Robust Resource Allocation via Competitive Subsidies
David X. Lin, Giannis Fikioris, Siddhartha Banerjee, Éva Tardos
TL;DR
The paper advances robust, non-monetary online resource allocation by introducing a simple competitive subsidies mechanism that allocates the item uniformly at random among bidders who request it and charges the winner proportionally to competition. With a carefully chosen payment rule, the scheme guarantees at least 0.625 of each agent’s ideal utility under alpha_i-aggressive strategies, constraining the power of adversarial behavior. It also shows this bound is optimal within a broad class of static payment rules and demonstrates how to realize approximate equilibria, achieving about 0.61 robustness at equilibrium and approaching the 1-1/e non-strategic bound. The authors further extend the design to asymmetric fair shares using a simulated-agent framework, preserving both robustness and equilibrium properties across heterogenous agents, thereby nearly closing the gap to the fundamental upper bound while maintaining simplicity and practicality.
Abstract
A canonical setting for non-monetary online resource allocation is one where agents compete over multiple rounds for a single item per round, with i.i.d. valuations and additive utilities across rounds. With $n$ symmetric agents, a natural benchmark for each agent is the utility realized by her favorite $1/n$-fraction of rounds; a line of work has demonstrated one can robustly guarantee each agent a constant fraction of this ideal utility, irrespective of how other agents behave. In particular, several mechanisms have been shown to be $1/2$-robust, and recent work established that repeated first-price auctions based on artificial credits have a robustness factor of $0.59$, which cannot be improved beyond $0.6$ using first-price and simple strategies. In contrast, even without strategic considerations, the best achievable factor is $1-1/e\approx 0.63$. In this work, we break the $0.6$ first-price barrier to get a new $0.625$-robust mechanism, which almost closes the gap to the non-strategic robustness bound. Surprisingly, we do so via a simple auction, where in each round, bidders decide if they ask for the item, and we allocate uniformly at random among those who ask. The main new ingredient is the idea of competitive subsidies, wherein we charge the winning agent an amount in artificial credits that decreases when fewer agents are bidding (specifically, when $k$ agents bid, then the winner pays proportional to $k/(k+1)$, varying the payment by a factor of 2 depending on the competition). Moreover, we show how it can be modified to get an equilibrium strategy with a slightly weaker robust guarantee of $5/(3e) \approx 0.61$ (and the optimal $1-1/e$ factor at equilibrium). Finally, we show that our mechanism gives the best possible bound under a wide class of auction-based mechanisms.