Mathematical Social Sciences最新文献

{"title":"Licensing a capacity-increasing innovation§","authors":"Stefano Colombo ,&nbsp;Siyu Ma","doi":"10.1016/j.mathsocsci.2026.102513","DOIUrl":"10.1016/j.mathsocsci.2026.102513","url":null,"abstract":"<div><div>The paper explores optimal licensing strategies for a capacity-increasing innovation in a Cournot duopoly with firms having asymmetric capacity constraints. When the innovation is invented by an outside innovator, the choice of licensing scheme determines which firm gets the technology. In an auction, the firm with a higher initial capacity wins the license. In a unit royalty scheme, if the initial capacity difference is large, the firm with a lower initial capacity gets it; otherwise, both firms get the license. Comparing different licensing schemes, including pre-set fees, auctions, per-unit royalties and two-part tariffs, the optimal choice for the innovator is to auction one exclusive license. However, when the innovation emerges from within the duopoly, it is used solely by the incumbent innovator without being licensed to the competitor.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102513"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188729","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 new approach for imprecise probabilities","authors":"Marcello Basili ,&nbsp;Luca Pratelli","doi":"10.1016/j.mathsocsci.2026.102509","DOIUrl":"10.1016/j.mathsocsci.2026.102509","url":null,"abstract":"<div><div>This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of sub–weak complementation, denoted by <span><math><mi>ψ</mi></math></span>, which assigns to each event <span><math><mi>H</mi></math></span> a corresponding event of uncertain eventualities. Interval probability measures for an event <span><math><mi>H</mi></math></span> can then be defined by taking into account its set of uncertain eventualities, which is contained in the standard complement <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>.</div><div>We characterize a broad class of interval probability measures and define their properties. Additionally, the interval distribution of a random variable is formulated, and a corresponding definition of stochastic dominance between two random variables is introduced. As a byproduct, a formal solution to the century-old Keynes–Ramsey controversy is presented.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102509"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188731","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":"Between proportionnality and envy-freeness: k-proportionality","authors":"Guillaume Chèze","doi":"10.1016/j.mathsocsci.2026.102515","DOIUrl":"10.1016/j.mathsocsci.2026.102515","url":null,"abstract":"<div><div>This article deals with the cake cutting problem. In this setting there exist, among others, two notions of fair division: proportional division (when there are <span><math><mi>n</mi></math></span> players, each player thinks to get at least <span><math><mrow><mn>1</mn><mo>/</mo><mi>n</mi></mrow></math></span> of the cake) and envy-free division (each player wants to keep his or her share because he or she does not envy the portion given to another player). Some results are valid for proportional division but not for envy-free division.</div><div>In the current paper, we introduce and study a scale between the proportional division and the envy-free division. The goal is to understand where is the gap between statements about proportional division and envy-free division. This scale comes from the notion introduced in this article: <span><math><mi>k</mi></math></span>-proportionality. When <span><math><mrow><mi>k</mi><mo>=</mo><mi>n</mi></mrow></math></span> this notion corresponds to the proportional division and when <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span> it corresponds to envy-free division.</div><div>With <span><math><mi>k</mi></math></span>-proportionality we can understand where some difficulties in fair division lie. First, we show that there are situations in which there is no <span><math><mi>k</mi></math></span>-proportional and equitable division of a pie with connected pieces when <span><math><mrow><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span>. This result was known only for envy-free division, i.e. <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span>.</div><div>Next, we prove that there are situations in which there is no Pareto-optimal <span><math><mi>k</mi></math></span>-proportional division of a cake with connected pieces when <span><math><mrow><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span>. This result was known only for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span>.</div><div>These theorems say that there are impossibility results even if we do not consider an envy-free division but a weaker notion.</div><div>Finally, <span><math><mi>k</mi></math></span>-proportionality allows to give a generalization with a uniform statement of theorems about strongly envy-free and strongly proportional divisions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102515"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188728","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":"New fairness criteria for truncated ballots in multi-winner ranked-choice elections","authors":"Adam Graham-Squire ,&nbsp;Matthew I. Jones ,&nbsp;David McCune","doi":"10.1016/j.mathsocsci.2026.102506","DOIUrl":"10.1016/j.mathsocsci.2026.102506","url":null,"abstract":"<div><div>In real-world elections where voters cast preference ballots, voters often provide only a partial ranking of the candidates. Despite this empirical reality, prior social choice literature frequently analyzes fairness criteria under the assumption that all voters provide a complete ranking of the candidates. We introduce new fairness criteria for multiwinner ranked-choice elections concerning truncated ballots. In particular, we define notions of the <em>independence of losing voters blocs</em> and <em>independence of winning voters blocs</em>, which state that the winning committee of an election should not change when we remove truncated ballots which rank only losing candidates, and the winning committee should change in reasonable ways when removing ballots which rank only winning candidates. Of the voting methods we analyze, the Chamberlin-Courant rule performs the best with respect to these criteria, the expanding approvals rule performs the worst, and the method of single transferable vote falls in between.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102506"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979659","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":"Candidate coalitions and strategic manipulation in multi-winner elections: An evaluation of committee scoring rules","authors":"Badr Bahloul,&nbsp;Ahmed Doghmi","doi":"10.1016/j.mathsocsci.2026.102504","DOIUrl":"10.1016/j.mathsocsci.2026.102504","url":null,"abstract":"<div><div>Strategic candidacy in multi-winner elections describes situations where candidates may enter or withdraw to influence which candidates are elected. Existing studies typically assume all eligible candidates are interested in participating. In reality, some eligible candidates are uninterested in winning but may enter strategically, while interested candidates may strategically withdraw; both types of moves can change the set of elected candidates. This paper extends the standard framework by distinguishing interested and uninterested candidates and studying manipulation via coordinated entry and exit. We focus on evaluating whether multi-winner rules are immune to manipulation by <em>coalitions of candidates</em> with respect to the number of voters <span><math><mi>n</mi></math></span> and the committee size <span><math><mi>k</mi></math></span>. Specifically, we say that a rule satisfies <em>candidate-coalition strategy-proofness</em> (CCSP) for an <em>election-point</em> <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span> if the “true” strategy profile—where candidates enter the election if and only if they are interested—constitutes a strong Nash equilibrium (i.e., no coalition of players can achieve a collective benefit by deviating from the actions dictated by their true types). Focusing on five committee-scoring rules—<span><math><mi>k</mi></math></span>-Borda, <span><math><mi>k</mi></math></span>-Anti-plurality, BLOC, <span><math><mi>k</mi></math></span>-Plurality, and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-CC—we provide complete characterizations of the election-points <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span> where each rule satisfies CCSP. Specifically, <span><math><mi>k</mi></math></span>-Plurality is CCSP exactly when <span><math><mrow><mi>n</mi><mo>&lt;</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></math></span>; <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-CC exactly when <span><math><mrow><mi>n</mi><mo>&lt;</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span>; BLOC only when <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span>; and <span><math><mi>k</mi></math></span>-Anti-plurality and <span><math><mi>k</mi></math></span>-Borda never satisfy CCSP.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102504"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979660","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 dynamic bicriteria fish war model with fish bank","authors":"Denis Kuzyutin ,&nbsp;Nadezhda Smirnova","doi":"10.1016/j.mathsocsci.2026.102511","DOIUrl":"10.1016/j.mathsocsci.2026.102511","url":null,"abstract":"<div><div>We introduce an extension of the standard dynamic fish war model with no-take marine reserve and migration in which the player’s economic utility function is supplemented with an environmental performance criterion. We derive and compare non-cooperative and cooperative solutions for this bicriteria model and its single-criterion counterpart. The impact of the fish bank size on the model behavior is explored for different levels of the players’ environmental concern.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102511"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188730","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":"Category-dependent preferences and stochastic choice","authors":"Matthew Ryan","doi":"10.1016/j.mathsocsci.2026.102514","DOIUrl":"10.1016/j.mathsocsci.2026.102514","url":null,"abstract":"<div><div>We introduce a generalisation of (Aguiar’s 2017) <em>random categorisation rule (RCR)</em> that relaxes (Aguiar’s 2017) <em>Acyclicity</em> axiom to an <em>Asymmetry</em> condition. Unlike other alternatives to the RCR, such as the models of Brady and Rehbeck (2016) and Cattaneo et al., (2020), our <em>generalised random categorisation rule (GRCR)</em> relaxes the linearity of preference, rather than varying the random consideration process. We show that the GRCR is also equivalent to allowing linear preferences to be <em>category-dependent</em>, with the requirement that the preferences associated with overlapping categories agree on the intersection. This allows the GRCR to capture intransitivities across categories, which may naturally arise when categorisation is used to frame choices. We provide a characterisation for the GRCR and compare it to the random utility model, as well as to the BR model, the RAM, and the model of Manzini and Mariotti (2014).</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102514"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189457","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":"Brand spillovers as shadow enforcement: Endogenous liability regimes in correlated experience goods markets","authors":"Yizheng Chen ,&nbsp;Jingkui Li ,&nbsp;Guoqiang Tian","doi":"10.1016/j.mathsocsci.2026.102512","DOIUrl":"10.1016/j.mathsocsci.2026.102512","url":null,"abstract":"<div><div>This paper develops a reputational equilibrium model for correlated experience goods markets with imperfect monitoring, incorporating strategic cross-market brand externalities. The central theoretical innovation demonstrates how high-end market brand spillover effects endogenously reshape quality incentives: High-end brand externalities create implicit liability constraints, sustaining Markov perfect equilibrium in quality provision without formal liability regimes when spillover intensity exceeds critical thresholds. Low-end markets replicate single-market failure patterns, necessitating hybrid reputation-liability mechanisms. The model provides microfoundations for international quality differentiation strategies, illustrating how developed economies can leverage emerging market participation to reduce domestic regulatory burdens while maintaining quality standards.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102512"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188727","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":"The conceivable scope of negligence rules for internalizing multidirectional externalities","authors":"Urs Schweizer","doi":"10.1016/j.mathsocsci.2025.102493","DOIUrl":"10.1016/j.mathsocsci.2025.102493","url":null,"abstract":"<div><div>In this paper, a game-theoretic setting with transferable utility serves to explore the scope of damages rules for internalizing multidirectional external effects. From the legal perspective, damages rules aim at compensating victims for the wrongdoing of others (compensation requirement). Yet, to be held liable, it must be an agent’s wrongdoing that has caused harm to the victim (causation requirement). The two requirements can be at conflict when causation is meant in the sense of the but-for test. The paper proposes a causation test that resolves this conflict quite generally. It combines the legal idea of the NESS test with the Shapley value of a suitable characteristic function. The resulting damages rules fully internalize externalities even if they are of multidirectional nature.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102493"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886247","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 the threshold representation of partial orderings","authors":"Daniele Caliari ,&nbsp;Davide Carpentiere","doi":"10.1016/j.mathsocsci.2026.102516","DOIUrl":"10.1016/j.mathsocsci.2026.102516","url":null,"abstract":"<div><div>In this paper, we provide a constructive proof for threshold representations of partial orderings in a finite setting and extend the construction to arbitrary sets. This contributes to a long-standing open problem posed in Nakamura (2002) and Aleskerov et al. (2007). We identify and discuss aspects of our proof that do not directly generalize to an infinite setting and, for each, provide intuitive sufficient conditions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102516"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397470","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}