# Equilibria and Learning in Modular Marketplaces

arXiv: https://arxiv.org/abs/2502.20346 · HTML: https://mlsanity.com/paper/2502.20346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [A Theoretical Framework for Modular Learning of Robust Generative Models](https://mlsanity.com/paper/2602.17554/) (2026)

## Abstract (arXiv)

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.