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The use of symmetry for models with variable-size variables 对具有可变大小变量的模型使用对称性
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-07-13 DOI: 10.1016/j.mathsocsci.2025.102437
Takeshi Fukasawa
{"title":"The use of symmetry for models with variable-size variables","authors":"Takeshi Fukasawa","doi":"10.1016/j.mathsocsci.2025.102437","DOIUrl":"10.1016/j.mathsocsci.2025.102437","url":null,"abstract":"<div><div>This paper presents a universal representation of symmetric (permutation-invariant) functions with multidimensional variable-size variables. These representations help justify approximation methods that aggregate information from each variable using moments. It further discusses how these findings provide insights into game-theoretic applications, including two-step policy function estimation, Moment-based Markov Equilibrium (MME), and aggregative games.</div><div>Regarding policy function estimation, under certain conditions, estimating a common policy function as a function of a firm’s own state and the sum of polynomial terms (moments) of competitors’ states is justified, regardless of the number of firms in a market, provided a sufficient number of moments are included. For MME, this study demonstrates that MME is equivalent to Markov Perfect Equilibrium if the number of moments reaches a certain level and regularity conditions are satisfied.</div><div>Regarding aggregative games, the paper establishes that any game satisfying symmetry and continuity conditions in payoff functions can be represented as a multidimensional generalized aggregative game. This extends previous research on generalized (fully) aggregative games by introducing multidimensional aggregates.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102437"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005420","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}
引用次数: 0
A look back at the core of games in characteristic function form: Some new axiomatization results 回顾特征函数形式下的游戏核心：一些新的公理化结果
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-07-29 DOI: 10.1016/j.mathsocsci.2025.102447
Anindya Bhattacharya
{"title":"A look back at the core of games in characteristic function form: Some new axiomatization results","authors":"Anindya Bhattacharya","doi":"10.1016/j.mathsocsci.2025.102447","DOIUrl":"10.1016/j.mathsocsci.2025.102447","url":null,"abstract":"<div><div>The main contribution of this paper is to provide three new results axiomatizing the core of games in characteristic function form (not necessarily with transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is bounded). One novelty of this exercise is that our domain is the <em>entire</em> class of such games: i.e., restrictions like “non-levelness” (a restriction not very appealing in several real-life situations) or “balancedness”, usually imposed in the related literature, are not required.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102447"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005421","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}
引用次数: 0
Strategic behavior in contests with sabotage 与蓄意破坏竞争中的战略行为
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-10-05 DOI: 10.1016/j.mathsocsci.2025.102470
Doron Klunover
{"title":"Strategic behavior in contests with sabotage","authors":"Doron Klunover","doi":"10.1016/j.mathsocsci.2025.102470","DOIUrl":"10.1016/j.mathsocsci.2025.102470","url":null,"abstract":"<div><div>Sabotage is incorporated into Dixit (1987)’s classic model of a two-player probabilistic symmetric contest to show that in contrast to his result and apart from a special case, a player will, if possible, commit to a level of effort different from that in Nash equilibrium. This implies that the subgame perfect equilibrium of the sequential contest differs from the Nash equilibrium of the corresponding simultaneous contest and that a player prefers to be the first mover in the former type of contest rather than participating in the latter type.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102470"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266842","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}
引用次数: 0
Rational bubbles in portfolios with fundamental value 具有基本价值的投资组合中的理性泡沫
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-09-22 DOI: 10.1016/j.mathsocsci.2025.102464
Lise Clain-Chamosset-Yvrard , Xavier Raurich , Thomas Seegmuller
{"title":"Rational bubbles in portfolios with fundamental value","authors":"Lise Clain-Chamosset-Yvrard ,&nbsp;Xavier Raurich ,&nbsp;Thomas Seegmuller","doi":"10.1016/j.mathsocsci.2025.102464","DOIUrl":"10.1016/j.mathsocsci.2025.102464","url":null,"abstract":"<div><div>In this paper, we provide a framework in which a stationary bubble can exist on a portfolio of dividend-yielding assets. Consistent with standard asset pricing theory, this portfolio bubble is defined as the difference between the portfolio market price and the present value of its future dividend stream. This bubble can coexist with a positive stationary fundamental value, without requiring the collapse of the latter over time. This result is obtained in an exchange overlapping generations economy featuring both newly issued and pre-existing financial assets that depreciate over time, and jointly constitute the asset portfolio. The introduction of new assets in each period decouples the return on bubbles from the effective discount rate applied to dividends. As a result, stationary equilibria can exist with both a positive bubble and a positive fundamental component in the portfolio value. Finally, our framework also allows us to discuss the role of the substitutability between financial assets on the level of bubbles and fundamental values.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102464"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159500","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}
引用次数: 0
Apportionment when seats are allocated in lots. The D’Hondt method case and political implications 座位按批次分配时的分配。D 'Hondt方法案例及其政治含义
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-11-10 DOI: 10.1016/j.mathsocsci.2025.102474
Juan Carlos Gonçalves-Dosantos, Joaquín Sánchez-Soriano
{"title":"Apportionment when seats are allocated in lots. The D’Hondt method case and political implications","authors":"Juan Carlos Gonçalves-Dosantos,&nbsp;Joaquín Sánchez-Soriano","doi":"10.1016/j.mathsocsci.2025.102474","DOIUrl":"10.1016/j.mathsocsci.2025.102474","url":null,"abstract":"<div><div>The apportionment problem involves determining how to distribute a given (non-negative) integer number among a group of individuals based on their respective sizes. In electoral systems with proportional representation, this problem arises in two situations: assigning seats to constituencies, if applicable, and distributing seats to political parties within each constituency. This paper addresses the scenario where seats are grouped into lots, extending the standard apportionment problem. We propose and analyze various apportionment methods based on the D’Hondt method for this new problem. Additionally, we examine the political implications of allocating seats not individually but in groups of varying sizes.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102474"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528488","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}
引用次数: 0
Truth-telling in dynamic reputational cheap talk 在动态的名誉廉价谈话中讲真话
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-11-01 DOI: 10.1016/j.mathsocsci.2025.102473
Dohui Woo
{"title":"Truth-telling in dynamic reputational cheap talk","authors":"Dohui Woo","doi":"10.1016/j.mathsocsci.2025.102473","DOIUrl":"10.1016/j.mathsocsci.2025.102473","url":null,"abstract":"<div><div>In the context of dynamic reputational cheap talk, experts are concerned not only with their current signal but also with how their past and future messages shape their perceived ability. This paper studies a two-stage environment in which an expert repeatedly receives private signals and sends unverifiable messages before the true state is revealed. A truth-telling equilibrium arises under a moderate prior on the state and a high prior on ability. Further analysis reveals that equilibria involving early silence are non-generic when messages from the early speaker are taken at face value.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102473"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145473982","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}
引用次数: 0
Connectedness in weighted consensus division of graphical cakes between two agents 两个agent间图形饼加权共识划分的连通性
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-09-17 DOI: 10.1016/j.mathsocsci.2025.102463
Josef Hanke , Ana Rita Pires
{"title":"Connectedness in weighted consensus division of graphical cakes between two agents","authors":"Josef Hanke ,&nbsp;Ana Rita Pires","doi":"10.1016/j.mathsocsci.2025.102463","DOIUrl":"10.1016/j.mathsocsci.2025.102463","url":null,"abstract":"<div><div>Austin’s moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exactly half of the cake.</div><div>We generalise this in two ways: we consider cakes modelled by graphs, and let the two agents have unequal, arbitrary entitlements. In this setting, we seek a weighted consensus division – one where each agent believes they received exactly the share they are entitled to – which also minimises the number of connected components that each agent receives.</div><div>First, we review the weighted consensus division of a circular cake, which gives exactly one connected piece to each agent. Next, by judiciously mapping a circle to a graph, we produce a weighted consensus division of a star graph cake that gives at most two connected pieces to each agent — and show that this bound on the number of connected pieces is tight. For a tree, each agent receives at most <span><math><mrow><mi>h</mi><mo>+</mo><mn>1</mn></mrow></math></span> connected pieces, where <span><math><mi>h</mi></math></span> is the minimal height of the tree. For a connected graphical cake, each agent receives <span><math><mrow><mi>r</mi><mo>+</mo><mn>2</mn></mrow></math></span> connected pieces, where <span><math><mi>r</mi></math></span> is the radius of the graph. Finally, for a graphical cake with <span><math><mi>s</mi></math></span> connected components, the division involves at most <span><math><mrow><mi>s</mi><mo>+</mo><mn>2</mn><mi>r</mi><mo>+</mo><mn>4</mn></mrow></math></span> connected pieces, where <span><math><mi>r</mi></math></span> is the maximum radius among all connected components.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102463"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107064","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}
引用次数: 0
Delegation and strategic altruism: A theoretical approach 授权与战略利他主义：一种理论途径
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-09-25 DOI: 10.1016/j.mathsocsci.2025.102465
Luciano Méndez-Naya
{"title":"Delegation and strategic altruism: A theoretical approach","authors":"Luciano Méndez-Naya","doi":"10.1016/j.mathsocsci.2025.102465","DOIUrl":"10.1016/j.mathsocsci.2025.102465","url":null,"abstract":"<div><div>In this paper we introduce two refinements of Nash equilibria for extensive form games: the quasi-stable equilibrium and the stable equilibrium. We then introduce the general strategic game with delegates and study new solutions in that context. We apply the new solution concepts to symmetric <span><math><mi>n</mi></math></span>-player games in which each player has two strategies. The main conclusion is that, in the prisoner’s dilemma, if the punishment payoff is sufficient, both players obtain the cooperative payoff when they choose strategically altruistic delegates.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102465"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159499","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}
引用次数: 0
A simple model on social connections, wages, and welfare 一个关于社会关系、工资和福利的简单模型
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-10-04 DOI: 10.1016/j.mathsocsci.2025.102468
Ying Wang , Richard T. Woodward
{"title":"A simple model on social connections, wages, and welfare","authors":"Ying Wang ,&nbsp;Richard T. Woodward","doi":"10.1016/j.mathsocsci.2025.102468","DOIUrl":"10.1016/j.mathsocsci.2025.102468","url":null,"abstract":"<div><div>In this paper, we develop a model of social connections to explore how, in the presence of social connections, an increase in an exogenous wage of one of the players does not necessarily lead to a Pareto improvement. Players are required to share resources to establish social connections. In this basic model, we show that the non-cooperative equilibrium is not Pareto efficient by introducing a compensation mechanism and showing that a Pareto improving trade could be made. We then show that if a wage increase for one player leads to a reduction in social connections, under some circumstances a mutually beneficial agreement could be reached in which the player foregoes the wage increase in exchange for a cash transfer. The model provides insights into why increases in income do not always translate into greater happiness.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102468"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333367","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}
引用次数: 0
Simplex subtraction to estimate unanimity violations in sequential majority voting 单纯形减法估计顺序多数表决中一致意见的违反
IF 0.7 4区 经济学
Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-09-16 DOI: 10.1016/j.mathsocsci.2025.102462
Christian Klamler
{"title":"Simplex subtraction to estimate unanimity violations in sequential majority voting","authors":"Christian Klamler","doi":"10.1016/j.mathsocsci.2025.102462","DOIUrl":"10.1016/j.mathsocsci.2025.102462","url":null,"abstract":"<div><div>Based on Saari’s geometry of voting (see Saari (1995)), we introduce a concise geometric “simplex subtraction” approach to measure the likelihood with which sequential majority voting overturns unanimous consent under the impartial anonymous culture assumption. This approach can be used as an alternative to Nehring et al. (2016) who establish worst-case bounds for discrete electorates. We treat vote shares as points in the reduced simplex after one candidate is unanimously rejected. By systematically removing the volumes of smaller corner sub-simplexes, we recover the probabilities determined by Nehring et al. (2016), which reaches its maximum for seven candidates. We then generalize our method to arbitrary supermajority rules and identify the exact threshold at which unanimity violations become impossible.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102462"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107063","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}
引用次数: 0
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