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The problem of fairly allocating a set of indivisible items is a well-knownchallenge in the field of (computational) social choice. In this scenario,there is a fundamental incompatibility between notions of fairness (such asenvy-freeness and proportionality) and economic efficiency (such asPareto-optimality). However, in the real world, items are not always allocatedonce and for all, but often repeatedly. For example, the items may be recurringchores to distribute in a household. Motivated by this, we initiate the studyof the repeated fair division of indivisible goods and chores, and propose aformal model for this scenario. In this paper, we show that, if the number ofrepetitions is a multiple of the number of agents, there always exists asequence of allocations that is proportional and Pareto-optimal. On the otherhand, irrespective of the number of repetitions, an envy-free andPareto-optimal sequence of allocations may not exist. For the case of twoagents, we show that if the number of repetitions is even, it is alwayspossible to find a sequence of allocations that is overall envy-free andPareto-optimal. We then prove even stronger fairness guarantees, showing thatevery allocation in such a sequence satisfies some relaxation of envy-freeness.Finally, in case that the number of repetitions can be chosen freely, we showthat envy-free and Pareto-optimal allocations are achievable for any number ofagents.

Repeated Fair Allocation of Indivisible Items