Parametrized Complexity of Manipulating Sequential Allocation
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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 parametrized approach to provide several new complexity results on this manipulation problem. Notably, we show that finding an optimal manipulation can be performed in polynomial time if the number of agents is a constant and that it is fixed-parameter tractable with respect to a parameter measuring the distance between the preference rankings of the agents. 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. Overall, our results show that manipulating the sequential allocation protocol can be performed efficiently for a wide range of instances.
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