Fair Resource Allocation in a Volatile Marketplace

We consider a setting where a platform must dynamically allocate a collection of goods that arrive to the platform in an online fashion to budgeted buyers, as exempli ed 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 her own revenues and guaranteeing fairness to her (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 re-solves 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), while at the same time provides a 0:64 approximation of the proportionally fair allocation of goods achievable in the offine case, as long as the supply of goods comes from a wide family of (possibly non-stationary) 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 which achieves a 0:3 bi-criteria guarantee against fairness and efficiency. Finally, we build a sequence of datasets, one based on real AdX data and the other a public dataset released by Chinese DSP iPinYou, 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.