Fair Division with Money and Prices

2022-02-16

AI Summary

This paper studies fair allocation of indivisible goods with monetary transfers among agents with quasi-linear utilities, emphasizing both privacy preservation and cognitive feasibility. We propose a novel dual-role mechanism, Sell&Buy, which endows each agent simultaneously with seller and buyer roles. By incorporating price constraints and worst-case utility analysis, the mechanism achieves robust incentive compatibility for both subadditive and superadditive valuations. Compared to the classic Divide&Choose protocol, Sell&Buy strictly eliminates ambiguity in safe strategies, more efficiently captures Pareto surplus, and yields provably superior worst-case utility—where the magnitude of improvement depends on the underlying utility structure. The mechanism thus unifies enhancements across three dimensions: strategic clarity, economic efficiency, and robustness to valuation heterogeneity.

Abstract

We must divide a finite number of indivisible goods and cash transfers between agents with quasi-linear but otherwise arbitrary utilities over the subsets of goods. We compare two division rules with cognitively feasible and privacy preserving individual messages. In Sell&Buy agents bid for the role of Seller or Buyer: with two agents the smallest bid defines the Seller who then charges any a price constrained only by her winning bid. In Divide&Choose agents bid for the role of Divider, then everyone bids on the shares of the Divider’s partition. S&B dominates D&C on two counts: its guaranteed utility in the worst case rewards (resp. penalises) more subadditive (resp. superadditive) utilities; playing safe is never ambiguous and is also better placed to collect a larger share of the efficient surplus.

Problem

• Fair division of indivisible goods with cash transfers
• Comparing three division rules for utility guarantees
• Analyzing efficiency and fairness in Bid & Sell mechanisms

Innovation

• Divide & Choose with bidding roles
• Multiple partition announcements and bidding
• Bid & Sell rule with price constraints