Pub Date : 2025-10-04DOI: 10.1016/j.mathsocsci.2025.102468
Ying Wang , Richard T. Woodward
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.
{"title":"A simple model on social connections, wages, and welfare","authors":"Ying Wang , 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":"2025-10-04","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}
Pub Date : 2025-09-29DOI: 10.1016/j.mathsocsci.2025.102466
Stefano Bosi , David Desmarchelier , Cuong Le Van
In the spirit of Goenka and Liu (2020), we study an endogenous growth model à la Lucas (1988) with an infectious disease spreading according to SIS dynamics and slowing human capital accumulation. Our model differs from theirs in some respects. We focus solely on the planner’s solution and cover both bounded and unbounded growth cases, under the assumption of more general preferences. Considering a single capital good allows us to provide a global analysis and in-depth understanding of the transition mechanisms. In the case of decreasing returns, the economy converges towards a stationary stock of human capital which decreases with the severity of the epidemic. In the case of unbounded growth, we recover the main results of Goenka and Liu (2020): the existence of a Balanced Growth Path with a negative impact of disease severity on growth rate. However, in our model, the growth path is only asymptotically balanced and confined within an exponential band during the transition.
{"title":"On human capital accumulation in times of epidemic","authors":"Stefano Bosi , David Desmarchelier , Cuong Le Van","doi":"10.1016/j.mathsocsci.2025.102466","DOIUrl":"10.1016/j.mathsocsci.2025.102466","url":null,"abstract":"<div><div>In the spirit of Goenka and Liu (2020), we study an endogenous growth model à la Lucas (1988) with an infectious disease spreading according to SIS dynamics and slowing human capital accumulation. Our model differs from theirs in some respects. We focus solely on the planner’s solution and cover both bounded and unbounded growth cases, under the assumption of more general preferences. Considering a single capital good allows us to provide a global analysis and in-depth understanding of the transition mechanisms. In the case of decreasing returns, the economy converges towards a stationary stock of human capital which decreases with the severity of the epidemic. In the case of unbounded growth, we recover the main results of Goenka and Liu (2020): the existence of a Balanced Growth Path with a negative impact of disease severity on growth rate. However, in our model, the growth path is only asymptotically balanced and confined within an exponential band during the transition.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102466"},"PeriodicalIF":0.7,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266843","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 : 2025-09-26DOI: 10.1016/j.mathsocsci.2025.102467
Neelanjan Sen , Uday Bhanu Sinha
We demonstrate how multimarket contact can negatively impact the quality choices in two different markets, resulting in a reduction in the availability of high-quality products and an increase in the availability of low-quality products. In our model, the firms can collude during the quality choice in different markets and may under-invest in product quality improvement. We also discuss the stability of these types of cartels. Consumer surplus decreases if both firms collude, such that either or both firms switch to the low-quality product in one or both markets. However, in doing so, the firms earn higher profits under collusion.
{"title":"Multimarket contact, cartel and product quality","authors":"Neelanjan Sen , Uday Bhanu Sinha","doi":"10.1016/j.mathsocsci.2025.102467","DOIUrl":"10.1016/j.mathsocsci.2025.102467","url":null,"abstract":"<div><div>We demonstrate how multimarket contact can negatively impact the quality choices in two different markets, resulting in a reduction in the availability of high-quality products and an increase in the availability of low-quality products. In our model, the firms can collude during the quality choice in different markets and may under-invest in product quality improvement. We also discuss the stability of these types of cartels. Consumer surplus decreases if both firms collude, such that either or both firms switch to the low-quality product in one or both markets. However, in doing so, the firms earn higher profits under collusion.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102467"},"PeriodicalIF":0.7,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221013","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 : 2025-09-25DOI: 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":"2025-09-25","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}
Pub 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":"2025-09-22","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 : 2025-09-17DOI: 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":"2025-09-17","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 : 2025-09-16DOI: 10.1016/j.mathsocsci.2025.102462
Christian Klamler
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.
{"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":"2025-09-16","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}
Pub Date : 2025-08-28DOI: 10.1016/j.mathsocsci.2025.102461
Davide Carpentiere, Angelo Enrico Petralia
We show that many models of choice can be alternatively represented as special cases of choice with limited attention (Masatlioglu, Nakajima, and Ozbay, 2012), singling out the properties of the unobserved attention filters that explain the observed choices. For each specification, information about the DM’s consideration sets and preference is inferred from violations of the contraction consistency axiom, and it is compared with the welfare indications obtained from equivalent models. Remarkably, limited attention always supports the elicitation of DM’s taste arising from alternative methods. Finally, we examine the intersections between subclasses, and we verify that each of them is independent of the others.
{"title":"Limited attention and models of choice: A behavioral equivalence","authors":"Davide Carpentiere, Angelo Enrico Petralia","doi":"10.1016/j.mathsocsci.2025.102461","DOIUrl":"10.1016/j.mathsocsci.2025.102461","url":null,"abstract":"<div><div>We show that many models of choice can be alternatively represented as special cases of <em>choice with limited attention</em> (Masatlioglu, Nakajima, and Ozbay, 2012), singling out the properties of the unobserved attention filters that explain the observed choices. For each specification, information about the DM’s consideration sets and preference is inferred from violations of the contraction consistency axiom, and it is compared with the welfare indications obtained from equivalent models. Remarkably, limited attention always supports the elicitation of DM’s taste arising from alternative methods. Finally, we examine the intersections between subclasses, and we verify that each of them is independent of the others.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102461"},"PeriodicalIF":0.7,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019303","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":"2025-08-09","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 : 2025-08-08DOI: 10.1016/j.mathsocsci.2025.102448
Alexei Parakhonyak , Sergey V. Popov
In a search and matching model with Nash bargaining, we find infinitely many asymmetric equilibria in which one sex receives a lower payoff than a similarly productive agent of the opposite sex. The mechanism resembles a social norm: if all agents on the opposite side of the marriage market become more demanding, continued searching yields diminished returns. However, if same-sex marriage is legalized and each side of the market includes a positive, arbitrarily small, share of bisexual agents, then only symmetric equilibria survive. This result highlights how restrictions on same-sex marriage reinforce asymmetries in opposite-sex matchings.
{"title":"Same-sex marriage, the great equalizer","authors":"Alexei Parakhonyak , Sergey V. Popov","doi":"10.1016/j.mathsocsci.2025.102448","DOIUrl":"10.1016/j.mathsocsci.2025.102448","url":null,"abstract":"<div><div>In a search and matching model with Nash bargaining, we find infinitely many asymmetric equilibria in which one sex receives a lower payoff than a similarly productive agent of the opposite sex. The mechanism resembles a social norm: if all agents on the opposite side of the marriage market become more demanding, continued searching yields diminished returns. However, if same-sex marriage is legalized and each side of the market includes a positive, arbitrarily small, share of bisexual agents, then only symmetric equilibria survive. This result highlights how restrictions on same-sex marriage reinforce asymmetries in opposite-sex matchings.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102448"},"PeriodicalIF":0.7,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010895","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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