Equal-quantile rules in resource allocation with uncertain demands

Assistant Professor of Economics, Singapore Management University.

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We consider the allocation problems in which agents have uncertain demands over a resource and allocation of the resource has to be made before the uncertainty resolves. We propose the class of equal-quantile rules that ensure all agents equal probability of being fully satisfied, with the probability bounded by a parameter. If the welfare loss due to unsatisfied demands and wasted resource are both linear, then an equal-quantile rule with a properly chosen parameter always selects the allocation that minimizes the total expected welfare loss. We further show that the class of equal-quantile rules are the only rules satisfying the following properties: consistency, continuity, strong ranking, and ordinality. In particular, ordinality requires the allocation to be invariant under any continuous and non-decreasing transformation of a problem.