We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.

We introduce PKR-QA (Procedural Knowledge Reasoning Question Answering), a new benchmark for question answering over procedural tasks that require structured reasoning. PKR-QA is constructed semi-automatically using a procedural knowledge graph (PKG), which encodes task-specific knowledge across diverse domains. The PKG is built by curating and linking information from the COIN instructional video dataset and the ontology, enriched with commonsense knowledge from ConceptNet and structured outputs from Large Language Models (LLMs), followed by manual verification. To generate question-answer pairs, we design graph traversal templates where each template is applied systematically over PKG. To enable interpretable reasoning, we propose a neurosymbolic approach called Knowledge Module Learning (KML), which learns procedural relations via neural modules and composes them for structured reasoning with LLMs. Experiments demonstrate that this paradigm improves reasoning performance on PKR-QA and enables step-by-step reasoning traces that facilitate interpretability.

Envy-freeness up to any good (EFX) is a popular and important fairness property in the fair allocation of indivisible goods, of which its existence in general is still an open question. In this work, we investigate the problem of determining the minimum number of EFX allocations for a given instance, arguing that this approach may yield valuable insights into the existence and computation of EFX allocations. We focus on restricted instances where the number of goods slightly exceeds the number of agents, and extend our analysis to weighted EFX (WEFX) and a novel variant of EFX for general monotone valuations, termed EFX+. In doing so, we identify the transition threshold for the existence of allocations satisfying these fairness notions. Notably, we resolve open problems regarding WEFX by proving polynomial-time computability under binary additive valuations, and establishing the first constant-factor approximation for two agents.

We study a model of sequential decision-making where voters have dynamic preferences over a set of candidates that are undesirable. This models scenarios such as the implementation of projects that are overall beneficial to society, but impose individual costs on certain affected individuals. We show that while minimizing the sum of agents' disutilities can be done in polynomial time, minimizing the maximum disutility obtained by any agent is computationally intractable, even in restricted cases. We then examine the potential for agents to engage in strategic manipulation in response to these welfare objectives, offering insights into possible misconduct within such decision-making environments.

We study a model of subscription-based platforms where users pay a fixed fee for unlimited access to content, and creators receive a share of the revenue. Existing approaches to detecting fraud predominantly rely on machine learning methods, engaging in an ongoing arms race with bad actors. We explore revenue division mechanisms that inherently disincentivize manipulation. We formalize three types of manipulation-resistance axioms and examine which existing rules satisfy these. We show that a mechanism widely used by streaming platforms, not only fails to prevent fraud, but also makes detecting manipulation computationally intractable. We also introduce a novel rule, ScaledUserProp, that satisfies all three manipulation-resistance axioms. Finally, experiments with both real-world and synthetic streaming data support ScaledUserProp as a fairer alternative compared to existing rules.

We study a temporal voting model where voters have dynamic preferences over a set of public chores---projects that benefit society, but impose individual costs on those affected by their implementation. We investigate the computational complexity of optimizing utilitarian and egalitarian welfare. Our results show that while optimizing the former is computationally straightforward, minimizing the latter is computationally intractable, even in very restricted cases. Nevertheless, we identify several settings where this problem can be solved efficiently, either exactly or by an approximation algorithm. We also examine the effects of enforcing temporal fairness and its impact on social welfare, and analyze the competitive ratio of online algorithms. We then explore the strategic behavior of agents, providing insights into potential malfeasance in such decision-making environments. Finally, we discuss a range of fairness measures and their suitability for our setting.

We study the computational problems associated with maximizing various welfare objectives—namely utilitarian welfare, egalitarian welfare, and Nash welfare—in perpetual voting, a sequential collective decision-making framework. Prior work look into notions of fairness over time and study extensions of single-round voting rules to the multi-round setting. We show that while a utilitarian-welfare maximizing outcome can be computed efficiently, an outcome that maximizes egalitarian or Nash welfare is computationally intractable, even in the case of two candidates. We complement this by showing that maximizing egalitarian welfare is fixed-parameter tractable in the number of agents, and maximizing egalitarian or Nash welfare is W[2]-hard and slicewise polynomial in the number of timesteps. We also provide an approximation algorithm for maximizing egalitarian welfare and study strategyproofness with respect to these welfare objectives. Finally, we show that a simple greedy algorithm can achieve approximate proportionality in this setting.

We investigate a model of sequential decision-making where a single alternative is chosen at each round. We focus on two objectives—utilitarian welfare (UTIL) and egalitarian welfare (EGAL)—and consider the computational complexity of the associated maximization problems, as well as their compatibility with strategyproofness and proportionality. We observe that maximizing UTIL is easy, but the corresponding decision problem for EGAL is NP-complete even in restricted cases. We complement this hardness result for EGAL with parameterized complexity analysis and an approximation algorithm. Additionally, we show that, while a mechanism that outputs a UTIL outcome is strategyproof, all deterministic mechanisms for computing EGAL outcomes fail a very weak variant of strategyproofness, called non-obvious manipulability (NOM). However, we show that when agents have non-empty approval sets at each timestep, choosing an EGAL-maximizing outcome while breaking ties lexicographically satisfies NOM. Regarding proportionality, we prove that a proportional (PROP) outcome can be computed efficiently, but finding an outcome that maximizes UTIL while guaranteeing PROP is NP-hard. We also derive upper and lower bounds on the price of proportionality with respect to UTIL and EGAL.