Manipulating picking sequences

Picking sequences are a natural way of allocating indivisible items to agents in a decentralized manner: at each stage, a designated agent chooses an item among those that remain available. We address the computational issues of the manipulation of picking sequences by an agent or a coalition of agents. We show that a single agent with additively separable preferences can compute an optimal manipulation in polynomial time. Then we consider several notions of coalitional manipulation, depending on whether transfers of items and/or side payments are allowed. We briefly consider agents with non-additive preferences. We also give a nontrivial upper bound on the impact of manipulation on the loss of social welfare.