Pub Date : 2024-11-04DOI: 10.1016/j.mathsocsci.2024.10.003
Sumit Goel , Wade Hann-Caruthers
We study a principal–agent project selection problem with asymmetric information. The principal must choose exactly one of projects, each defined by the utility it provides to the principal and to the agent. The agent knows all the utilities, and the principal can commit to a mechanism (without transfers) that maps the agent’s report about the utilities to a chosen project. Unlike the typical literature, which assumes the agent can lie arbitrarily, we examine the principal’s problem under partial verifiability constraints. We characterize the class of truthful mechanisms under a family of partial verifiability constraints and study the principal’s problem for the specific cases of no-overselling and no-underselling. Our results suggest significant benefits for the principal from identifying or inducing such partial verifiability constraints, while also highlighting the simple mechanisms that perform well.
我们研究的是一个信息不对称的委托代理项目选择问题。委托人必须从 N 个项目中准确地选择一个，每个项目由它为委托人和代理人提供的效用所决定。代理人知道所有的效用，而委托人可以承诺采用一种机制（无需转让），将代理人关于效用的报告映射到所选项目上。与假定代理人可以任意撒谎的典型文献不同，我们研究的是部分可验证性约束下的委托人问题。我们描述了一系列部分可验证性约束条件下的真实机制，并研究了无过度销售和无遗漏销售等特定情况下的委托人问题。我们的结果表明，识别或诱导这类部分可验证性约束对委托人大有裨益，同时也强调了表现良好的简单机制。
{"title":"Project selection with partially verifiable information","authors":"Sumit Goel , Wade Hann-Caruthers","doi":"10.1016/j.mathsocsci.2024.10.003","DOIUrl":"10.1016/j.mathsocsci.2024.10.003","url":null,"abstract":"<div><div>We study a principal–agent project selection problem with asymmetric information. The principal must choose exactly one of <span><math><mi>N</mi></math></span> projects, each defined by the utility it provides to the principal and to the agent. The agent knows all the utilities, and the principal can commit to a mechanism (without transfers) that maps the agent’s report about the utilities to a chosen project. Unlike the typical literature, which assumes the agent can lie arbitrarily, we examine the principal’s problem under partial verifiability constraints. We characterize the class of truthful mechanisms under a family of partial verifiability constraints and study the principal’s problem for the specific cases of no-overselling and no-underselling. Our results suggest significant benefits for the principal from identifying or inducing such partial verifiability constraints, while also highlighting the simple mechanisms that perform well.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 105-113"},"PeriodicalIF":0.5,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.mathsocsci.2024.10.002
Shurojit Chatterji , Peng Liu
A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.
{"title":"On the decomposability of fractional allocations","authors":"Shurojit Chatterji , Peng Liu","doi":"10.1016/j.mathsocsci.2024.10.002","DOIUrl":"10.1016/j.mathsocsci.2024.10.002","url":null,"abstract":"<div><div>A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 79-89"},"PeriodicalIF":0.5,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a novel family of node centralities in social networks, named family of position centralities, which explicitly takes into account the importance of the links to assess the centrality of the nodes that support them through the Position value (Meessen, 1988). Our proposal shares with the family of Myerson centralities (Gómez et al., 2003) that it is a game-theoretic family of measures that allows to consider the functionality of the network modelled by a symmetric cooperative game. We prove that, like the Myerson centrality measures, every Position centrality measure also satisfies essential properties expected of a centrality measure. We analyse in detail the main differences between the Myerson and the position families of centrality measures. Specifically, we study the differences regarding the connection structures that share dividends and the fairness and stability properties. Along this analysis we consider the case of hub-and-spoke clusters, a prevalent model for studying transportation networks. Finally, a characterisation of the Position Attachment centrality is given, which is the Position centrality obtained when the functionality of the network is modelled by the attachment game. Some comparisons are made with the Attachment centrality introduced by Skibski et al. (2019), which is the analogue member of the family of Myerson centralities.
{"title":"Node centrality based on its edges importance: The Position centrality","authors":"Susana López , Elisenda Molina , Martha Saboyá , Juan Tejada","doi":"10.1016/j.mathsocsci.2024.10.001","DOIUrl":"10.1016/j.mathsocsci.2024.10.001","url":null,"abstract":"<div><div>We propose a novel family of node centralities in social networks, named <em>family of position centralities</em>, which explicitly takes into account the importance of the links to assess the centrality of the nodes that support them through the Position value (Meessen, 1988). Our proposal shares with the family of Myerson centralities (Gómez et al., 2003) that it is a game-theoretic family of measures that allows to consider the functionality of the network modelled by a symmetric cooperative game. We prove that, like the Myerson centrality measures, every Position centrality measure also satisfies essential properties expected of a centrality measure. We analyse in detail the main differences between the Myerson and the position families of centrality measures. Specifically, we study the differences regarding the connection structures that share dividends and the fairness and stability properties. Along this analysis we consider the case of hub-and-spoke clusters, a prevalent model for studying transportation networks. Finally, a characterisation of the Position Attachment centrality is given, which is the Position centrality obtained when the functionality of the network is modelled by the attachment game. Some comparisons are made with the Attachment centrality introduced by Skibski et al. (2019), which is the analogue member of the family of Myerson centralities.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 90-104"},"PeriodicalIF":0.5,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-25DOI: 10.1016/j.mathsocsci.2024.09.006
Antonio Jiménez-Martínez, Isabel Melguizo-López
We investigate an interesting type of equilibrium of a game where a collective decision is reached by aggregating the preferred alternatives of a group of Receivers. A Sender that cares about the collective decision must make efforts (not below a normative-minimum) to gather evidence relevant for the Receivers to gauge their preferred alternatives. Research efforts may be unsuccessful, which allows for strategic concealment. Each Receiver cares only about her preferred alternative so that the goal of the Sender is achieved by affecting the beliefs of a single representative Receiver (e.g., pivotal voter). Disagreement between the players about the best alternative is based solely on heterogeneous priors. The type of equilibrium that we study arises when the Sender and the representative Receiver agree based on their priors but disagree based on some evidence. In such situations, while unfavorable evidence is concealed always, both disclosure and concealment of favorable evidence may happen with positive probability. Interestingly, for sufficiently low normative-minimum efforts, there arises a continuum of equilibria in which the Sender discloses favorable evidence with higher probability.
{"title":"Evidence disclosure with heterogeneous priors","authors":"Antonio Jiménez-Martínez, Isabel Melguizo-López","doi":"10.1016/j.mathsocsci.2024.09.006","DOIUrl":"10.1016/j.mathsocsci.2024.09.006","url":null,"abstract":"<div><div>We investigate an interesting type of equilibrium of a game where a collective decision is reached by aggregating the preferred alternatives of a group of Receivers. A Sender that cares about the collective decision must make efforts (not below a normative-minimum) to gather evidence relevant for the Receivers to gauge their preferred alternatives. Research efforts may be unsuccessful, which allows for strategic concealment. Each Receiver cares only about her preferred alternative so that the goal of the Sender is achieved by affecting the beliefs of a single representative Receiver (e.g., pivotal voter). Disagreement between the players about the best alternative is based solely on heterogeneous priors. The type of equilibrium that we study arises when the Sender and the representative Receiver agree based on their priors but disagree based on some evidence. In such situations, while unfavorable evidence is concealed always, both disclosure and concealment of favorable evidence may happen with positive probability. Interestingly, for sufficiently low normative-minimum efforts, there arises a continuum of equilibria in which the Sender discloses favorable evidence with higher probability.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 69-74"},"PeriodicalIF":0.5,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.mathsocsci.2024.09.005
Benjamin Bachi, Shiran Rachmilevitch
We introduce a new solution concept for -person strategic games — very weak dominance — which is weaker than ordinary weak dominance, but stronger than Nash equilibrium. One of the attractive features of this concept is that it can provide intuitive predictions to games in which weakly dominant strategies exist, but they seem unappealing.
我们为 n 人策略博弈引入了一个新的解概念--极弱优势，它比普通的弱优势弱，但比纳什均衡强。这个概念的一个吸引人的特点是，它可以为存在弱支配策略的博弈提供直观的预测，但这些策略似乎并不吸引人。
{"title":"Very weakly dominant strategies","authors":"Benjamin Bachi, Shiran Rachmilevitch","doi":"10.1016/j.mathsocsci.2024.09.005","DOIUrl":"10.1016/j.mathsocsci.2024.09.005","url":null,"abstract":"<div><div>We introduce a new solution concept for <span><math><mi>n</mi></math></span>-person strategic games — <em>very weak dominance</em> — which is weaker than ordinary weak dominance, but stronger than Nash equilibrium. One of the attractive features of this concept is that it can provide intuitive predictions to games in which weakly dominant strategies exist, but they seem unappealing.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 75-78"},"PeriodicalIF":0.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-17DOI: 10.1016/j.mathsocsci.2024.09.004
Abhimanyu Khan , Ronald Peeters
We develop a framework to analyse stable cartelisation when firms can form multiple cartels. This contrasts with the existing literature which generally assumes, without further justification, that at most one cartel may form. We define cartelisation to be stable in the multiple cartels framework if: (i) a firm in a cartel does not find it more profitable to leave the cartel and operate independently, (ii) a firm that operates independently does not find it more profitable to join an existing cartel, (iii) a firm in a cartel does not find it more profitable to join another existing cartel or form a new cartel with an independent firm, and (iv) two independent firms do not find it more profitable to form a new cartel. In the context of quantity competition in differentiated markets, we show that a single cartel is never stable whenever multiple cartels may be formed. We completely characterise the stable cartelisation structure — there is at most one firm that is not a part of any cartel while each of the remaining firms is part of a two-firm cartel. The implication for competition policy is that efforts towards the detection of cartels should also be directed at smaller cartels that may operate in less concentrated markets rather than only on large dominant cartels in concentrated markets.
{"title":"Stable cartel configurations and product differentiation: The case of multiple cartels","authors":"Abhimanyu Khan , Ronald Peeters","doi":"10.1016/j.mathsocsci.2024.09.004","DOIUrl":"10.1016/j.mathsocsci.2024.09.004","url":null,"abstract":"<div><div>We develop a framework to analyse stable cartelisation when firms can form multiple cartels. This contrasts with the existing literature which generally assumes, without further justification, that at most one cartel may form. We define cartelisation to be stable in the multiple cartels framework if: (i) a firm in a cartel does not find it more profitable to leave the cartel and operate independently, (ii) a firm that operates independently does not find it more profitable to join an existing cartel, (iii) a firm in a cartel does not find it more profitable to join another existing cartel or form a new cartel with an independent firm, and (iv) two independent firms do not find it more profitable to form a new cartel. In the context of quantity competition in differentiated markets, we show that a single cartel is never stable whenever multiple cartels may be formed. We completely characterise the stable cartelisation structure — there is at most one firm that is not a part of any cartel while each of the remaining firms is part of a two-firm cartel. The implication for competition policy is that efforts towards the detection of cartels should also be directed at smaller cartels that may operate in less concentrated markets rather than only on large dominant cartels in concentrated markets.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 57-68"},"PeriodicalIF":0.5,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000866/pdfft?md5=b025962ed7c1720027752a67cfc7b0f2&pid=1-s2.0-S0165489624000866-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-10DOI: 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.
{"title":"The ascending auction with flexible reporting","authors":"Xieji Zhang","doi":"10.1016/j.mathsocsci.2024.09.003","DOIUrl":"10.1016/j.mathsocsci.2024.09.003","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 28-39"},"PeriodicalIF":0.5,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 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.
{"title":"Weighted school choice problems and the weighted top trading cycles mechanism","authors":"Nadja Stroh-Maraun","doi":"10.1016/j.mathsocsci.2024.09.001","DOIUrl":"10.1016/j.mathsocsci.2024.09.001","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 49-56"},"PeriodicalIF":0.5,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000817/pdfft?md5=20c6d6ce7944d3dcfc320f58184efcf4&pid=1-s2.0-S0165489624000817-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 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.
{"title":"Rent dissipation in difference-form contests","authors":"Ratul Lahkar","doi":"10.1016/j.mathsocsci.2024.09.002","DOIUrl":"10.1016/j.mathsocsci.2024.09.002","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"132 ","pages":"Pages 40-48"},"PeriodicalIF":0.5,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-16DOI: 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。
{"title":"Some further results on random OBIC rules","authors":"Madhuparna Karmokar , Dipjyoti Majumdar , Souvik Roy","doi":"10.1016/j.mathsocsci.2024.08.005","DOIUrl":"10.1016/j.mathsocsci.2024.08.005","url":null,"abstract":"<div><p>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 <em>generic</em> (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.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"131 ","pages":"Pages 102-112"},"PeriodicalIF":0.5,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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