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Merging Mechanisms for Ads and Organic Items in E-commerce Platforms

Nan An, Weian Li, Qi Qi, Liang Zhang

TL;DR

This paper tackles the problem of merging ads and organic items on multi-slot e-commerce search pages while preserving incentive compatibility and individual rationality. It formulates a unified mechanism design that balances revenue and user experience, and proves form stability properties to facilitate analysis. The authors propose two simple mechanisms, G-FIX and G-CHANGE, with rigorous approximation guarantees: a $(4/5)^3$-approximation in the 3-item, 2-slot setting and near-optimal performance for G-FIX in general, with G-CHANGE achieving optimality in the simplest case and a 1/2-approximation more generally. The work provides theoretical foundations for merging ads with organic recommendations and lays groundwork for further improvements and multi-slot extensions in practice.

Abstract

In contemporary e-commerce platforms, search result pages display two types of items: ad items and organic items. Ad items are determined through an advertising auction system, while organic items are selected by a recommendation system. These systems have distinct optimization objectives, creating the challenge of effectively merging these two components. Recent research has explored merging mechanisms for e-commerce platforms, but none have simultaneously achieved all desirable properties: incentive compatibility, individual rationality, adaptability to multiple slots, integration of inseparable candidates, and avoidance of repeated exposure for ads and organic items. This paper addresses the design of a merging mechanism that satisfies all these properties. We first provide the necessary conditions for the optimal merging mechanisms. Next, we introduce two simple and effective mechanisms, termed the generalized fix mechanism and the generalized change mechanism. Finally, we theoretically prove that both mechanisms offer guaranteed approximation ratios compared to the optimal mechanism in both simplest and general settings.

Merging Mechanisms for Ads and Organic Items in E-commerce Platforms

TL;DR

This paper tackles the problem of merging ads and organic items on multi-slot e-commerce search pages while preserving incentive compatibility and individual rationality. It formulates a unified mechanism design that balances revenue and user experience, and proves form stability properties to facilitate analysis. The authors propose two simple mechanisms, G-FIX and G-CHANGE, with rigorous approximation guarantees: a -approximation in the 3-item, 2-slot setting and near-optimal performance for G-FIX in general, with G-CHANGE achieving optimality in the simplest case and a 1/2-approximation more generally. The work provides theoretical foundations for merging ads with organic recommendations and lays groundwork for further improvements and multi-slot extensions in practice.

Abstract

In contemporary e-commerce platforms, search result pages display two types of items: ad items and organic items. Ad items are determined through an advertising auction system, while organic items are selected by a recommendation system. These systems have distinct optimization objectives, creating the challenge of effectively merging these two components. Recent research has explored merging mechanisms for e-commerce platforms, but none have simultaneously achieved all desirable properties: incentive compatibility, individual rationality, adaptability to multiple slots, integration of inseparable candidates, and avoidance of repeated exposure for ads and organic items. This paper addresses the design of a merging mechanism that satisfies all these properties. We first provide the necessary conditions for the optimal merging mechanisms. Next, we introduce two simple and effective mechanisms, termed the generalized fix mechanism and the generalized change mechanism. Finally, we theoretically prove that both mechanisms offer guaranteed approximation ratios compared to the optimal mechanism in both simplest and general settings.

Paper Structure

This paper contains 22 sections, 15 theorems, 105 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Main Contribution
  3. Related Works
  4. Model and Preliminaries
  5. Merging Mechanism
  6. Characterization of IC, IR, and Feasibility
  7. Form Stability in the Optimal Mechanisms
  8. Generalized Fix Mechanism
  9. Generalized Change Mechanism
  10. Conclusion
  11. Missing Proofs in Section \ref{['sec:fs']}
  12. Proof of Proposition \ref{['prop: k from n optimal']}
  13. Statement 1:
  14. Statement 2:
  15. Statement 3:
  16. ...and 7 more sections

Key Result

Lemma 1

A merging mechanism $\mathcal{M}$ satisfies IC and IR if and only if the following conditions are met:

Figures (5)

  • Figure 1: The relationship between $h_1(t)$ and $h_2(t)$ when $o_1 \leq \underset{a_1}{\mathbb{E}}[a_1]$.
  • Figure 2: The relationship between $h_1(t)$ and $h_2(t)$ when $o_1 > \underset{a_1}{\mathbb{E}}[a_1]$ and $h_1(o_1)\geq h_2(o_1)$.
  • Figure 3: The relationship between $h_1(t)$ and $h_2(t)$ when $o_1 > \underset{a_1}{\mathbb{E}}[a_1]$ and $h_1(o_1)< h_2(o_1)$.
  • Figure 4: The relationship between $h_3(t)$ and $h_4(t)$ when $a_3>o_1$ and $h_4(0,a_3)< h_3(0,a_3)$.
  • Figure 5: The relationship between $h_5(t)$ and $h_6(t)$ when $o_1>\underset{a_1}{\mathbb{E}}[a_1]$, $h_6(0)< h_5(0)$ and $h_6(\min\{o_1,o_2\})> h_5(\min\{o_1,o_2\})$.

Theorems & Definitions (39)

  • Definition 1: Merging Mechanism
  • Definition 2: Incentive Compatibility
  • Definition 3: Individual Rationality
  • Lemma 1: M81
  • Lemma 2: Form Stability LMZWZYXZD24
  • Lemma 3: LMZWZYXZD24
  • Lemma 4: LMZWZYXZD24
  • Proposition 1
  • Corollary 1
  • Lemma 5
  • ...and 29 more