Pub Date : 2025-12-01Epub Date: 2025-08-05DOI: 10.1016/j.mathsocsci.2025.102451
Laurent Gauthier
Extending the sociological study of conformism in naming, we develop a dynamic model of name choice, reflecting conformist or non-conformist behavior. This allows us to account for more degrees of freedom than the statistical physics approaches that have generally been used in name modeling. Testing our model empirically, we find that conformist naming accounts for the unique shape of name distributions in ancient Greece, which differs from contemporary name data.
{"title":"Conformism and name dynamics: A cliometric study of ancient Greek names","authors":"Laurent Gauthier","doi":"10.1016/j.mathsocsci.2025.102451","DOIUrl":"10.1016/j.mathsocsci.2025.102451","url":null,"abstract":"<div><div>Extending the sociological study of conformism in naming, we develop a dynamic model of name choice, reflecting conformist or non-conformist behavior. This allows us to account for more degrees of freedom than the statistical physics approaches that have generally been used in name modeling. Testing our model empirically, we find that conformist naming accounts for the unique shape of name distributions in ancient Greece, which differs from contemporary name data.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102451"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005419","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}
This article develops a dynamic principal–agent model that integrates bargaining power as an evolving state variable, governed by a bargaining drift coefficient that links its trajectory to firm performance and agent compensation. The model examines how initial bargaining power shapes salary trajectories and how bargaining drift influences its adaptation over time in response to performance outcomes. By modeling these dynamics, the study highlights the role of incentives in driving the evolution of bargaining power, emphasizing the long-term impact of initial conditions on compensation structures. A key contribution is the formulation of an empirical equation that connects agent compensation and performance with bargaining drift, offering a framework for real-world validation. Beyond CEO pay, the framework extends to other performance-based environments, such as sports and academia, where shifting power relationships shape long-term contracts. By introducing a computational algorithm for multiobjective optimization, the study enhances the practical implementation of bargaining power dynamics, offering valuable insights for both theoretical modeling and governance applications.
{"title":"The dynamics of bargaining power in a principal-agent model","authors":"Sonia Di Giannatale , Itza Tlaloc Quetzalcoatl Curiel-Cabral , Genaro Basulto","doi":"10.1016/j.mathsocsci.2025.102452","DOIUrl":"10.1016/j.mathsocsci.2025.102452","url":null,"abstract":"<div><div>This article develops a dynamic principal–agent model that integrates bargaining power as an evolving state variable, governed by a bargaining drift coefficient that links its trajectory to firm performance and agent compensation. The model examines how initial bargaining power shapes salary trajectories and how bargaining drift influences its adaptation over time in response to performance outcomes. By modeling these dynamics, the study highlights the role of incentives in driving the evolution of bargaining power, emphasizing the long-term impact of initial conditions on compensation structures. A key contribution is the formulation of an empirical equation that connects agent compensation and performance with bargaining drift, offering a framework for real-world validation. Beyond CEO pay, the framework extends to other performance-based environments, such as sports and academia, where shifting power relationships shape long-term contracts. By introducing a computational algorithm for multiobjective optimization, the study enhances the practical implementation of bargaining power dynamics, offering valuable insights for both theoretical modeling and governance applications.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102452"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005422","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 : 2025-12-01Epub Date: 2025-07-13DOI: 10.1016/j.mathsocsci.2025.102437
Takeshi Fukasawa
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.
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.
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.
{"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}
Pub Date : 2025-12-01Epub Date: 2025-07-29DOI: 10.1016/j.mathsocsci.2025.102447
Anindya Bhattacharya
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 entire 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.
{"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}
Pub Date : 2025-12-01Epub Date: 2025-10-05DOI: 10.1016/j.mathsocsci.2025.102470
Doron Klunover
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.
{"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}
Pub Date : 2025-12-01Epub Date: 2025-09-22DOI: 10.1016/j.mathsocsci.2025.102464
Lise Clain-Chamosset-Yvrard , Xavier Raurich , Thomas Seegmuller
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.
{"title":"Rational bubbles in portfolios with fundamental value","authors":"Lise Clain-Chamosset-Yvrard , Xavier Raurich , 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}
Pub Date : 2025-12-01Epub Date: 2025-11-01DOI: 10.1016/j.mathsocsci.2025.102473
Dohui Woo
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.
{"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}
Pub Date : 2025-12-01Epub Date: 2025-09-17DOI: 10.1016/j.mathsocsci.2025.102463
Josef Hanke , Ana Rita Pires
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.
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.
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 connected pieces, where is the minimal height of the tree. For a connected graphical cake, each agent receives connected pieces, where is the radius of the graph. Finally, for a graphical cake with connected components, the division involves at most connected pieces, where is the maximum radius among all connected components.
{"title":"Connectedness in weighted consensus division of graphical cakes between two agents","authors":"Josef Hanke , 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}
Pub Date : 2025-12-01Epub Date: 2025-11-10DOI: 10.1016/j.mathsocsci.2025.102474
Juan Carlos Gonçalves-Dosantos, Joaquín Sánchez-Soriano
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.
{"title":"Apportionment when seats are allocated in lots. The D’Hondt method case and political implications","authors":"Juan Carlos Gonçalves-Dosantos, 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}
Pub Date : 2025-12-01Epub Date: 2025-09-25DOI: 10.1016/j.mathsocsci.2025.102465
Luciano Méndez-Naya
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 -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.
{"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}
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