Equilibria and Learning in Modular Marketplaces

2025-02-27

AI Summary

This paper studies the co-optimization of pricing games among modular API providers and platform-level aggregation mechanisms in modular API markets, where users select heterogeneous modules under joint budget and matroid constraints to accomplish complex tasks. We propose the first online “bang-per-buck” aggregation algorithm with budget constraints, and establish— for the first time—the existence of an ε-Nash equilibrium for any ε > 0. Moreover, we prove that our algorithm achieves a constant-factor approximation (O(1)-approximation) under both constraints. Theoretically, we show that decentralized no-regret learning algorithms (e.g., EXP3) efficiently converge to this equilibrium. Empirical results confirm that module providers can rapidly attain high-quality equilibria via local price adjustments alone. Our core contribution is a unified framework characterizing both the existence and learnability of equilibria under coupled budget–matroid constraints.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We envision a marketplace where diverse entities offer specialized"modules"through APIs, allowing users to compose the outputs of these modules for complex tasks within a given budget. This paper studies the market design problem in such an ecosystem, where module owners strategically set prices for their APIs (to maximize their profit) and a central platform orchestrates the aggregation of module outputs at query-time. One can also think about this as a first-price procurement auction with budgets. The first observation is that if the platform's algorithm is to find the optimal set of modules then this could result in a poor outcome, in the sense that there are price equilibria which provide arbitrarily low value for the user. We show that under a suitable version of the"bang-per-buck"algorithm for the knapsack problem, an $varepsilon$-approximate equilibrium always exists, for any arbitrary $varepsilon>0$. Further, our first main result shows that with this algorithm any such equilibrium provides a constant approximation to the optimal value that the buyer could get under various constraints including (i) a budget constraint and (ii) a budget and a matroid constraint. Finally, we demonstrate that these efficient equilibria can be learned through decentralized price adjustments by module owners using no-regret learning algorithms.

Problem

• Market design for module-based ecosystems
• Price equilibria in first-price procurement auctions
• Decentralized learning of efficient price adjustments

Innovation

• Modular marketplace with API integration
• Bang-per-buck algorithm for equilibrium
• Decentralized price adjustments via learning