Search arXivSearch

arXiv · 2605.06711

Pricing, Matching, and Bundling: an Equilibrium Analysis of Online Platforms

Abstract

Modern online platforms such as marketplaces, ride-hailing services, and food-delivery systems serve a dual role: they are both markets where participants interact and transact, and operators that design and govern how these markets function. These platforms connect multiple sides, for example buyers, sellers, and couriers, facilitating access that would otherwise be difficult to achieve. By setting the rules of the market, platforms determine who participates, how interactions take place, and how value is created and distributed. In response to these rules, participants may behave strategically, deciding whether to join the platform and which transactions to pursue. This thesis studies how platform design affects market outcomes through three key levers: pricing that determines participants' gains when operating on a platform; matching that governs which interactions are feasible among participants; and bundling that shapes the structure of supply when the platform itself acts as a market participant. Across these levers, the goal in this thesis is to understand how platforms can be designed to balance platform profitability with overall market welfare. The first part of this thesis studies pricing, including both the commission fees that participants pay to a platform and the prices associated with each transaction. The second part of this thesis studies matching. By shaping recommendation systems and consumer search, platforms influence which transactions take place. The third part of this thesis analyzes bundling. As a marketplace operator, a platform may be able to source products from sellers and offer them as bundled packages to buyers. Collectively, this thesis shows how pricing, matching, and bundling serve as complementary design levers through which platforms can shape market outcomes.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gary Qiurui Ma. 2026-05-06. Pricing, Matching, and Bundling: an Equilibrium Analysis of Online Platforms. https://arxiv.org/abs/2605.06711

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Ascending Auctions for Combinatorial Markets with Frictions: A Unified Framework via Discrete Convex Analysis

We develop a unified ascending-auction framework for computing Walrasian equilibria in combinatorial markets with strong substitutes valuations and piecewise-linear payment functions. Our auction extends the celebrated ascending auctions of Gul and Stacchetti (2000) and Ausubel (2006) to accommodate payment frictions (e.g., transaction taxes or commission fees). This is achieved by incorporating directional price updates that reflect heterogeneous payment structures. Our framework also generalizes the unit-demand imperfectly transferable utility models of Alkan (1989, 1992) to a fully combinatorial setting, thereby unifying these paradigms. Furthermore, this is the first study to compute the minimum -- also known as the buyer-optimal -- equilibrium in combinatorial markets with such frictions. Our analysis builds upon discrete convex analysis. Our main technical contribution is a characterization of valid price-update directions, together with a strongly polynomial-time algorithm for computing them. Notably, the algorithm uses only demand- and exchange-oracle queries and never requires handling information of exponential size. To compute such a direction, we formulate a lexicographic extension of the polymatroid sum problem and characterize its dual solution via a reduction to a convex flow problem. Exploiting the $\text{L}^\natural$-convexity of the dual objective, we show that the desired direction can be constructed from the minimal dual solution. This convexity also yields transparent economic and potential-based interpretations of the auction dynamics, strengthening the connection between ascending auctions and discrete optimization.

cs.GT

Beyond Provenance: The Economics and Governance of Personalized AI Memory

Personalized AI memories, defined as persistent decision-relevant states distilled by platforms from long-run human-AI interaction, are increasingly portable, provenance-certifiable, and tradable. Provenance answers the question of origin, but it does not settle who holds which rights over a memory, nor how wider deployment affects its future supply. We develop a unified model in which memory use is non-rival, while refresh, the maintenance of continued validity, is relationally co-produced by the represented individual and the platform. Even assuming perfect provenance and complete information, the model still yields a set of inherent limitations. First, there is an extraction ceiling: decision value is bounded by lived experience. Second, a rights-separation theorem shows that no budget-balanced ownership assignment can make both co-producers residual claimants, and that control rights and cash-flow rights operate on distinct margins. Third, a depletion result indicates that reach-expanding policies such as portability, interoperability, and competition raise current access but shrink the long-run memory stock. Fourth, we offer a formal comparison between memory ownership as it ought to be (subject-held) and as it is (platform-held); the welfare ranking reduces to two measurable quantities, both dominated by interior renewable-claim bundles. Finally, endogenous-quality and market-formation results show that uncompensated markets pollute their own raw material, that transparency and compensation are complements, and that the de facto platform-ownership regime is self-perpetuating. On the design side, the analysis points to separated provenance, performance, and permission credentials; compensation indexed to quality-deployment; and portability and salience, rather than nominal ownership, as the binding policy margins.

cs.GT

How Can Incentives and Cut Layer Selection Influence Data Contribution in Split Federated Learning?

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, despite its advantages, existing SFL studies have largely overlooked the strategic interactions among self-interested participants during the SFL process. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption from both computation and networking during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner while achieving a well-balanced trade-off between model accuracy and the associated computing and networking overhead during the SFL process.

cs.GT