Mathematical Social Sciences最新文献_第6页

A new value for cooperative games on intersection-closed systems 交闭系统上合作对策的一个新值

IF 0.7 4区经济学

Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-08-08 DOI: 10.1016/j.mathsocsci.2025.102450

Martin Černý

{"title":"A new value for cooperative games on intersection-closed systems","authors":"Martin Černý","doi":"10.1016/j.mathsocsci.2025.102450","DOIUrl":"10.1016/j.mathsocsci.2025.102450","url":null,"abstract":"<div><div>In the model of cooperative games with restricted cooperation, certain coalitions are infeasible, meaning they cannot form, which directly influences payoff allocation. We consider a scenario where coalitions are no longer categorized as feasible or infeasible, but rather as known or unknown. In this setting, coalitions with unknown values are still feasible, but their values remain unknown in the allocation process. Classical allocation methods for games with restricted cooperation, such as the R-value, become unsuitable for such scenarios.</div><div>We introduce a new allocation rule called the <em>uniform-dividend value</em> (UD-value), designed specifically for cooperative games where some coalition values remain unknown (so-called <em>incomplete cooperative games</em>). The UD-value allocates payoffs by evenly distributing the total surplus within each group of <em>indistinguishable</em> coalitions. We demonstrate that for <em>intersection-closed</em> set systems, the UD-value is uniquely determined and can also be viewed as the expected Shapley value computed over all totally positive (i.e., nonnegative-surplus) extensions of the incomplete cooperative game. We compare the UD-value to two existing allocation rules for intersection-closed games: the R-value, defined as the Shapley value of a game that sets surplus of absent coalition values to zero, and the IC-value, tailored specifically for intersection-closed systems. Specifically, we provide axiomatic characterizations of the UD-value motivated by characterizations of the IC-value and discuss further properties such as fairness and balanced contributions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102450"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005418","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

Envy-freeness and maximum Nash welfare for mixed divisible and indivisible goods 可分与不可分混合商品的无嫉妒性与最大纳什福利

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.2025.102449

Koichi Nishimura , Hanna Sumita

{"title":"Envy-freeness and maximum Nash welfare for mixed divisible and indivisible goods","authors":"Koichi Nishimura , Hanna Sumita","doi":"10.1016/j.mathsocsci.2025.102449","DOIUrl":"10.1016/j.mathsocsci.2025.102449","url":null,"abstract":"<div><div>We study fair allocation of resources consisting of both divisible and indivisible goods to agents with additive valuations. When only divisible or indivisible goods exist, it is known that an allocation that achieves the maximum Nash welfare (MNW) satisfies the classic fairness notions based on envy. Moreover, the literature shows the structures and characterizations of MNW allocations when valuations are binary and linear (i.e., divisible goods are homogeneous). In this paper, we show that when all agents’ valuations are binary linear, an MNW allocation for mixed goods satisfies the envy-freeness up to any good for mixed goods (EFXM). This notion is stronger than an existing one called envy-freeness for mixed goods (EFM), and our result generalizes the existing results for the case when only divisible or indivisible goods exist. When all agents’ valuations are binary over indivisible goods and identical over divisible goods (e.g., the divisible good is money), we extend the known characterization of an MNW allocation for indivisible goods to mixed goods, and also show that an MNW allocation satisfies EFXM. For the general additive valuations, we also provide a formal proof that an MNW allocation satisfies a weaker notion than EFM.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"138 ","pages":"Article 102449"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010801","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

Multimarket contact, cartel and product quality 多市场联系，卡特尔和产品质量

IF 0.7 4区经济学

Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-09-26 DOI: 10.1016/j.mathsocsci.2025.102467

Neelanjan Sen , Uday Bhanu Sinha

引用次数: 0

Limited attention and models of choice: A behavioral equivalence 有限注意力和选择模型：行为等价

IF 0.7 4区经济学

Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-08-28 DOI: 10.1016/j.mathsocsci.2025.102461

Davide Carpentiere, Angelo Enrico Petralia

引用次数: 0

Revealing compatible choices 显示兼容的选择

IF 0.7 4区经济学

Mathematical Social Sciences Pub Date : 2025-12-01 Epub Date: 2025-11-06 DOI: 10.1016/j.mathsocsci.2025.102475

Salvador Candelas

引用次数: 0

A stricter canon: General Luce models for arbitrary menu sets 更严格的标准：用于任意菜单集的通用Luce模型

IF 0.5 4区经济学

Mathematical Social Sciences Pub Date : 2025-07-01 Epub Date: 2025-06-18 DOI: 10.1016/j.mathsocsci.2025.102431

José A. Rodrigues-Neto , Matthew Ryan , James Taylor

{"title":"A stricter canon: General Luce models for arbitrary menu sets","authors":"José A. Rodrigues-Neto , Matthew Ryan , James Taylor","doi":"10.1016/j.mathsocsci.2025.102431","DOIUrl":"10.1016/j.mathsocsci.2025.102431","url":null,"abstract":"<div><div>Alós-Ferrer and Mihm (2025, Corollary 1) recently provided a characterisation the classical Luce model (Luce, 1959) when choices are observed for an arbitrarily restricted collection of menus, as is typical in experimental settings or when working with field data. They also characterise the general Luce model (<em>ibid.</em>, Theorem 1), which allows choice probabilities to be zero, for the same setting. The latter characterisation involves a single axiom – the <em>general product rule (GPR)</em>. An important special case of the general Luce model is obtained when the mapping from menus to the support of choice probabilities can be rationalised by a weak order. Cerreia-Vioglio et al. (2021) show that this special case is characterised by Luce’s (1959) <em>choice axiom</em>, provided choice is observed for all possible (finite) menus. The choice axiom is thus a fundamental “canon of probabilistic rationality”. We show that a natural – and surprisingly simple – strengthening of the GPR characterises the model of Cerreia-Vioglio et al. (2021) when the menu set is arbitrarily restricted. Our axiom implies the choice axiom, and is therefore a “stricter canon”.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"136 ","pages":"Article 102431"},"PeriodicalIF":0.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366077","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

Cooperation and balance in signed networks: A model of multiplex formation 签名网络中的合作与平衡：一个多元形成的模型

IF 0.5 4区经济学

Mathematical Social Sciences Pub Date : 2025-07-01 Epub Date: 2025-06-18 DOI: 10.1016/j.mathsocsci.2025.102430

Rajendra P. Kundu, Siddhi Gyan Pandey

{"title":"Cooperation and balance in signed networks: A model of multiplex formation","authors":"Rajendra P. Kundu, Siddhi Gyan Pandey","doi":"10.1016/j.mathsocsci.2025.102430","DOIUrl":"10.1016/j.mathsocsci.2025.102430","url":null,"abstract":"<div><div>We propose a game theoretic model for multiplexity in signed networks through strategic interactions amongst <span><math><mi>n</mi></math></span> players who are linked to each other in an existing signed network of friendships and enmities <span><math><mi>g</mi></math></span>, which shape the incentive structure faced by players in their pairwise interactions with each other. These interactions take the form of simultaneous move cooperation games of complete information, wherein network effects create incentives to cooperate due to the presence of common friends as well common enemies. The set of pure strategy Nash equilibria in the strategic interactions between players <span><math><mi>i</mi></math></span> and <span><math><mi>j</mi></math></span> determine the nature of the tie between them in <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span>, which is the new layer of the signed multiplex. We investigate how properties of structural balance in the existing signed social network <span><math><mi>g</mi></math></span> influence balance in the new signed network <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span>, identifying conditions on the existing network that yield a structurally balanced new layer of the multiplex.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"136 ","pages":"Article 102430"},"PeriodicalIF":0.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517767","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

Jump bidding in the war of attrition 在消耗战中跳投

IF 0.5 4区经济学

Mathematical Social Sciences Pub Date : 2025-07-01 Epub Date: 2025-06-27 DOI: 10.1016/j.mathsocsci.2025.102432

Wei Bi , Huiyun Ding

引用次数: 0

Aggregating incomplete rankings 汇总不完全排名

IF 0.5 4区经济学

Mathematical Social Sciences Pub Date : 2025-07-01 Epub Date: 2025-06-11 DOI: 10.1016/j.mathsocsci.2025.102423

Yasunori Okumura

引用次数: 0

Existence of Berge equilibrium in finite games 有限对策中Berge均衡的存在性