Competitive Division of a Mixed Manna
Competitive Division of a Mixed Manna
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DOI：
10.2139/ssrn.2914241
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Anna Bogomolnaia;H. Moulin;Fedor Sandomirskiy;E. Yanovskaya
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文献类型：
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作者：
Anna Bogomolnaia;H. Moulin;Fedor Sandomirskiy;E. Yanovskaya
一个混合的吗哪包含好的（每个人都喜欢的），坏的（每个人都不喜欢的），以及对一些代理人来说是好的，但对其他人来说是坏的或令人满意的物品。如果所有物品都是商品，并且效用函数是位似的、凹的（且单调的），那么收入均等的竞争均衡会使效用的纳什积最大化：因此它是福利主义的（由可行的产品集从效用角度确定）、单值的且易于计算。我们将Gale-Eisenberg定理推广到混合甘露。竞争部门仍然是福利主义的，与公用事业或非公用事业的产品有关。如果零效用分布（在任何甘露之前）是帕累托支配的，那么竞争分布是唯一的，并且仍然使效用的乘积最大化。如果零过程不可行，则竞争过程是效率边界上非效用产品的临界点，多样性是普遍存在的。特别是分配混合吗哪的任务，对每个人来说都是好消息，或者是坏消息。我们在线性偏好的实际重要情况下得到了我们的结果，在这种情况下，商品划分和商品划分之间的公理化比较特别尖锐。当我们分配货物和吗哪改善时，每个人都在竞争规则下微弱地贝内;但没有合理的分配坏的规则可以类似地资源单调。此外，更大的“非嫉妒”和“有经验”的bads分区可以被断开，这样它就不允许连续选择。
A mixed manna contains goods (that everyone likes), bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homothetic, concave (and monotone), the Competitive Equilibrium with Equal Incomes maximizes the Nash product of utilities: hence it is welfarist (determined utility-wise by the feasible set of pro les), single-valued and easy to compute. We generalize the Gale-Eisenberg Theorem to a mixed manna. The Competitive division is still welfarist and related to the product of utilities or disutilities. If the zero utility pro le (before any manna) is Pareto dominated, the competitive pro le is unique and still maximizes the product of utilities. If the zero pro le is unfeasible, the competitive pro les are the critical points of the product of disutilities on the eciency frontier, and multiplicity is pervasive. In particular the task of dividing a mixed manna is either good news for everyone, or bad news for everyone. We re ne our results in the practically important case of linear preferences, where the axiomatic comparison between the division of goods and that of bads is especially sharp. When we divide goods and the manna improves, everyone weakly bene ts under the competitive rule; but no reasonable rule to divide bads can be similarly Resource Monotonic. Also, the much larger set of Non Envious and Ecient divisions of bads can be disconnected so that it will admit no continuous selection.