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Dynamic max-min fair allocation (DMMF) is a simple and popular mechanism for the repeated allocation of a shared resource among competing agents: in each round, each agent can choose to request or not for the resource, which is then allocated to the requesting agent with the least number of allocations received till then. Recent work has shown that under DMMF, a simple threshold-based request policy enjoys surprisingly strong robustness properties, wherein each agent can realize a significant fraction of her optimal utility irrespective of how other agents' behave. While this goes some way in mitigating the possibility of a 'tragedy of the commons' outcome, the robust policies require that an agent defend against arbitrary (possibly adversarial) behavior by other agents. This however may be far from optimal compared to real world settings, where other agents are selfish optimizers rather than adversaries. Therefore, robust guarantees give no insight on how agents behave in an equilibrium, and whether outcomes are improved under one. Our work aims to bridge this gap by studying the existence and properties of equilibria under DMMF. To this end, we first show that despite the strong robustness guarantees of the threshold based strategies,no Nash equilibrium existswhen agents participate in DMMF, each using some fixed threshold-based policy. On the positive side, however, we show that for the symmetric case, a simple data-driven request policy guarantees that no agent benefits from deviating to a different fixed threshold policy. In our proposed policy agents aim to match the historical allocation rate with a vanishing drift towards the rate optimizing overall welfare for all users. Furthermore, the resulting equilibrium outcome can be significantly better compared to what follows from the robustness guarantees. Our results are built on a complete characterization of the steady-state distribution under DMMF, as well as new techniques for analyzing strategic agent outcomes under dynamic allocation mechanisms; we hope these may prove of independent interest in related problems. 

We study the problem of jointly pricing and designing a smart transit system, where a transit agency (the platform) controls a fleet of demand-responsive vehicles (cars) and a fixed line service (buses). The platform offers commuters a menu of options (modes) to travel between origin and destination (e.g., direct car trip, a bus ride, or a combination of the two), and commuters make a utility-maximizing choice within this menu, given the price of each mode. The goal of the platform is to determine an optimal set of modes to display to commuters, prices for these modes, and the design of the transit network in order to maximize the social welfare of the system. In this work, we tackle the commuter choice aspect of this problem, traditionally approached via computationally intensive bilevel programming techniques. In particular, we develop a framework that efficiently decouples the pricing and network design problem: Given an efficient (approximation) algorithm for centralized network design without prices, there exists an efficient (approximation) algorithm for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world data set. We moreover explore the dependence of metrics such as welfare, revenue, and mode usage on (i) transfer costs and (ii) cost of contracting with on-demand service providers and exhibit the welfare gains of a fully integrated mobility system. Funding: This work was supported by the National Science Foundation [Awards CMMI-2308750, CNS-1952011, and CMMI-2144127]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0452 . 

We devise an online learning algorithm -- titled Switching via Monotone Adapted Regret Traces (SMART) -- that adapts to the data and achieves regret that is instance optimal, i.e., simultaneously competitive on every input sequence compared to the performance of the follow-the-leader (FTL) policy and the worst case guarantee of any other input policy. We show that the regret of the SMART policy on any input sequence is within a multiplicative factor e/(e−1)≈1.58 of the smaller of: 1) the regret obtained by FTL on the sequence, and 2) the upper bound on regret guaranteed by the given worst-case policy. This implies a strictly stronger guarantee than typical `best-of-both-worlds' bounds as the guarantee holds for every input sequence regardless of how it is generated. SMART is simple to implement as it begins by playing FTL and switches at most once during the time horizon to the worst-case algorithm. Our approach and results follow from an operational reduction of instance optimal online learning to competitive analysis for the ski-rental problem. We complement our competitive ratio upper bounds with a fundamental lower bound showing that over all input sequences, no algorithm can get better than a 1.43-fraction of the minimum regret achieved by FTL and the minimax-optimal policy. We also present a modification of SMART that combines FTL with a ``small-loss" algorithm to achieve instance optimality between the regret of FTL and the small loss regret bound. 

We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision-maker must commit to an allocation for these individuals before moving on to the next round. In contrast to prior work, we consider a setting in which resources are perishable and individuals' utilities are potentially non-linear (e.g., goods exhibit complementarities). The goal is to construct a sequence of allocations that is envy-free and efficient. We design an algorithm that takes as input (i) a prediction of the perishing order, and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand and perishing to adaptively choose one of two carefully constructed guardrail quantities. We characterize conditions under which our algorithm achieves the optimal envy-efficiency Pareto frontier. We moreover demonstrate its strong numerical performance using data from a partnering food bank. 

We design online algorithms for the fair allocation of public goods to a set of N agents over a sequence of T rounds and focus on improving their performance using predictions. In the basic model, a public good arrives in each round, and every agent reveals their value for it upon arrival. The algorithm must irrevocably decide the investment in this good without exceeding a total budget of B across all rounds. The algorithm can utilize (potentially noisy) predictions of each agent’s total value for all remaining goods. The algorithm’s performance is measured using a proportional fairness objective, which informally demands that every group of agents be rewarded proportional to its size and the cohesiveness of its preferences. We show that no algorithm can achieve better than Θ(T/B) proportional fairness without predictions. With reasonably accurate predictions, the situation improves significantly, and Θ(log(T/B)) proportional fairness is achieved. We also extend our results to a general setting wherein a batch of L public goods arrive in each round and O(log(min(N,L) ·T/B)) proportional fairness is achieved. Our exact bounds are parameterized as a function of the prediction error, with performance degrading gracefully with increasing errors.