Parameterized Complexity of Manipulating Sequential Allocation

26 Nov 2019  ·  Flammini Michele, Gilbert Hugo ·

The sequential allocation protocol is a simple and popular mechanism to allocate indivisible goods, in which the agents take turns to pick the items according to a predefined sequence. While this protocol is not strategy-proof, it has been shown recently that finding a successful manipulation for an agent is an NP-hard problem (Aziz et al., 2017)... Conversely, it is also known that finding an optimal manipulation can be solved in polynomial time in a few cases: if there are only two agents or if the manipulator has a binary or a lexicographic utility function. In this work, we take a parameterized approach to provide several new complexity results on this manipulation problem. More precisely, we give a complete picture of its parameterized complexity w.r.t. the following three parameters: the number $n$ of agents, the number $\mu(a_1)$ of times the manipulator $a_1$ picks in the picking sequence, and the maximum range $\mathtt{rg}^{\max}$ of an item. This third parameter is a correlation measure on the preference rankings of the agents. In particular, we show that the problem of finding an optimal manipulation can be solved in polynomial time if $n$ or $\mu(a_1)$ is a constant, and that it is fixed-parameter tractable w.r.t. $\mathtt{rg}^{\max}$ and $n+\mu(a_1)$. Interestingly enough, we show that w.r.t. the single parameters $n$ and $\mu(a_1)$ it is W[1]-hard. Moreover, we provide an integer program and a dynamic programming scheme to solve the manipulation problem and we show that a single manipulator can increase the utility of her bundle by a multiplicative factor which is at most 2. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Computer Science and Game Theory

Datasets


  Add Datasets introduced or used in this paper