calibrated revenue prediction, and supports launching an auction CPA advertising program.
- Online A/B tests produced statistically significant user-metric improvements and positive revenue gains, followed by production deployment.
2. Background and Related Work
This section explains standard expected-revenue ranking for fixed-monetization ads and motivates marginal revenue for auctions. Because auction revenue accumulates through evolving prices, one more impression should be valued by its incremental revenue above the locked-in baseline.
- Sponsored-search systems commonly rank candidate ads using expected revenue per impression, or eCPM, alongside alternative ranking and constraint approaches.
- For CPC and fixed-price CPA, the monetizing event and revenue per event are known in advance, while engagement remains a binary outcome.
- Auction listings differ because their final price is unknown at ranking time and prior bids create revenue already locked into the auction.
- Marginal eCPM values the incremental revenue generated by one additional impression above the locked-in baseline.
- For CPC and fixed-price CPA, marginal eCPM equals standard eCPM because revenue is all-or-none and no partial revenue accumulates over time.
3. Methods
The method extends eCPM to auction and ABIN listings by valuing the incremental revenue from one more impression as prices evolve. It combines auction-state information, bid probabilities, and expected price uplift into unified revenue-based scores, while simplifying implementation for deployment.
- Pure Auction Format: Proxy bidding makes current price evolve from submitted maximum bids, so past visible price represents revenue already locked in.Future impressions should be valued by incremental revenue above the current locked-in amount.
- Marginal eCPM Derivation: The greedy meCPM approximation values only the next impression using valid-bid probability, auction state, and expected price uplift.A full remaining-impression treatment could instead use dynamic programming over auction states.
- Marginal eCPM Derivation: The auction formulation integrates bid-through probability with the expected visible-price increase conditional on a valid bid.The bid-value distribution is conditioned on valid submitted maxima, with survival-integral terms capturing price-uplift cases.
- Reserve Prices: When a reserve is unmet, meCPM accounts for the probability that a valid bid clears the reserve rather than treating current price as guaranteed revenue.In the common reserve case, the score becomes ad rate × valid-bid probability × reserve-clearing probability × reserve price.
- ABIN Format: ABIN meCPM adds the immediate Buy It Now revenue event to the auction-format meCPM appropriate to the listing’s current state.After the first bid, the Buy It Now option typically disappears, so the formula collapses to the auction case.
- Unified Ranking: Fixed-price and auction formats share an r × P(event | imp) × price-signal structure, enabling unified revenue-based ranking across listing types.For fixed-price CPA, standard eCPM is already marginal because there is no locked-in partial revenue.
- Simplified Implementation: The production implementation uses practical simplifications because a full meCPM implementation remains future work and may avoid requiring hidden auction values.The simplified form is intended to bootstrap auction-specific data and models for later refinement.
4. Experiments
Live experiments and production-impression evaluation tested auction ranking, revenue calibration, and transfer from fixed-price models. Auction listings produced positive business and user outcomes, while simplified modeling transferred well but exhibited offsetting calibration effects.
- Online Tests: Positive ad-revenue gains and statistically significant engagement improvements followed auction-listing integration, without buyer-experience degradation in guardrail metrics.Gains were driven primarily by newly monetized auction-dominated queries with little prior CPA coverage.
- Model Evaluation: 93% as high as fixed-price inventory AUC-ROC was achieved by the repurposed p(sale) model on auction and ABIN listings.The model had never been trained specifically for auctions, supporting transfer for the sale-prediction task.
- Model Evaluation: Higher MAPE on auction and ABIN p(sale) calibration reflected over-predicted per-impression sale probability for auction listings.Multiple impressions can collect bids without producing an immediate purchase from each impression.
- Model Evaluation: Opposing miscalibration effects partially offset, yielding revenue predictions that were well calibrated and closely tracked y = x.Price underprediction and other system scaling effects helped reduce the impact of component-level miscalibration.
5. Discussion
The discussion reports that auction listings can be integrated into expected-value ranking with positive user and business effects, while highlighting query-segment differences and a simplified implementation that leaves a fuller formulation for future work.
- Auction listings were integrated into expected-value ranking with positive business and user-experience impact.
- Ad System Tradeoffs: Revenue gains were concentrated in mixed-query groups, while auction-heavy and fixed-price-heavy groups showed little net change.
- Toward the Full Marginal eCPM Formulation: The production system is a simplified approximation of the full marginal eCPM objective.
- Toward the Full Marginal eCPM Formulation: The full formulation requires valid-bid-through-rate and conditional bid-value distribution estimators that were unavailable at cold start.
- Toward the Full Marginal eCPM Formulation: As auction-specific data accumulates, future work can evaluate the full meCPM approach and whether its gain justifies added modeling complexity.
6. Conclusion
The conclusion presents meCPM as a unified expected-revenue objective for fixed-price, pure-auction, and ABIN listings in sponsored search. It reports that a simplified cold-start implementation was tested on production traffic with statistically significant user and business gains.
- meCPM unifies fixed-price, pure-auction, and ABIN listings within Cost-per-Acquisition sponsored-search ranking.
- The formulation represents monetization as the probability of a revenue-generating event times expected price uplift above locked-in revenue.
- The paper uses a simplified approximation to address the cold-start problem of launching a new ad program without prior data.
- Live production-traffic tests showed statistically significant gains in user and business metrics.
A. Notation
The notation defines ad rates, prices, bid thresholds, and the predicted final selling price used to describe fixed-price, auction, and ABIN listing states.
- The ad rate r is the fraction of final selling price paid by the seller to the platform, with r∈[0, 1].
- The notation distinguishes fixed-price p_FP, starting bid p_0, current visible price p_cur, reserve price p_R, and Buy It Now price p_BIN.
- The minimum bid increment δ is piecewise constant by price range and is treated as a single value at current price p_cur for the meCPM derivation.
- The predicted final selling price p_f(s) is the expected final selling price for items of a given type and state.
B. meCPM Derivation: Auction Without Reserve Price
The derivation models the incremental revenue from an additional impression in a no-reserve auction by combining valid-bid probability with expected price uplift under proxy bidding. It expresses meCPM in terms of the auction state, bid distribution, and price-change function.
- With no reserve price, an existing bid locks in revenue p_cur·r, so additional impressions are valued only through incremental price increases.
- The valid-bid threshold in the post-bid setting is τ=p_cur+δ, and valid-bid probability is modeled as P(valid bid | imp, s).
- Conditional on a valid bid, the bidder’s maximum V follows the state-specific conditional CDF F_s, with expectation restricted to V≥τ.
- Proxy bidding produces four price-update cases depending on whether the challenger raises the visible price, reaches the leader’s maximum, or takes the lead.
- The price uplift is Δp_cur(V)=p_new(V)−p_cur for valid bids and zero otherwise.
- meCPM_auction = r·P(valid bid | imp, s)·E_V~F_s[Δp_cur(V; p_cur, M, δ)].The formulation factors marginal revenue into ad rate, valid-bid probability, and expected price uplift.
B.3. Sanity Checks
The sanity checks establish non-negativity, monotonicity in hidden upside, and limiting behavior for the auction meCPM. Monotonicity in current price is conditional because auction-state-dependent bid behavior can offset lower expected uplift.
- Non-negativity: meCPM is non-negative because all probability, uplift, and survival-integral components are non-negative.Its units are price per impression, or Cost-per-Mille after multiplying by 1000.
- Monotonicity in p_cur: Raising current price p_cur does not guarantee lower meCPM because it changes both expected uplift and the auction-state-dependent valid-bid probability.Higher visible prices may also create social-proof effects that increase future bidding.
- Monotonicity in M: Raising hidden maximum M monotonically increases meCPM because it expands potential price upside while leaving the state-conditioned distributions unchanged.This gives listings with more hidden upside greater marginal value to the platform.
- Term magnitudes: The hidden-upside integral dominates when M is substantially above p_cur, while the baseline and third bracket terms are each O(δ).This identifies the main source of marginal value when substantial price headroom remains.
- Extreme and zero-bid cases: When M = p_cur, both integral terms vanish and meCPM reduces to the bid-through probability times the revenue rate and one bid increment.In the zero-bid case, locked-in revenue is zero and meCPM instead uses the full starting price p0.
C. meCPM Derivation: Auction With Reserve Price
The reserve-price extension adapts the auction meCPM derivation to listings that sell only when the winning bid exceeds the reserve. It therefore requires separate regimes based on whether the reserve has been met.
- Reserve-price extension: The derivation extends pure-auction meCPM to auctions with a reserve price p_R.A reserve creates distinct cases depending on whether the current visible price has crossed the seller’s threshold.
- Reserve regimes: The item sells only when the winning bid exceeds p_R, producing two reserve-dependent regimes.The subsequent formulas distinguish reserve-met from reserve-not-met states.
C.1. Reserve Already Met (𝑝cur ≥𝑝𝑅)
When the reserve is unmet, locked-in revenue is zero, so marginal value comes from reserve-clearing bids and their expected settlement price. The resulting formula combines a floor settlement value with any additional upside up to the cap.
- Reserve already met: When the reserve is already met, the item will sell and meCPM is identical to the post-bid pure-auction case.Locked-in revenue is p_cur · r in this regime.
- Reserve not met: When the reserve is unmet, bids below p_R generate zero incremental revenue under the greedy next-impression assumption.Reserve-clearing bids generate the full settlement price because no revenue is locked in.
- Settlement simplification: For reserve-clearing bids, settlement simplifies to min(V, C), where C = max{p_R, M + δ}.The reserve acts as a floor when M + δ is below p_R; otherwise the proxy-bidding cap determines settlement.
- Expected settlement: The valid reserve-clearing threshold is L = max{p_R, τ}, and expected settlement is computed by splitting the integral at C.This captures only bids that are both valid and sufficient to clear the reserve.
- Reserve-not-met formula: The reserve-not-met meCPM equals r · P(valid bid | imp, s) times min(L, C)S_s(L) + J_s(L, C).The first term is the floor settlement contribution, while J_s captures additional expected upside.
- Post-bid simplification: In most post-bid reserve-not-met cases, the formula reduces to r · P(valid bid | imp, s) · p_R · S_s(L), with only a narrow edge case adding upside bounded by δ.The reduction applies when p_R ≥ M + δ.
D. Summary
The summary table gives marginal eCPM formulas for fixed-price, auction, and ABIN listings. These rows provide a unified revenue-based scoring basis across listing formats and auction states.
- Fixed Price: Fixed-price meCPM is r · P(sale | imp) · p_FP.This is the standard expected revenue per impression for a fixed-price listing.
- Auction: Auction meCPM varies by bid and reserve state, including post-bid, zero-bid, reserve-met, and reserve-unmet cases.The table includes distinct formulas for zero-bid auctions and reserve-not-met auctions.
- Auction: Zero-bid no-reserve auction meCPM is r · P(valid bid | imp, s) · p0.The starting bid price is the full price signal when no revenue is locked in.
- ABIN: ABIN meCPM equals r · P(BIN | imp, s) · p_BIN plus the auction meCPM for the listing’s current state.This combines mutually exclusive Buy It Now and auction revenue opportunities.