Fair Allocation in Dynamic Mechanism Design

TL;DR

This paper develops a dynamic mechanism design framework for fair allocation of indivisible goods over multiple rounds, balancing revenue maximization with fairness constraints for different buyer groups.

Contribution

It introduces a novel dynamic mechanism that incorporates subsidization, participation bonuses, and entry fees to ensure fair and truthful allocation over multiple rounds.

Findings

Optimal static mechanism involves subsidization to boost allocation probabilities.

Dynamic mechanism characterizes recursive functions for optimal allocations and payments.

Approximation scheme efficiently computes near-optimal fair allocations.

Abstract

We consider a dynamic mechanism design problem where an auctioneer sells an indivisible good to groups of buyers in every round, for a total of $T$ rounds. The auctioneer aims to maximize their discounted overall revenue while adhering to a fairness constraint that guarantees a minimum average allocation for each group. We begin by studying the static case ($T=1$) and establish that the optimal mechanism involves two types of subsidization: one that increases the overall probability of allocation to all buyers, and another that favors the groups which otherwise have a lower probability of winning the item. We then extend our results to the dynamic case by characterizing a set of recursive functions that determine the optimal allocation and payments in each round. Notably, our results establish that in the dynamic case, the seller, on the one hand, commits to a participation bonus to incentivize truth-telling, and on the other hand, charges an entry fee for every round. Moreover, the optimal allocation once more involves subsidization, which its extent depends on the difference in future utilities for both the seller and buyers when allocating the item to one group versus the others. Finally, we present an approximation scheme to solve the recursive equations and determine an approximately optimal and fair allocation efficiently.