讲座题目： Fair division under objective constraints and ordinal input（客观约束和序数投入下的公平分配）

主讲人：Anna Bogomolnaia University of Glasgow （格拉斯哥大学）  教授

讲座时间：2024年4月10日15:40

讲座地点：学院121

讲座内容摘要：

A set A of m indivisible objects is to be fully allocated between n agents; each agent i is to get exactly qi objects. Agents only report their ordinal preference orderings of single objects in A. Thus, a mechanism designer can only partially compare allocations of an agent, based on stochastic dominance.

The paper shows the existence of an allocation rule, which satisfies Ordinal Efficiency (weaker condition than full efficiency, unreachable in this model), Ordinal Proportionality up to one object exchange (oPRO1) and Ordinal Envy-Freeness up to one object exchange (oEF1) (stronger conditions then cardinal ones). It is proven by demonstrating that an appropriate generalization of Round Robin rule (gRR) always exists for the case of different entitlements qi, and satisfies a plethora of attractive normative properties.

Concepts of fairness "up to one object exchange" are introduced as necessary modifications for our new model of classical "up to one object" fairness properties used in standard fair division literature.

一组包含m个不可分物品的集合A需要完全分配给n个代理人；每个代理人i需获得确切的物品qi个物品。代理人只能报告他们对A中单个对象的序数偏好顺序。因此，机制设计者只能基于随机优势部分比较代理人的分配情况。本文证明了存在一种分配规则，满足序数效率（比完全效率条件更弱，在这个模型中无法达到），一次物品交换的序数比例公平性（oPRO1），以及一次物品交换的序数无嫉妒性（oEF1）（比基于基数的条件更强）。通过证明适当推广的轮流法则（gRR）总是存在于不同权力qi的情况下，并且满足大量有吸引力的规范性质。在我们的新模型中，公平性的概念“一次对象交换”被引入为对标准公平分配文献中使用的传统“一次对象”公平性的必要修改。

主讲人信息：

Anna Bogomolnaia received her PhD in Economics from Universitat Autonoma de Barcelona, Spain, in 1998. She also holds Master degree in Mathematics from St. Petersburg University, Russia. Before joining University of Glasgow in 2013, she worked at University of Nottingham, Southern Methodist University, and Rice University.

Anna Bogomolnaia，教授，1998年获得西班牙巴塞罗那自治大学经济学博士学位，还拥有俄罗斯圣彼得堡大学数学硕士学位。在2013年加入格拉斯哥大学之前，她曾在诺丁汉大学、南卫理公会大学和莱斯大学工作。研究成果发表于Econometrica，Journal of Economic Theory，Theoretical Economics，Games and Economic Behavior，Management Science，Mathematics of Operations Research等国际期刊。