We evaluate the fairness of a rule allocating among agents with equal rights by computing their utility for a hypothetical worst-case share, that only depends on their own valuation and the number of agents. For indivisible goods, Budish [J. Political Econ., 2011] proposed the maximin share : the least utility of a bundle in the best partition of the objects; unfortunately maximin share is not always satisfiable. Earlier, Hill [Ann. Probab., 1987] proposed the worst maximin share over all utilities with the same largest possible single-object value. More conservative than maximin share, it is guaranteed to be satisfiable for any possible profile of utilities and its computation is elementary whereas it is NP-hard to compute maximin share. We apply Hill’s approach to the allocation of indivisible bads (objects with disutilities) and compute in closed form the worst-case minimax share for a given value of the worst single bad. We show that the worst-case minimax share is close to the original minimax share and that its monotonic closure is the best guaranteed share for all allocation instances with a common upper bound on the value of the worst single bad.

Bo Li

Herve Moulin

Ankang Sun

Yu Zhou

ACM Transactions on Economics and Computation

The ACM Transactions on Economics and Computation welcomes submissions of the highest quality that concern the intersection of computer science and economics. Of interest to the journal is any topic relevant to both economists and computer scientists, including but not limited to the following:    Agents in networks  Algorithmic game theory  Computation of equilibria  Computational social choice  Cost of strategic behavior and cost of decentralization ("price of anarchy")  Design and analysis of electronic markets  Economics of computational advertising  Electronic commerce  Learning in games and markets  Mechanism design  Paid search auctions  Privacy  Recommendation / reputation / trust systems  Systems resilient against malicious agents.

The ACM Transactions on Economics and Computation welcomes submissions of the highest quality that explore the intersection of computer science and economics. The journal is interested in topics relevant to both economists and computer scientists, including but not limited to: agents in networks, algorithmic game theory, computation of equilibria, computational social choice, the cost of strategic behavior and decentralization ("price of anarchy"), design and analysis of electronic markets, economics of computational advertising, electronic commerce, learning in games and markets, mechanism design, paid search auctions, privacy, recommendation/reputation/trust systems, and systems resilient against malicious agents.

《ACM Transactions on Economics and Computation》欢迎提交高质量的论文，探讨计算机科学与经济学的交叉领域。期刊关注的主题包括但不限于：网络中的代理、算法博弈论、均衡计算、计算社会选择、战略行为和去中心化的成本（"无序价格"）、电子市场的设计与分析、计算广告的经济学、电子商务、游戏与市场中的学习、机制设计、付费搜索拍卖、隐私、推荐/声誉/信任系统，以及抵御恶意代理的系统。

On Hill's Worst-Case Guarantee for Indivisible Bads

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Journal Info

Category	Quartile
COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS	4