Complexity of Manipulating Sequential Allocation

TL;DR

This paper investigates the computational complexity of manipulating sequential allocation, disproves previous claims about best response algorithms, and establishes that computing a best response is NP-complete, highlighting the problem's inherent difficulty.

Contribution

The paper corrects prior claims by showing the NP-completeness of computing a best response in sequential allocation, and clarifies the limitations of existing algorithms.

Findings

Previous claims about the polynomial-time algorithm are false.

Computing a best response is NP-complete.

Results for two-agent cases still hold.

Abstract

Sequential allocation is a simple allocation mechanism in which agents are given pre-specified turns and each agents gets the most preferred item that is still available. It has long been known that sequential allocation is not strategyproof. Bouveret and Lang (2014) presented a polynomial-time algorithm to compute a best response of an agent with respect to additively separable utilities and claimed that (1) their algorithm correctly finds a best response, and (2) each best response results in the same allocation for the manipulator. We show that both claims are false via an example. We then show that in fact the problem of computing a best response is NP-complete. On the other hand, the insights and results of Bouveret and Lang (2014) for the case of two agents still hold.