Fair Resource Allocation in a Volatile Marketplace

We consider a setting where a platform dynamically allocates a collection of goods that arrive to the platform in an online fashion to budgeted buyers, as exemplified by online advertising systems where platforms decide which impressions to serve to various advertisers. Such dynamic resource allocation problems are challenging for two reasons. (a) The platform must strike a balance between optimizing the advertiser's own revenues and guaranteeing fairness to the advertiser's (repeat) buyers, and (b) the problem is inherently dynamic due to the uncertain, time-varying supply of goods available with the platform. We propose a stochastic approximation scheme akin to a dynamic market equilibrium. Our scheme relies on frequent resolves of an Eisenberg-Gale convex program and does not require the platform to have any knowledge about how the goods' arrival processes evolve over time. The scheme fully extracts buyer budgets (thus maximizing platform revenues) and at the same time provides a 0.64 approximation of the proportionally fair allocation of goods achievable in the offline case, as long as the supply of goods comes from a wide family of (possibly nonstationary) Gaussian processes. We then deal with a multi-objective problem where the platform is concerned with both the proportional fairness and efficiency of the allocation and propose a hybrid algorithm that achieves a 0.3 bicriteria guarantee against fairness and efficiency. Finally, we build a sequence of datasets, one public dataset released by the DSP iPinYou and the second based on real Google AdX data, and use them to test the empirical performance of our schemes. We find that across these datasets there is a surprising relationship between fairness and efficiency that can be used to tune the schemes to nearly optimal performance in practice.