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Understanding Strategic Platform Entry and Seller Exploration: A Stackelberg Model

Garrett Seo, Xintong Wang, David C. Parkes

Abstract

Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.

Understanding Strategic Platform Entry and Seller Exploration: A Stackelberg Model

Abstract

Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.
Paper Structure (35 sections, 1 theorem, 17 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 35 sections, 1 theorem, 17 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. A Single-Seller Model with Platform Entry
  4. A Stackelberg Model of Platform Entry
  5. Shared Product Space.
  6. The Seller's Problem.
  7. The Platform's Policy.
  8. Seller's Optimal Policy Under $\boldsymbol{\pi_p}$
  9. Finding the Optimal Platform Policy
  10. Global Entry
  11. Global Entry and Transaction Fee
  12. Heterogeneous Entry
  13. Computation and Complexity
  14. An Illustration of Platform Policy Choice
  15. A Multi-Seller Model with Platform Entry
  16. ...and 20 more sections

Key Result

proposition 1

A platform's policy $\boldsymbol{\pi_p}$ preserves the products as independent stochastic processes, only if the seller acts optimally in response. The seller's optimal policy is the Gittins-index policy.

Figures (3)

  • Figure 1: Expected utility metrics for the platform (blue), sellers (green), and buyers (yellow) as a function of $T_p$ on left. Products explored (yellow), product variety (blue), and cluster rate (purple) as a function of $T_p$ on right. These metrics are based on the results of 4,000 environment simulations. The range at each $T_p$ denotes outcomes from multiple equilibria. In C1, optimal entry is early, $T^*_p \approx 2$, to capture value from the clustered product. In C2, optimal entry is delayed, $T^*_p \approx 5$, to cover high innovation costs. In D1, optimal entry, $T^*_p \approx 2$, has a muted effect on innovation. In D2, optimal entry is delayed, $T^*_p \approx 11$.
  • Figure 2: Gittins indices for Product Type A and Product Type B as a function of global $T_p$.
  • Figure 3: Boundaries and regions induced by Product Type A and Product Type B for heterogeneous $\mathbf{T_p}$

Theorems & Definitions (1)

  • proposition 1