2022/12/02 by Zheng Chen, Chen, Zheng, Bo Li +5
Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2212.01031
openalex publication_date 2022/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by real-world applications, we study the fair allocation of graphical resources, where the resources are the vertices in a graph. Upon receiving a set of resources, an agent's utility equals the weight of a maximum matching in the induced subgraph. We care about maximin share (MMS) fairness and envy-freeness up to one item (EF1). Regarding MMS fairness, the problem does not admit a finite approximation ratio for heterogeneous agents. For homogeneous agents, we design constant-approximation polynomial-time algorithms, and also note that significant amount of social welfare is sacrificed inevitably in order to ensure (approximate) MMS fairness. We then consider EF1 allocations whose existence is guaranteed. However, the social welfare guarantee of EF1 allocations cannot be better than 1/n for the general case, where n is the number of agents.Fortunately, for three special cases, binary-weight, two-agents and homogeneous-agents, we are able to design polynomial-time algorithms that also ensure a constant fractions of the maximum social welfare.