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AI-Mediation in Retail Markets: Revenue Effects and Assortment Optimization

Omar El Housni, Marouane Ibn Brahim

arXiv:2610.12917v1cs.AIecon.GNmath.OCq-fin.EC

TL;DR

The paper asks how AI-generated product shortlists affect retailers’ revenue and assortment choices. It combines observed AI rankings with customer-preference scenarios and analyzes deterministic mediation algorithms. Ignoring mediation produces substantial losses relative to the PL optimum, while a deterministic plug-in has much smaller average losses.

  • Problem

    When an AI filters or ranks products before customers see them, retailers control the catalog but not necessarily the customer-facing assortment, raising questions about revenue effects and assortment decisions.

    Source: §1 · p. 2

  • Method

    The paper estimates PL models from controlled AI rankings, combines them with synthetic customer MNL preferences, and studies deterministic-mediation assortment optimization.

    Source: §1 · p. 2

  • Results

    2.52%–11.37% mean revenue losses result from ignoring mediation versus the PL optimum, compared with 0.08%–0.53% for the deterministic plug-in.

    Source: §1.1 · p. 5

  • Takeaways & Limitations

    For any fixed number of customer segments, deterministic-mediation assortment optimization admits a fully polynomial-time approximation scheme.

    Source: §1.1 · p. 6

    Customer preferences are modeled with segment-specific MNL choice models and an outside option.

    Source: §2.1 · p. 10

Abstract

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AI shopping assistants increasingly influence which products consumers consider. We study retail assortment planning under AI mediation, where a retailer chooses a catalog, an AI intermediary forms a customer-facing shortlist, and the customer chooses from that shortlist according to a multinomial logit model. We consider both deterministic mediation, in which the AI follows a fixed segment-specific ranking, and stochastic mediation based on the Plackett-Luce model. Empirically, we construct a dataset of product rankings from leading AI models, estimate Plackett-Luce ranking models, and evaluate their predictive performance on held-out assortments. Combining these estimates with synthetic customer preferences, we find that accounting for AI mediation can materially change optimal assortments and revenue. Across the tested capacity configurations, ignoring mediation yields mean revenue losses between 2.52% and 11.37% relative to the PL optimum. A much simpler deterministic plug-in, based only on the ordering of fitted AI utilities, performs substantially better, with mean losses of at most 0.53%. Motivated by this performance, we study assortment optimization under deterministic mediation. We characterize its computational complexity and show that, for any fixed number of customer segments, the problem admits a fully polynomial-time approximation scheme.

1 Introduction

AI intermediation separates the retailer’s machine-facing catalog from the customer-facing shortlist, raising questions about revenue and assortment choice. The paper combines AI-ranking data and customer-choice models to study these effects and analyzes assortment optimization under deterministic mediation.

1 Introduction

  • The paper models a retailer choosing a catalog, an AI generating a segment-dependent shortlist, and a customer choosing from it under an MNL model.It combines controlled AI rankings with synthetic customer preferences for economic analysis and studies deterministic-mediation algorithms theoretically.Source: §1 · p. 2

1.1 Main Contributions and Technical Ideas

  • Fitted PL utilities match the AI’s first-ranked product in 78.8% of held-out observations, with average negative log-likelihood 3.312 per held-out ranking versus 3.360 on training data.The held-out offer sets were not used for estimation.Source: §1.1 · p. 4
  • The direct-MNL assortment contains 1.48 to 4.15 more products on average than the PL-optimal assortment, and retailers may either allow AI filtering or offer no more than K products.The retailer’s response depends on the AI’s display limit K.Source: §1.1 · pp. 4–5
  • 2.52%–11.37% mean revenue losses arise when retailers ignore mediation, while a deterministic plug-in loses only 0.08%–0.53% on average relative to the PL optimum.The losses from ignoring mediation tend to be larger when the AI displays fewer products.Source: §1.1 · p. 5
  • At ρ = 0, direct-MNL mean losses range from 5.75% to 24.06%, versus 0.59%–5.74% at ρ = 1; active filtering is more common at higher alignment.At ρ = 0.95, active filtering occurs in 44.4% to 66.7% of instances, compared with at most 8.9% at ρ = 0.Source: §1.1 · p. 5
  • When the number of segments is unrestricted, the problem is NP-hard even with K = 1 and B = n; fixing both segments and display capacity yields an exact polynomial-time algorithm.With one segment, it is polynomial-time solvable for arbitrary K, while fixing m ≥ 2 alone does not ensure exact polynomial-time solvability.Source: §1.1 · p. 6
  • For any fixed number of customer segments, the deterministic-mediation assortment problem admits an FPTAS with revenue at least 1 − ϵ times optimal.The algorithm enumerates segment-specific threshold products and approximates a conditional sum-of-ratios objective.Source: §1.1 · p. 6

1.2 Related Literature

  • Unlike consider-then-choose models with consumer-generated consideration sets, this setting uses ranking-based mediation by an AI that can be queried with chosen products and profiles.The paper distinguishes this retailer-facing assortment problem from work where an AI is the final product chooser or acts on a consumer’s behalf.Source: §1.2 · pp. 7–8

2 Model Formulation

The model separates the retailer’s machine-facing catalog from the customer-facing products selected by a segment-specific AI, then evaluates customer choice and revenue after mediation. It focuses on deterministic rankings and stochastic Plackett–Luce rankings, each displaying up to K products.

2.1 General Model of AI-Mediation

  • The retailer chooses one feasible assortment without observing the arriving customer’s segment, and the AI maps it to a customer-facing subset using a segment-specific probability kernel.The general kernel formalizes retailer–AI–customer interaction; the retailer takes the mediation rule as given and influences the displayed set through its assortment choice.Source: §2.1 · p. 10

2.2 Ranking-Based Mediation

  • The general mediation kernel is an umbrella framework, so the analysis specializes it to ranking-based rules that display the top K products, or the entire assortment when it has fewer than K.The ranking may be deterministic or stochastic and is specific to the customer segment.Source: §2.1 · p. 10, §2.2 · p. 11

2.1 General Model of AI-Mediation

  • Customers in each segment choose from the displayed set according to a segment-specific multinomial logit model, with an outside option.Segments capture heterogeneity in both customer preferences and AI behavior; a segment can combine a customer profile with an AI system.Source: §2.1 · p. 10

2.2 Ranking-Based Mediation

  • The two studied ranking rules are a fixed segment-specific ranking and a Plackett–Luce ranking generated from segment-specific positive product weights.Under either rule, the AI displays the highest-ranked available products up to its capacity.Source: §2.2 · p. 11

2.3 Deterministic Rankings

  • Deterministic mediation makes the AI’s displayed subset fixed for each segment and assortment, providing a benchmark for assortment optimization.Any stochastic ranking rule can be represented exactly by a distribution over deterministic rankings, but that representation may require exponentially many rankings and segments.Source: §2.3 · p. 12
  • The paper defines separate retailer revenue functions and assortment-optimization problems for deterministic and Plackett–Luce mediation.These formulations apply the corresponding mediation rules to the assortment decision.Source: §2.3 · p. 12, §2.4 · p. 13

2.4 Plackett–Luce Rankings

  • In the Plackett–Luce model, independent standard Gumbel shocks are added to nominal AI utilities, and the resulting scores induce a random product ranking.The resulting AI-side weights are distinct from the customer-side MNL weights governing final choice.Source: §2.4 · pp. 12–13
  • For a retailer assortment, the Plackett–Luce mediation kernel gives the probability that each customer-facing subset occupies the AI ranking’s first K positions.The probability of a displayed set sums the probabilities of ordered rankings of its products.Source: §2.4 · pp. 12–13

3 AI-Ranking Data, Estimation, and Validation

The paper constructs AI-ranking data by prompting AI models across product categories and market segments, estimates a separate Plackett–Luce model for each segment, and evaluates prediction on held-out offer sets. It also derives a deterministic counterpart by ordering products according to fitted utilities.

3 AI-Ranking Data, Estimation, and Validation

  • The researchers prompt AI models with randomly sampled product offer sets for each market segment, estimate a separate Plackett–Luce model per segment, and assess predictive performance on test samples.The estimation procedure expresses the likelihood of observed recommendations and establishes concavity of the log-likelihood.Source: §3 · p. 13
  • Products ranked by fitted Plackett–Luce utilities provide a deterministic counterpart to stochastic recommendations, which the paper evaluates against the stochastic benchmark.The deterministic model assigns one ranking per segment, whereas stochastic recommendations can vary between queries.Source: §3 · p. 14

3.1 Data Generation and Prompting Protocol

  • The study uses three product universes—25 Lightning chargers, 22 robot vacuums, and 25 pet leashes—with product titles, prices, brands or stores, and category-specific attributes.The 72 products come from Amazon Reviews 2023 product metadata.Source: §3.1 · p. 14

Appendix A.1.

The appendix details the product and prompting design, estimation of segment-specific Plackett–Luce models, and their held-out predictive validation. The reported results show little train-to-test deterioration and substantial agreement between fitted rankings and AI recommendations.

Appendix A.1.

  • The study presents product universes and the information available to AI ranking models; the cited passage gives no counts or further description of product records.Source: Table 1 · p. 14
  • The prompting design presents ten products and asks the AI to return its ranked top five, using persona-specific instructions and product descriptions.Each product’s prompt information includes its number, title, listed price, brand or store, and category-specific attributes.Source: Appendix A.1 · p. 15
  • The experiment samples 600 distinct ten-product offer sets per category, splits them into 500 training and 100 test sets, and randomizes two presentation orders per set.Both presentations of an offer set stay in the same partition; the design totals 32,400 rankings across three categories and nine model–persona segments.Source: Appendix A.1 · pp. 15–16

3.2 Estimating the Plackett–Luce Model

  • The Plackett–Luce log-likelihood is concave in product utilities, making the segment-specific estimation problem computationally tractable.The paper uses the standard likelihood and partial-ranking variants for observed ordered top-K recommendations.Source: §3.2 · p. 16
  • Segment-specific Plackett–Luce parameters are estimated by ridge-regularized maximum likelihood because separation can make the unregularized likelihood lack a finite maximizer.The selected penalty is θ = 0.04; it reduced extreme fitted-utility differences while increasing average training NLL by less than 0.01 per ranking.Source: §3.2 · p. 17

3.3 Out-of-Sample Validation

  • 3.359555 training NLL and 3.311885 held-out NLL indicate essentially no predictive deterioration, and held-out NLL is below the 10.32 uniform benchmark.The reported pooled values are compared with the uniform reference and with each other.Source: Table 2 · p. 18, §3.3 · p. 18
  • 78.8% first-product agreement, 68.4% first-three set agreement, 66.6% Top-5 set agreement, and 0.879 mean Top-5 Jaccard similarity quantify pooled held-out ranking agreement.Set agreement ignores order within the first K positions; Jaccard similarity compares the AI’s and fitted model’s Top-5 sets.Source: §3.3 · p. 18
  • Performance varies across categories and more substantially across AI models; in this experiment, Gemini has lower NLL and higher agreement than ChatGPT and Claude.The fitted rank center’s strong agreement with recommendations supports using fitted utility ordering as a deterministic approximation.Source: §3.3 · p. 19

4 Experimental Effects of AI Mediation

AI mediation often leads retailers to offer smaller assortments, and ignoring it can reduce revenue; a deterministic plug-in based on fitted AI rankings has small average losses. The experiments also examine how these effects vary with customer–AI preference alignment.

4.1 Experimental Setup

  • Customer preferences combine AI-derived persona preferences with independent Gaussian variation, with ρ controlling alignment; customer weights vary by persona, not AI model.The experiment compares policies over synthetic preferences and fitted AI-ranking models.Source: §4.1 · pp. 19–20

4.2.1 Pooled Analysis

  • Mediation is active in 96.1% of K = 3 instances and 66.0% at K = 7, through realized filtering or endogenous avoidance.The mediated share varies with display capacity and is essentially invariant to the retailer’s assortment cardinality bound within the tested grid.Source: §4.2.1 · p. 22, Figure 2 · p. 23
  • Direct-MNL assortments exceed PL-optimal assortments by 1.48 to 4.15 products on average; tight display capacity can prompt contraction to avoid filtering.The reported average difference is largest when display capacity K is smaller.Source: §4.2.1 · pp. 23–24
  • Mean direct-MNL revenue loss is 2.52%–11.37%, versus 0.08%–0.53% for the deterministic plug-in across seven capacity environments.The deterministic plug-in performs close to the PL optimum on average across the tested grid.Source: Table 3 · p. 24, §4.2.1 · p. 24

4.2.2 Role of Preference Alignment

  • Direct-MNL losses generally fall as alignment rises (5.75%–24.06% at ρ = 0 versus 0.59%–5.74% at ρ = 1), though some configurations reverse locally.The endpoint loss is lower at ρ = 1 than at ρ = 0 in every configuration.Source: §4.2.2 · p. 25
  • Deterministic losses remain small but are not monotone in ρ, so alignment predicts the cost of ignoring mediation better than plug-in accuracy.The deterministic approximation remains strong across the alignment range, including when customer preferences are weakly aligned with AI preferences.Source: §4.2.2 · p. 25

Appendix B.2 for the sake of readability.

As customer–AI alignment rises, the PL-aware retailer becomes more willing to offer assortments above display capacity, leaving more discretion to the AI. The appendix reports both assortment-size response and active filtering by alignment.

Appendix B.2 for the sake of readability

  • At ρ = 0, active filtering occurs in at most 8.9% of instances, versus 44.4%–66.7% at ρ = .95; endogenous avoidance remains sizeable at both alignments.At ρ = 0, endogenous avoidance accounts for 62.2%–84.4% of instances; at ρ = .95, it accounts for 22.2%–33.3%.Source: Appendix B.2 · p. 25, Figure 5 · p. 26
  • Mean |S⋆PL|−K ranges from −0.74 to 0.13 products at ρ = 0 and from 0.37 to 1.96 at ρ = .95.The statistic is the mean difference between the PL-optimal assortment size and display capacity K.Source: Appendix B.2 · p. 25, Figure 5 · p. 26

5 Deterministic Ranking Mediation

This section studies assortment optimization under deterministic AI rankings, examining computational complexity across parameter regimes and an FPTAS for a fixed number of customer segments. It also reports that accounting for AI mediation affects revenue and assortment choices.

5.1 Computational Complexity

  • When m can scale with the input, AIMD cannot be approximated in polynomial time within O(n^(1−ϵ)), even for K = 1 and B = n, unless P = NP.This hardness holds for every fixed ϵ > 0.Source: §5.1 · p. 27
  • For fixed m and K, an optimal assortment of size at most mK exists, enabling polynomial-time enumeration; with m = 1, optimization is polynomial-time for arbitrary K.The single-segment case reduces to cardinality-constrained MNL assortment optimization (Rusmevichientong et al., 2010, Theorem 2.2).Source: §5.1 · p. 28
  • For fixed m ≥ 2 and arbitrary K, AIMD is NP-hard, since it captures assortment optimization under a mixture of multinomial logit models.The hardness applies even with two segments in the corresponding mixture model.Source: §5.1 · p. 29

5.2 An FPTAS for a Fixed Number of Segments

  • For every fixed m and ε ∈ (0, 1), a feasible assortment achieving at least (1 − ε)R_D(S*) is computable in time polynomial in the instance’s binary encoding length and 1/ε.The method evaluates all returned assortments, together with S̄, under the original revenue function and retains the best.Source: §5.2 · p. 29, §5.2.4 · p. 34
  • For an optimum with |S*| ≤ K, every segment sees the full assortment, and a mixture-of-MNL FPTAS supplies the candidate; the algorithm separately handles |S*| > K.The section defines mediation as inactive when |S| ≤ K and active when |S| > K.Source: §5.2 · p. 29

5.2.1 A threshold reformulation

  • For active mediation, the threshold reformulation enumerates each segment’s lowest-ranked displayed product and restricts assortments to include thresholds and exclude products below all thresholds.For the optimal threshold vector, the conditional objective equals deterministic-mediated revenue and the optimal assortment is feasible.Source: §5.2.1 · p. 30

5.2.2 A framework for sums of ratios

  • The FPTAS framework of Mittal and Schulz (2013) applies to sums of a fixed number of affine-function ratios when the associated exact problem is solvable in pseudopolynomial time.The framework yields a (1 − ϵ)-approximate solution.Source: §5.2.2 · p. 31

5.2.3 Verifying the exact-solvability condition

  • The conditional problem meets the framework’s positivity and affine-coefficient conditions, and its exact problem reduces to multidimensional knapsack for pseudopolynomial solution.A positive shift to each numerator ensures strict positivity while preserving an approximation guarantee for the original objective.Source: §5.2.3 · pp. 32–33

6 Conclusion

  • 2.52%–11.37% mean revenue losses result from ignoring mediation versus the PL optimum, while deterministic utility-ordering has mean losses of at most 0.53% across tested capacities.The numerical comparisons under stochastic mediation use exactly optimized deterministic assortments.Source: §6 · p. 35

5.2.4 Completing the proof

  • For any fixed number of customer segments and arbitrary display capacity, the deterministic-mediation assortment problem admits an FPTAS.For fixed m, the running-time bound is polynomial in L and 1/ϵ.Source: §6 · p. 35, §5.2.4 · p. 35

6 Conclusion

  • Accounting for mediation leads to smaller assortments on average and can induce retailers to limit catalogs so every offered product is displayed.Source: §6 · p. 35

A.1 AI-Ranking Data Generation Details

The appendix documents how AI-ranking prompts were constructed and reports preference-alignment comparisons across tested capacity configurations.

A.1 AI-Ranking Data Generation Details

  • The product records supplied to the AI include titles, listed prices, brand or store, and available category-specific attributes.Fields with missing values are omitted.Source: §A.1 · p. 38
  • The value-seeking prompt prioritizes price-to-quality tradeoffs; budget-sensitive and premium-seeking prompts retain the template but change the persona instruction.The value-seeking persona accepts higher prices for meaningful quality gains but not marginal improvements or brand name alone.Source: §A.1 · p. 38
  • The ranking task asks the assistant to select five products only from the offered set and return them in ranked JSON format.The instructions prohibit duplicate or unoffered product numbers.Source: §A.1 · pp. 38–39
  • All three providers receive the same logical prompt and response structure, with provider-specific settings for output limits and generation controls.OpenAI and Anthropic use temperature 1.0; Gemini uses JSON mode and minimal thinking, with several sampling settings unset.Source: §A.1 · p. 39

B.1 Preference Alignment Across Capacity Configurations

  • Figure 6 compares mean revenue loss by ρ for direct-MNL and the deterministic plug-in across all seven (B, K) configurations.The supplied passage describes the figure’s scope but does not report its plotted values.Source: §B.1 · p. 39

B.2 Preference Alignment and Filtering Mechanisms

Figure 7 reports two filtering-related measures across all seven tested capacity configurations.

B.2 Preference Alignment and Filtering Mechanisms

  • Figure 7 reports mean |PL|−K across the seven tested (B, K) configurations.The supplied passages identify the measure and scope, but not plotted values.Source: §B.2 · p. 39
  • Figure 7 also reports the active-filtering share for all seven tested (B, K) configurations.The passages do not state the values or comparisons shown.Source: §B.2 · p. 39
  • The reported measures extend the filtering-mechanism analysis to the complete set of tested capacity configurations.The section covers seven configurations.Source: §B.2 · p. 39

C.1 Proof of Theorem 5.1

The proof reduces assortment planning under ranking preferences to AIMD while preserving revenue for every assortment. The reduction transfers the source problem’s approximation hardness to AIMD.

C.1 Proof of Theorem 5.1

  • In the ranking-preferences model, each segment buys its highest-ranked offered product from its willing-product list, or makes no purchase if none is offered.The ranking-preferences objective is to maximize expected revenue over assortments.Source: §C.1 · p. 40
  • The construction sets K = 1 and B = n, doubles each product’s revenue, and preserves each segment’s ordering of willing products.Products in the segment’s preference list rank above products outside it.Source: §C.1 · p. 41
  • For every assortment, the constructed AIMD instance and ranking-preferences instance generate equal revenue and therefore have the same optimal value.Because B = n, every assortment is feasible in the constructed instance.Source: §C.1 · p. 41
  • AIMD inherits the ranking-preferences problem’s O(n^(1−ϵ))-approximation hardness consequence through the reduction.The source problem is NP-hard to approximate within that factor for every fixed ϵ > 0.Source: §C.1 · pp. 40, 42

C.2.1 Proof of Lemma 5.4

The proof relates the mediated revenue to a target revenue for assortments satisfying the stated constraints. It also establishes that an optimal assortment can be chosen within A.

C.2.1 Proof of Lemma 5.4

  • For an assortment in Xτ*, the proof identifies the displayed products as the K highest-ranked products and equates the resulting revenues after summing across segments.The segment-weighted revenue equality is RD(S) = Rτ*(S).Source: §C.2.1 · p. 42
  • The proof considers an optimal assortment S* in the active regime, where its size exceeds K and is at most B.It also notes that M is contained in S*.Source: §C.2.1 · p. 42
  • A product outside A has hit = 0 for every segment, so removing it preserves revenue and supports an optimal assortment contained in A.The proof uses this revenue-preserving removal to contradict the minimum-cardinality choice if an optimal assortment contains such a product.Source: §C.2.1 · pp. 42–43

C.2.2 Proof of Lemma 5.7

The proof relates feasible solutions of an exact problem to solutions of formulation (14). It uses nonnegative summands to establish the required equalities and feasibility condition.

C.2.2 Proof of Lemma 5.7

  • Restricting a feasible exact-problem solution to I yields a feasible solution to (14) with profit exactly P.The passage also states the converse begins from a feasible x with profit at least P.Source: §C.2.2 · p. 43
  • The proof shows that a sum of nonnegative terms equals zero, so each term must equal zero.This follows from the stated feasibility and the condition that x has profit at least P.Source: §C.2.2 · p. 43
  • Setting xi = 1 for every i in M therefore yields a feasible solution to the exact problem.Source: §C.2.2 · p. 43
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