Limiting Inequalities in Repeated House and Task Allocation

We consider house and task allocation markets over multiple rounds, where agents have endowments and valuations at each given round. The endowments encode allocations of agents at the previous rounds. The valuations encode the preferences of agents at the current round. For these problems, we define novel axiomatic norms, denoted as JFXRC, JFXRR, JF1RC, JF1RR, and JF1B, that limit inequalities in allocations gradually. When the endowments are equal, we prove that computing JFXRC and JFXRR allocations may take exponential time whereas computing JF1RC and JF1RR allocations takes polynomial time. However, when the endowments are unequal, JF1RC or JF1RR allocations may not exist whereas computing JF1B allocations takes polynomial time. Finally, our work offers a number of polynomial-time algorithms for limiting inequalities in repeated house and task allocation markets.