cs.MAMar 15, 2026

Understanding Strategic Platform Entry and Seller Exploration: A Stackelberg Model

Authors: Garrett Seo, Xintong Wang, David C. Parkes

Organizations: Rutgers University, New Brunswick, NJ, USA · Harvard University, Cambridge, MA, USA

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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.

Figures & tables

 Type AType B
Cost50120
Reward100, 50200, 0
Probability0.5, 0.50.2, 0.8
Table 1. Type A represents a product with moderate, stable payoffs and a relatively low cost, whereas Type B a riskier product with the potential of higher reward but higher cost.
Table 2. Agent utility and seller exploration metrics on markets with different product compositions.
Figure 1. Expected utility metrics for the platform (blue), sellers (green), and buyers (yellow) as a function of TpT_{p} on left. Products explored (yellow), product variety (blue), and cluster rate (purple) as a function of TpT_{p} on right. These metrics are based on the results of 4,000 environment simulations. The range at each TpT_{p} denotes outcomes from multiple equilibria. In C1, optimal entry is early, Tp∗≈2T^{*}_{p}\approx 2 , to capture value from the clustered product. In C2, optimal entry is delayed, Tp∗≈5T^{*}_{p}\approx 5 , to cover high innovation costs. In D1, optimal entry, Tp∗≈2T^{*}_{p}\approx 2 , has a muted effect on innovation. In D2, optimal entry is delayed, Tp∗≈11T^{*}_{p}\approx 11 .
Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2. Gittins indices for Product Type A and Product Type B as a function of global TpT_{p} .
Figure 3. Boundaries and regions induced by Product Type A and Product Type B for heterogeneous Tp\mathbf{T_{p}}
ParamValue
LR0.0001
Discount factor0.9
Batch Size32
Buffer Size450000 states
Exploration Decay0.99995
Exploration Factor1 →\rightarrow 0.25
Appendix
Hyperparameters for Training: All hyperparameters omitted from Iterative Best-Response share the same hyperparameters as IQL-DQN.
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