{"title":"The set of pure-strategy equilibria in max–min two-group contests with a private good prize","authors":"Mario Gilli, Andrea Sorrentino","doi":"10.1016/j.mathsocsci.2025.102471","DOIUrl":"10.1016/j.mathsocsci.2025.102471","url":null,"abstract":"<div><div>We characterize the set of pure-strategy equilibria in a deterministic group contest with the weakest-link impact function and a private good prize, complementing the results obtained by Lee (2012) and Chowdhury et al. (2016). We consider a two-stage two-group model, where in the first stage the agents simultaneously choose the sharing rule, while in the second stage they choose efforts. We find that there are continua of subgame perfect equilibria, which means that in equilibrium players’ behavior is indeterminate. By additional restrictions on the effort levels of each class of effort equilibria, we are able to computationally characterize the set of subgame perfect Nash equilibria in pure strategies.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102471"},"PeriodicalIF":0.7,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362519","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":"Note on intertemporal preference with loss aversion","authors":"Kyoung Jin Choi , Junkee Jeon , Hyeng Keun Koo","doi":"10.1016/j.mathsocsci.2025.102469","DOIUrl":"10.1016/j.mathsocsci.2025.102469","url":null,"abstract":"<div><div>We study two models of intertemporal preferences exhibiting loss aversion: one based on utility changes relative to a reference point, and another incorporating mental adjustment costs. Within a multi-period (possibly infinite-horizon) framework, we show that the two formulations are theoretically equivalent. The resulting preferences are neither monotone nor concave in general. We derive necessary and sufficient conditions for monotonicity and concavity, and provide a continuous-time extension that preserves the equivalence. Our results offer a tractable and rigorous foundation for modeling intertemporal behavior under reference-dependent preferences.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102469"},"PeriodicalIF":0.7,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266841","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":"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":"2025-10-05","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}
{"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}
{"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}
{"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}
{"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}
Lise Clain-Chamosset-Yvrard , Xavier Raurich , Thomas Seegmuller
{"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}
{"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}
{"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}
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