Egalitarian Resource Sharing Over Multiple Rounds

It is often beneficial for agents to pool their resources in order to better accommodate fluctuations in individual demand. Many multi-round resource allocation mechanisms operate in an online manner: in each round, the agents specify their demands for that round, and the mechanism determines a corresponding allocation. In this paper, we focus instead on the offline setting in which the agents specify their demand for each round at the outset. We formulate a specific resource allocation problem in this setting, and design and analyze an associated mechanism based on the solution concept of lexicographic maximin fairness. We present an efficient implementation of our mechanism, and prove that it is Pareto-efficient, envy-free, non-wasteful, resource monotonic, population monotonic, and group strategyproof. We also prove that our mechanism guarantees each agent at least half of the utility that they can obtain by not sharing their resources. We complement these positive results by proving that no maximin fair mechanism can improve on the aforementioned factor of one-half.