{"title":"Optimal influence under observational learning","authors":"Nikolas Tsakas","doi":"10.1016/j.mathsocsci.2024.01.011","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2024.01.011","url":null,"abstract":"<div><p>We study the optimal targeting problem of a firm that is seeking to maximize the diffusion of a product in a society where agents learn from their neighbors. The firm can seed the product to a subset of the population and our goal is to find which the optimal subset to target is. We provide a condition that characterizes the optimal targeting strategy for any network structure. The key parameter in this condition is the agents’ decay centrality, which takes into account how close an agent is to others, in a way that distant agents are weighted less than closer ones.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 41-51"},"PeriodicalIF":0.6,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674116","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}
{"title":"A game-theoretic implication of the Riemann hypothesis","authors":"Christian Ewerhart","doi":"10.1016/j.mathsocsci.2024.01.007","DOIUrl":"10.1016/j.mathsocsci.2024.01.007","url":null,"abstract":"<div><p>The Riemann hypothesis (RH) is one of the major unsolved problems in pure mathematics. In the present paper, a parameterized family of non-cooperative games is constructed with the property that, if RH is true, then any game in the family admits a unique Nash equilibrium. We argue that this result is not degenerate. Indeed, neither is the conclusion a tautology, nor is RH used to define the family of games.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 52-59"},"PeriodicalIF":0.6,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000167/pdfft?md5=f43e23ae61ca2ca71d6971f39fd4c1a4&pid=1-s2.0-S0165489624000167-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579252","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}
{"title":"Dynamics of opinion polarization in a population","authors":"Ricardo Cano Macias , Jorge Mauricio Ruiz Vera","doi":"10.1016/j.mathsocsci.2024.01.009","DOIUrl":"10.1016/j.mathsocsci.2024.01.009","url":null,"abstract":"<div><p>This article addresses the polarization of the population around an idea and proposes a simple model that describes its dynamics in a society characterized by asymmetries in freedom of expression. The model considers a population divided into followers of an idea, consisting of moderate sympathizers and staunch defenders, and a group of opponents who try to spread their position but are also susceptible to opinion change. An analysis of stability of the proposed system of differential equations is conducted to examine policies that prevent homogenization around the idea. The results reveal conditionally stable equilibrium points that represent the coexistence of opinions and the extinction of polarization. Two threshold values are proposed to determine the persistence of polarization over time. Furthermore, the results of the model are validated through the analysis of two real cases of polarization in Colombian society, demonstrating its ability to reproduce the general behavior of opinion divergence and its utility in polarization control.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 31-40"},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000180/pdfft?md5=b0c31f70280598cc4da3168bdced3416&pid=1-s2.0-S0165489624000180-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579116","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}
Elpiniki Bakaouka , Marc Escrihuela-Villar , Walter Ferrarese
{"title":"Horizontal mergers with Bertrand competition and convex costs","authors":"Elpiniki Bakaouka , Marc Escrihuela-Villar , Walter Ferrarese","doi":"10.1016/j.mathsocsci.2024.01.010","DOIUrl":"10.1016/j.mathsocsci.2024.01.010","url":null,"abstract":"<div><p>We discuss horizontal mergers in a homogeneous good industry where firms compete à la Bertrand with increasing marginal production costs. We show that profitable mergers can occur even for lower post-merger prices with respect to the pre-merger scenario, thus implying an increase in consumer surplus. The driving force of the result is the ability of the merged entity cutting production costs by sharing the output among its plants. This output rationalization effect can compensate for the revenue loss due to the merged entity producing less than the cumulated pre-merger production of the merging parties.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 60-67"},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000192/pdfft?md5=c2982eb677dc27e32d813c92c257f903&pid=1-s2.0-S0165489624000192-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139633610","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}
{"title":"Note on “A classification of peak-pit maximal Condorcet domains” by Guanhao Li, Mathematical Social Sciences 125 (2023), 42–57","authors":"Clemens Puppe , Arkadii Slinko","doi":"10.1016/j.mathsocsci.2024.01.006","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2024.01.006","url":null,"abstract":"<div><p>The note presents a counter example to <span>Li (2023)</span>.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 16-17"},"PeriodicalIF":0.6,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000155/pdfft?md5=360a99936da19b82d0674a578e5ae61e&pid=1-s2.0-S0165489624000155-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139503737","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}
{"title":"Expectations for the MPC chair and interest rate persistence","authors":"Yuta Saito","doi":"10.1016/j.mathsocsci.2024.01.005","DOIUrl":"10.1016/j.mathsocsci.2024.01.005","url":null,"abstract":"<div><p>This paper examines how the public’s expectations for the chair of the monetary policy committee influence policy outcomes. We show that the expectation that the chair will propose their ideal policy at the meeting can lead a majority of the committee to reject the policy change. The result suggests that the expectation of the chair’s agenda setting is a determinant of interest rate persistence.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 25-30"},"PeriodicalIF":0.6,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000143/pdfft?md5=2cd8a5d7e3ec5abf6b6cb2cbb5efd2f2&pid=1-s2.0-S0165489624000143-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139516384","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}
{"title":"Externalities and the (pre)nucleolus in cooperative games","authors":"Mikel Álvarez-Mozos , Lars Ehlers","doi":"10.1016/j.mathsocsci.2024.01.003","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2024.01.003","url":null,"abstract":"<div><p>In most economic applications of cooperative games, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the prenucleolus to games with coalitional externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 10-15"},"PeriodicalIF":0.6,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016548962400012X/pdfft?md5=1b6e1ab17b414c1b38ceb0b8c2bee407&pid=1-s2.0-S016548962400012X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139493356","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}
Olivier Cailloux , Matthieu Hervouin , Ali I. Ozkes , M. Remzi Sanver
{"title":"Classification aggregation without unanimity","authors":"Olivier Cailloux , Matthieu Hervouin , Ali I. Ozkes , M. Remzi Sanver","doi":"10.1016/j.mathsocsci.2024.01.002","DOIUrl":"10.1016/j.mathsocsci.2024.01.002","url":null,"abstract":"<div><p>A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson’s (1972) and Arrow’s (1951) impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 6-9"},"PeriodicalIF":0.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489624000088/pdfft?md5=0187f37c798bf0c6a8c9bf69de97a8da&pid=1-s2.0-S0165489624000088-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422830","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}
{"title":"Characterizations of approval ranking","authors":"Hiroyuki Komatsu","doi":"10.1016/j.mathsocsci.2024.01.001","DOIUrl":"10.1016/j.mathsocsci.2024.01.001","url":null,"abstract":"<div><p><span>In this paper, we consider those voting situations in which each voter decides whether he or she approves each candidate. Given a list of such approvals, a “social preference function” picks a ranking of the candidates. We are interested in finding out which social preference functions are </span><em>non-manipulable</em>. We show that a particular social preference function, referred to as <em>approval ranking</em>, is more decisive than any other social preference functions satisfying <em>completeness</em>, <em>neutrality</em>, <em>anonymity</em>, and <em>non-manipulability</em>. In addition, we show that approval ranking is axiomatized by these four axioms and <em>tie-breakability</em>.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 18-24"},"PeriodicalIF":0.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421449","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}
{"title":"Strategy-proof allocation of objects: A characterization result","authors":"Tommy Andersson, Lars-Gunnar Svensson","doi":"10.1016/j.mathsocsci.2023.12.004","DOIUrl":"10.1016/j.mathsocsci.2023.12.004","url":null,"abstract":"<div><p>This paper considers an allocation problem with a finite number of objects and unit-demand agents. The main result is a characterization of a class of strategy-proof price mechanisms on a general domain where preferences over pairs of objects and houses are rational, monotonic, and continuous. A mechanism belongs to this class if and only if the price space is restricted in a special way and, given this restriction, that the mechanism selects minimal equilibrium prices.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"128 ","pages":"Pages 1-5"},"PeriodicalIF":0.6,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165489623001038/pdfft?md5=bc4467fdedc7062bd578e1c3b0ee345a&pid=1-s2.0-S0165489623001038-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066781","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}