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 A
Type B
Cost
50
120
Reward
100, 50
200, 0
Probability
0.5, 0.5
0.2, 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 Tp on left. Products explored (yellow), product variety (blue), and cluster rate (purple) as a function of Tp on right. These metrics are based on the results of 4,000 environment simulations. The range at each Tp denotes outcomes from multiple equilibria. In C1, optimal entry is early, Tp∗≈2 , to capture value from the clustered product. In C2, optimal entry is delayed, Tp∗≈5 , to cover high innovation costs. In D1, optimal entry, Tp∗≈2 , has a muted effect on innovation. In D2, optimal entry is delayed, Tp∗≈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 Tp .
Figure 3. Boundaries and regions induced by Product Type A and Product Type B for heterogeneous Tp
Param
Value
LR
0.0001
Discount factor
0.9
Batch Size
32
Buffer Size
450000 states
Exploration Decay
0.99995
Exploration Factor
1 → 0.25
Appendix
Hyperparameters for Training: All hyperparameters omitted from Iterative Best-Response share the same hyperparameters as IQL-DQN.
Generative model ecosystems increasingly operate as competitive multi-platform markets, where platforms strategically select models from a shared pool and users with heterogeneous preferences choose among them. Understanding how platforms interact, when market equilibria exist, how outcomes are shaped by model-providers, platforms, and user behavior, and how social welfare is affected is critical for fostering a beneficial market environment. In this paper, we formalize a three-layer model-platform-user market game and identify conditions for the existence of pure Nash equilibrium. Our analysis shows that market structure, whether platforms converge on similar models or differentiate by selecting distinct ones, depends not only on models' global average performance but also on their localized attraction to user groups. We further examine welfare outcomes and show that expanding the model pool does not necessarily increase user welfare or market diversity. Finally, we design novel best-response training schemes that allow model providers to strategically introduce new models into competitive markets.
On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical arguments suggest that ignoring competitors induces model misspecification and inefficiency, yet findings from algorithmic collusion suggest that ignoring competitor prices may, surprisingly, facilitate collusive outcomes and improve profits. We study this problem in a competitive market with unknown noisy demand, in which sellers repeatedly set prices, either incorporating competitor prices in learning their demand models (informed), or ignoring them (oblivious). We show that, relative to a monopolist, an oblivious seller in a competitive market must conduct more aggressive price exploration to compensate for the loss of dynamic competitor information. When all sellers are oblivious, prices converge to the competitive outcome under persistent exploration, while a continuum of pseudo-equilibria arises when exploration is "insufficient." In markets with a mix of oblivious and informed sellers, the informed strictly out-earn the oblivious. In game-theoretic terms, the unique Nash equilibrium is the all-informed market, in which prices converge to the competitive outcome efficiently, and oblivious modeling does not robustly lead to collusive patterns.
Online marketplaces increasingly do more than simply match buyers and sellers: they route orders across competing sellers and, in many categories, offer ancillary fulfillment services that make seller inventory a source of platform revenue. We investigate how a platform can use intertemporal demand allocation to influence sellers' inventory choices without directly controlling stock. We develop a model in which the platform observes aggregate demand, allocates orders across sellers over time, and sellers choose between two fulfillment options, fulfill-by-merchant (FBM) and fulfill-by-platform (FBP), while replenishing inventory under state-dependent base-stock policies. The key mechanism we study is informational: by changing the predictability of each seller's sales stream, the platform changes sellers' safety-stock needs even when average demand shares remain unchanged. We focus on nondiscriminatory allocation policies that give sellers the same demand share and forecast risk. Within this class, uniform splitting minimizes forecast uncertainty, whereas any higher level of uncertainty can be implemented using simple low-memory allocation rules. Moreover, increasing uncertainty above the uniform benchmark requires routing rules that prevent sellers from inferring aggregate demand from their own sales histories. These results reduce the platform's problem to choosing a level of forecast uncertainty that trades off adoption of platform fulfillment against the inventory held by adopters. Our analysis identifies demand allocation as a powerful operational and informational design lever in digital marketplaces.
Rene Caldentey, Tong Xie
Booth School of Business, The University of Chicago, Chicago, IL 60637