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The ascending auction with flexible reporting 灵活报告的升序拍卖
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-09-10 DOI: 10.1016/j.mathsocsci.2024.09.003
Xieji Zhang

In the assignment problem where multiple heterogeneous indivisible items are assigned to unit-demand bidders, we introduce a novel ascending auction called the Flexible Reporting Ascending Auction to balance the privacy preservation and the speed of the ascending auction. Assuming bidders behave truthfully, it always results in a Walrasian equilibrium, along with the minimum Walrasian equilibrium price vector. If each bidder reports without a contradiction, bidders’ truthful behavior forms a Nash equilibrium. Our auction generalizes some well-known ascending auctions in literature, and we also provide simulation results to compare these auctions.

在将多个异质不可分割物品分配给单位需求竞标者的分配问题中,我们引入了一种名为 "灵活报告递升拍卖 "的新型递升拍卖,以平衡隐私保护和递升拍卖的速度。假设竞拍者的行为都是真实的,那么它总是会产生一个瓦尔拉斯均衡以及最小瓦尔拉斯均衡价格向量。如果每个出价人的报告都没有矛盾,出价人的真实行为就会形成纳什均衡。我们的拍卖概括了文献中一些著名的升序拍卖,我们还提供了模拟结果来比较这些拍卖。
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引用次数: 0
Weighted school choice problems and the weighted top trading cycles mechanism 加权择校问题和加权顶层交易循环机制
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-09-05 DOI: 10.1016/j.mathsocsci.2024.09.001
Nadja Stroh-Maraun

There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.

在许多择校问题中,学生根据其在学校所占座位数的不同而具有异质性。我们提出了一种加权择校问题,为每个学生分配一个所谓的权重,并制定了加权顶层交易循环算法(WTTC)来寻找匹配。WTTC 不受策略影响,并能实现帕累托效率匹配。虽然引入权重后,WTTC 是 TTC 的稳健扩展,但即使学校的总体容量超过权重之和,也不能保证每个学生都能获得一个座位。此外,WTTC 还引入了权重和优先级之间的权衡,因为与优先级相同但权重较小的学生相比,权重较高的学生在匹配到特定学校时处于劣势。
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引用次数: 0
Rent dissipation in difference-form contests 差异形式竞赛中的租金消散
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-09-05 DOI: 10.1016/j.mathsocsci.2024.09.002
Ratul Lahkar

We consider rent-seeking contests where the impact function, which measures how much impact effort has, takes an exponential form. The resulting contest success function (CSF) is a difference-form CSF and the contest is a difference-form contest. Rent dissipation measures the rent lost due to rent-seeking. Cost functions in our difference-form contest are also exponential. We establish the equivalence between such difference-form contests and Tullock contests. We then solve finite-player symmetric difference-form contests in closed form. But if there are asymmetries, the contest cannot be solved. We, therefore, approximate an asymmetric difference-form contest with a large population contest, which can be solved. Rent dissipation in the large population contest is the ratio of the elasticity of the impact function to that of the cost function. Hence, this ratio also approximates rent dissipation in a finite-player contest.

我们考虑的是寻租竞赛,在这种竞赛中,衡量努力产生多大影响的影响函数是指数形式的。由此产生的竞赛成功函数(CSF)是一种差分形式的 CSF,竞赛也是一种差分形式的竞赛。租金耗散衡量的是因寻租而损失的租金。我们的差分形式竞赛中的成本函数也是指数函数。我们建立了这种差异形式竞赛与塔洛克竞赛之间的等价关系。然后,我们以封闭形式求解有限玩家对称差分形式竞赛。但如果存在不对称性,竞赛就无法求解。因此,我们用可以求解的大人口竞赛来近似非对称差分形式竞赛。大量人口竞争中的租金耗散是影响函数弹性与成本函数弹性之比。因此,这一比率也近似于有限参与者竞赛中的租金耗散。
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引用次数: 0
Some further results on random OBIC rules 关于随机 OBIC 规则的一些进一步结果
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-16 DOI: 10.1016/j.mathsocsci.2024.08.005
Madhuparna Karmokar , Dipjyoti Majumdar , Souvik Roy

We study the structure of probabilistic voting rules that are ordinal Bayesian incentive compatible (OBIC) with respect to independently distributed prior beliefs that can be considered generic (Majumdar and Sen (2004)). We first identify a class of priors, such that for each prior in that class there exists a probabilistic voting rule that puts a positive probability weight on “compromise” candidates. The class of priors include generic priors. Next, we consider a class of randomized voting rules that have a “finite range”. For this class of rules, we identify an appropriate generic condition on priors such that, any rule in this class is OBIC with respect to a prior satisfying the generic condition if and only if the rule is a random dictatorship.

我们研究了概率投票规则的结构,这些规则在独立分布的先验信念方面是顺序贝叶斯激励兼容(OBIC)的,可被视为通用规则(Majumdar 和 Sen (2004))。我们首先确定一类先验,对于该类先验中的每个先验,都存在一种概率投票规则,该规则对 "折中 "候选人赋予正概率权重。该类先验包括一般先验。接下来,我们考虑一类具有 "有限范围 "的随机投票规则。对于这一类规则,我们确定了一个关于先验的适当的通用条件,这样,当且仅当该规则是一个随机独裁规则时,这一类规则中的任何规则对于满足通用条件的先验都是 OBIC 的。
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引用次数: 0
Expert’s reputation concern and consumer information 专家的声誉关切和消费者信息
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-16 DOI: 10.1016/j.mathsocsci.2024.08.004
Hiromasa Ogawa

Serious information asymmetry exists between consumers and expert sellers in the credit-goods market. This study develops a generic model to investigate the relationship between consumer information and expert fraud in the credence goods market. The unique features of the model are that (i) the state of the consumer is multidimensional, (ii) the expert seller has concerns about their reputation, and (iii) information asymmetry exists between the consumer and the expert seller regarding the necessity of the provided treatment ex-ante and ex-post. On average, the equilibrium amount of the recommended treatment is greater than the necessary level. The contingent effect of any consumer information on expert overtreatment can be evaluated by analyzing the posterior variance of the number of problems updated by the information. Consumer information on only part of the problem hardly reduces expert overtreatment in certain situations. The unconditional effect of consumer information on expert seller fraud varies considerably with state distribution.

在信用商品市场上,消费者与专家卖家之间存在严重的信息不对称。本研究建立了一个通用模型来研究信用商品市场中消费者信息与专家欺诈之间的关系。该模型的独特之处在于:(i) 消费者的状态是多维的;(ii) 专家卖方对自己的声誉有顾虑;(iii) 消费者与专家卖方之间存在事前和事后信息不对称,不知道所提供的治疗是否必要。平均而言,推荐治疗的均衡数量大于必要水平。任何消费者信息对专家过度治疗的或有影响都可以通过分析信息更新的问题数量的后验方差来评估。在某些情况下,仅涉及部分问题的消费者信息很难减少专家的过度治疗。消费者信息对专家卖方欺诈的无条件影响随状态分布的不同而有很大差异。
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引用次数: 0
Full downside risk aversion 全面规避下行风险
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-13 DOI: 10.1016/j.mathsocsci.2024.08.003
Donald C. Keenan , Arthur Snow

It is shown that well-behaved notions of greater or less downside risk aversion, via utility transformations, lead not to just one, but two, dual, notions of absolute aversion to downside risk: one, the more evident but weaker condition, requires that the prudence measure be positive, given a positive Arrow–Pratt measure of risk aversion, whereas the other, stronger, but less obvious, condition requires that the prudence measure be greater than three times the corresponding Arrow–Pratt measure. The reason for the appearance of these two extreme conditions, bounding the spectrum of reasonable alternative notions of downside risk aversion, or equivalently of downside risk loving, are explained, and consequences of this divergence in the possible meanings of downside risk aversion are explored.

研究表明,通过效用转换,对较大或较小的下行风险规避概念的良好处理,导致对下行风险绝对规避的双重概念不只是一个,而是两个:一个是更明显但较弱的条件,要求谨慎度量为正,给定一个正的阿罗-普拉特风险规避度量;而另一个是更强但不那么明显的条件,要求谨慎度量大于相应的阿罗-普拉特度量的三倍。本文解释了出现这两个极端条件的原因,这两个极端条件限定了下行风险规避或等同于下行风险爱护的合理替代概念的范围,并探讨了下行风险规避的可能含义出现分歧的后果。
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引用次数: 0
Symmetry groups for social preference functions 社会偏好函数的对称组
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-13 DOI: 10.1016/j.mathsocsci.2024.07.004
Daniela Bubboloni, Francesco Nardi

We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by an unsolved problem posed by Kelly in 1991, we investigate the problem of recognizing which permutation groups may arise as anonymity, neutrality and symmetry groups of a social preference function. A complete description is provided for neutrality groups. In the case of anonymity groups, we derive a sufficient condition, which largely captures the desired class of objects. Our approach also is of relevance for the notion of representability by Boolean functions and, therefore, the results of this paper also shed some light on this field of study.

我们介绍了社会偏好函数的匿名组、中立组和对称组。受凯利在 1991 年提出的一个尚未解决的问题的启发,我们研究了如何识别哪些置换群可能作为社会偏好函数的匿名群、中立群和对称群出现。我们对中立组进行了完整的描述。对于匿名组,我们推导出了一个充分条件,它在很大程度上捕捉到了所需的对象类别。我们的方法也与布尔函数的可表示性概念相关,因此,本文的结果也为这一研究领域提供了一些启示。
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引用次数: 0
Signaling through Bayesian persuasion 通过贝叶斯说服传递信息
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-12 DOI: 10.1016/j.mathsocsci.2024.08.002
Jonas Hedlund

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems.

本文研究了在知情劝说中出现分离结果的条件,即在贝叶斯劝说设置中,发送者在承诺进行实验之前私下了解了与报酬相关的状态。我们考虑的是一种具有有限报酬相关状态的环境,发送者的报酬在接收者的后验信念中是连续和单调的。本文发现,如果完全公开与报酬相关的状态会降低发送者在任何共同先验下的预期报酬(即,如果发送者的报酬函数是外凹的),那么就会出现单一交叉的特性,这样高报酬类型的发送者就可以通过选择信息量更大的实验来与低报酬类型的发送者区分开来。这种单一交叉条件导致 D1 准则选择了 "代价最小 "的分离均衡,即发送者对实验的选择表明了他的类型。此外,分离均衡的特征是简单的受限最大化问题。
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引用次数: 0
The role of grandparents in grandchildren’s education for human capital accumulation in an overlapping generations model 世代重叠模型中祖父母在孙辈教育中对人力资本积累的作用
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-08-08 DOI: 10.1016/j.mathsocsci.2024.08.001
Mauro Maria Baldi, Raffaella Coppier, Elisabetta Michetti

We develop an overlapping generations model to explore the role of grandparents in grandchildren’s education and its impact on human capital growth. We examine the quantity–quality (Q–Q) trade-off faced by parents in choosing the number and education of children, incorporating an active role for grandparents. Findings underscore the significance of the elderly in human capital accumulation, fertility, and economic growth. When grandparents invest more time, resources are freed, fostering greater human capital growth and mitigating the effects of the Q–Q trade-off.

我们建立了一个世代重叠模型,以探讨祖父母在孙辈教育中的作用及其对人力资本增长的影响。我们研究了父母在选择子女数量和教育时所面临的数量-质量(Q-Q)权衡,并将祖父母的积极作用纳入其中。研究结果强调了老年人在人力资本积累、生育率和经济增长中的重要性。当祖父母投入更多时间时,就能释放资源,促进更多的人力资本增长,减轻 Q-Q 权衡的影响。
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引用次数: 0
Shannon meets Myerson: Information extraction from a strategic sender 香农遇上迈尔森从战略发送者那里提取信息
IF 0.5 4区 经济学 Q4 ECONOMICS Pub Date : 2024-07-25 DOI: 10.1016/j.mathsocsci.2024.07.002
Anuj S. Vora , Ankur A. Kulkarni

We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to a strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required while communicating with a strategic sender. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, non-cooperative regime of communication involving a strategic sender.

我们研究了这样一种情况:接收者必须设计一份调查问卷,以恢复策略发送者已知的符号序列,而策略发送者的效用可能与激励不兼容。我们允许接收者选择调查问卷中的备选方案,从而将序列各部分的决策联系起来。我们证明,尽管有策略发送者和信道中的噪声,接收者仍能恢复指数级数量的序列,而且指数级数量的序列即使采用最佳策略也无法恢复。我们将恢复序列数量的增长率定义为信息提取能力。作为香农容量的一般化,它描述了与策略发送者通信时所需的最佳通信资源量。我们推导出了在许多情况下精确评估信息提取能力的界限。我们的研究成果构成了一种新颖的、涉及策略发送者的非合作性通信机制的基石。
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引用次数: 0
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Mathematical Social Sciences
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