Welfare Maximization with Deferred Acceptance Auctions in Reallocation Problems

TL;DR

This paper develops approximate, strategy-proof auction mechanisms for resource reallocation problems like spectrum and bandwidth, using greedy algorithms within the deferred acceptance framework to achieve near-optimal social welfare.

Contribution

It introduces simple greedy-based deferred acceptance auctions for reallocation problems, ensuring strategy-proofness and approximate optimality in complex resource transfer scenarios.

Findings

Achieves approximately optimal social welfare in reallocation auctions.

Designs strategy-proof procurement and selling auctions for resource rights.

Ensures feasibility and minimal constraints in resource reallocation.

Abstract

We design approximate weakly group strategy-proof mechanisms for resource reallocation problems using Milgrom and Segal's deferred acceptance auction framework: the radio spectrum and network bandwidth reallocation problems in the procurement auction setting and the cost minimization problem with set cover constraints in the selling auction setting. Our deferred acceptance auctions are derived from simple greedy algorithms for the underlying optimization problems and guarantee approximately optimal social welfare (cost) of the agents retaining their rights (contracts). In the reallocation problems, we design procurement auctions to purchase agents' broadcast/access rights to free up some of the resources such that the unpurchased rights can still be exercised with respect to the remaining resources. In the cost minimization problem, we design a selling auction to sell early termination rights to agents with existing contracts such that some minimal constraints are still satisfied with remaining contracts. In these problems, while the "allocated" agents transact, exchanging rights and payments, the objective and feasibility constraints are on the "rejected" agents.