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Register a new userBounded Incentives in Manipulating the Probabilistic Serial Rule
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Jie Zhang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The Probabilistic Serial mechanism is well-known for its desirable fairness and efficiency properties. It is one of the most prominent protocols for the random assignment problem. However, Probabilistic Serial is not incentive-compatible, thereby these desirable properties only hold for the agents declared preferences, rather than their genuine preferences. A substantial utility gain through strategic behaviors would trigger self-interested agents to manipulate the mechanism and would subvert the very foundation of adopting the mechanism in practice. In this paper, we characterize the extent to which an individual agent can increase its utility by strategic manipulation. We show that the incentive ratio of the mechanism is $frac{3}{2}$. That is, no agent can misreport its preferences such that its utility becomes more than 1.5 times of what it is when reports truthfully. This ratio is a worst-case guarantee by allowing an agent to have complete information about other agents reports and to figure out the best response strategy even if it is computationally intractable in general. To complement this worst-case study, we further evaluate an agents utility gain on average by experiments. The experiments show that an agent incentive in manipulating the rule is very limited. These results shed some light on the robustness of Probabilistic Serial against strategic manipulation, which is one step further than knowing that it is not incentive-compatible.
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The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is well-known for its superior fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We examine computational and non-computational aspects of strategising under the PS rule. Firstly, we study the computational complexity of an agent manipulating the PS rule. We present polynomial-time algorithms for optimal manipulation. Secondly, we show that expected utility best responses can cycle. Thirdly, we examine the existence and computation of Nash equilibrium profiles under the PS rule. We show that a pure Nash equilibrium is guaranteed to exist under the PS rule. For two agents, we identify two different types of preference profiles that are not only in Nash equilibrium but can also be computed in linear time. Finally, we conduct experiments to check the frequency of manipulability of the PS rule under different combinations of the number of agents, objects, and utility functions.
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