Allocating positions fairly: auctions and Shapley value

The paper by Van Essen and Wooders published in the Journal of Economic Theory studies the properties of an auction that fairly and efficiently allocates heterogenous items, priorities, positions, or property rights when participants all have equal claims. The auction is designed to allocate heterogeneous items when the participants have different values for the items, and when each participant’s values for the items are known only to the participant. Examples of this type of problem include allocating items to heirs in an estate, allocating priority of service in a queue, and allocating rights to exploit resources (e.g., fish, oil, etc.) in different geographic regions. Read the paper here: https://doi.org/10.1016/j.jet.2021.105315

The paper has several main findings:

• It characterizes the allocation of items and the associated money transfers between participants that are “fair” in Shapley’s sense. The Shapley value is a fundamental solution concept in cooperative game theory that is often used as a benchmark for fair allocations.

• It shows that each participant in the auction has a cautious strategy that guarantees him a payoff that is at least as great as what he would obtain were the items allocated randomly among participants. When every bidder follows the cautious strategy, then the allocation that results is the Shapley value allocation.

• In the equilibrium of the auction (i.e., when all the participants bid optimally), then items are allocated to participants in a way that maximizes the participants’ total payoffs, i.e., the allocation is efficient.

This work shows how to fairly and efficiently allocate heterogenous items when the participants are privately informed about their own values for the items. Future work will use laboratory experiments to investigate the practical performance of this new auction.