Allocating Indivisible Objects With a Parallel Method Insensitive to Identities

Sequential allocation is a decentralized mechanism for allocating indivisible objects to agents, in which agents sequentially pick their favorite objects among the remainder based on a pre-defined priority ordering of agents (a sequence). The problem of choosing the “best” sequence of agents to achieve the optimal social welfare has been investigated and conjectured to be NP-hard. We propose a simple parallel allocation protocol that is insensitive to agents’ identities. In every round of the parallel allocation process, every agent asks for an object among those that remain, and every reported object will be allocated randomly to an agent reporting it. Supposing additive utilities and independence between the agents, we compare the average (and worst-case) social welfare achieved by a parallel protocol and a sequential protocol. Theoretical and empirical results show that parallel protocol outperforms a sequential protocol (even when the best sequence of agents is applied). We also show that under the parallel mechanism, some manipulation problems (e.g., finding a successful strategy for a target set and finding an optimal strategy under some scoring function) can be solved in polynomial time.