Manipulations in two-agent sequential allocation with random sequences

Sequential allocation is one of the most fundamental models for allocating indivisible items to agents in a decentralized manner, in which agents sequentially pick their favorite items among the remainder based on a pre-defined priority ordering of agents (a sequence). In recent years, algorithmic issues about agents' manipulations have also been investigated, such as the computational complexity of verifying whether a given bundle of items is achievable and maximizing one's utility under a given additive utility function. In this paper we consider a slightly modified model, where the selection process is divided into rounds, each agent obtains exactly one item in each round, and the sequence per round is determined uniformly at random. It is natural to expect that finding a profitable manipulation is difficult even for the case of two agents, since a manipulator must consider exponentially many possible sequences with respect to the number of rounds due to randomization. To our surprise, however, an optimal manipulation can be computed without any exploration for exponentially decaying utilities. Furthermore, for general additive utilities, although some exploration is required, it can still be done in polynomial time with respect to the number of rounds.