We consider the problem of allocating a set of indivisible goods to a set of strategic agents with arbitrary weights. While truthful mechanism is hard to guarantee any non-trivial fairness, Amanatidis et al. (WINE 2021 and MOR 2024) studied the fairness guarantees of the equilibria of the Round-Robin mechanism. They show that when all agents have the same weight, every pure Nash equilibrium of Round-Robin leads to an envy-free up to one item (EF1) allocation, with respect to agents' true valuations. In this paper, we investigate the weighted setting where agents are asymmetric and study the weighted picking sequence protocol, which is a natural extension of Round-Robin in the weighted setting. More specifically, we show that the weighted picking sequence protocol always has pure Nash equilibria and all the corresponding allocations are weighted EF1 with respect to the true valuation functions for two agents.
We study the facility location problem in the context of individual fairness to propose the Individual Preference Facility Location (IPFL) problem. In the vanilla facility location problem, the goal is to select a subset of facilities to serve all clients while minimizing total opening and connection costs. IPFL aims to optimize the facility location objective while meeting individual preferences by requiring that each client is served by a facility within its fair radius. The fair radius is defined as the distance between a client and its τ -th nearest neighbor, where τ is a carefully designed parameter. IPFL balances facility load by opening more facilities in dense areas. However, a few clients may disproportionately affect the final costs or violate the individual preference constraints. To address this, we extend IPFL to its outlier variant, IPFLO, where up to m clients can remain unserved. As our contribution, we provide 2-approximation algorithms for both IPFL and IPFLO using a dual fitting technique.
This work focuses on the strategyproofness of voting systems in which voters select multiple options from a set of possibilities. These systems include those that are used for Participatory Budgeting, where elections are held to determine the allocation of a community budget (e.g., city or regional level) for funding various projects. We present a model for analyzing voting mechanisms and the Constrained Change Property (CCP), which serves as a criterion for designing strategyproof voting mechanisms. Additionally, we define a new concept of a social choice function and leverage it to develop a new class of utilitarian voting mechanisms, referred to as score voting. We prove that the mechanisms designed with core voting with a neutral score function are equivalent to knapsack voting on the same instance. Furthermore, we demonstrate that a score voting mechanism based on a total score function is strategyproof if and only if its score function satisfies CCP. Building on these findings, we propose an algorithm capable of identifying the closest total score function that ensures the strategyproofness of any given score voting mechanism.
We study the stable matching problem with partial information, where agents submit only partial approval preferences, and the goal is to find a matching that is as stable as possible in the worst-case scenario. Unlike previous studies that focus solely on the Stable Marriage setting and measure stability by the number of blocking pairs, we explore another well-explored stability measure: the number of blocking agents. Additionally, we extend our analysis to both the Stable Roommates and Hospital/Residents problems. Our findings offer a comprehensive view of the computational complexity across these problem variants, highlighting interesting contrasts between blocking agents and blocking pairs, as well as among the three stable matching settings.
This paper investigates waitlist mechanisms for public housing allocation, introducing the pay-per-offer mechanism as a novel alternative to the deferral-based approach. Through a Markov decision process, dynamically arriving items are allocated to waiting agents with heterogeneous values for different items and diverse outside options. Key contributions include analysis of optimal strategies for agents in these mechanisms, evaluation of how evaluation metrics vary based on the distribution of outside options and waitlist parameters. We provide valuable insights into the design and impact of various waitlist mechanisms.
