Bounding the Incentive Ratio of the Probabilistic Serial Rule

Bo Li, Ankang Sun, Shiji Xing

Abstract: Probabilistic Serial (PS) is a well-studied allocation rule used for distributing resources among multiple agents. Although it satisfies certain notable fairness and welfare properties, it is not truthful. This means that agents have incentives to misreport their preferences in order to influence the allocation in their favor. An interesting research question is to understand the extent to which an agent can gain from manipulation. A widely-accepted concept employed for this exploration is the incentive ratio, defined as the supreme ratio, across all instances of the problem, between the utility an agent obtains by employing an optimal manipulation strategy and the utility they receive when being truthful. Wang et al. [AAAI, 2020] examined the incentive ratio of PS for the setting when the number of items m equals the number of agents n and proved that the incentive ratio is 1.5. In this paper, we study the general scenario in which m and n can be arbitrary. We prove that in this case, the tight incentive ratio of PS is 2- 1 over 2n/i>-1.