Mathematical Social Sciences最新文献

英文中文

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 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-08-08 DOI: 10.1016/j.mathsocsci.2025.102450

Martin Černý

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.

We introduce a new allocation rule called the uniform-dividend value (UD-value), designed specifically for cooperative games where some coalition values remain unknown (so-called incomplete cooperative games). The UD-value allocates payoffs by evenly distributing the total surplus within each group of indistinguishable coalitions. We demonstrate that for intersection-closed 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.

在限制合作的合作博弈模型中，某些联盟是不可行的，即无法形成，这直接影响到收益分配。我们考虑这样一种情况，即联盟不再被划分为可行或不可行，而是已知或未知。在这种情况下，具有未知值的联盟仍然是可行的，但其值在分配过程中仍然是未知的。限制合作博弈的经典分配方法（如r值）不适合这种情况。我们引入了一种新的分配规则，称为一致红利值（UD-value），专门设计用于一些联盟值仍然未知的合作博弈（所谓的不完全合作博弈）。美元价值通过在每组不可区分的联盟中平均分配总盈余来分配收益。我们证明了对于相交闭集系统，ud值是唯一确定的，并且可以看作是在不完全合作对策的所有全正（即非负剩余）扩展上计算的期望Shapley值。我们将ud值与两个现有的交叉口封闭博弈分配规则进行比较：r值，定义为将缺席联盟值的盈余设置为零的博弈的Shapley值，以及ic值，专门为交叉口封闭系统量身定制。具体来说，我们提供了由ic值特征驱动的ud值的公理化特征，并进一步讨论了公平性和平衡贡献等性质。

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引用次数: 0

Conformism and name dynamics: A cliometric study of ancient Greek names 符合性与名称动力学：古希腊名称的地理计量学研究

IF 0.7 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-08-05 DOI: 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.

在命名从众的社会学研究的基础上，我们建立了一个反映从众或不从众行为的动态命名模型。这使我们能够考虑到比通常用于名称建模的统计物理方法更多的自由度。通过实证检验我们的模型，我们发现，从众命名解释了古希腊名字分布的独特形状，这与当代的名字数据不同。

引用次数: 0

A look back at the core of games in characteristic function form: Some new axiomatization results 回顾特征函数形式下的游戏核心：一些新的公理化结果

IF 0.7 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-29 DOI: 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.

这篇论文的主要贡献在于提供了三个新的结果，将游戏的核心公式化为特征函数形式（不一定具有可转移的效用），服从无害的条件（单个理性支付向量的集合是有界的）。这个练习的一个新颖之处在于，我们的领域是这类游戏的整个类别：也就是说，通常在相关文献中强加的“非平等性”或“平衡性”等限制并不是必需的。

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 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-29 DOI: 10.1016/j.mathsocsci.2025.102449

Koichi Nishimura , Hanna Sumita

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.

我们研究了由可分商品和不可分商品组成的资源公平分配给具有附加价值的代理。当只有可分或不可分的商品存在时，已知实现纳什福利最大化的分配满足基于嫉妒的经典公平概念。此外，文献显示了二元和线性估值时MNW分配的结构和特征（即，可分商品是同质的）。在本文中，我们证明了当所有主体的估值都是二元线性时，混合商品的MNW分配满足混合商品的任意商品的嫉妒自由度（EFXM）。这个概念比现有的一个称为混合商品的嫉妒自由（EFM）的概念更强，并且我们的结果推广了只有可分或不可分商品存在的情况下的现有结果。当所有主体对不可分割商品的估价是二元的，而对可分割商品的估价是相同的（例如，可分割商品是货币），我们将不可分割商品的MNW分配的已知特征扩展到混合商品，并证明了MNW分配满足EFXM。对于一般的加性估值，我们还提供了一个形式证明，证明MNW分配满足比EFM更弱的概念。

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引用次数: 0

The use of symmetry for models with variable-size variables 对具有可变大小变量的模型使用对称性

IF 0.7 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-13 DOI: 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.

本文给出了具有多维变大小变量的对称（置换不变）函数的一个通用表示。这些表示有助于证明使用矩聚合来自每个变量的信息的近似方法。它进一步讨论了这些发现如何为博弈论应用提供见解，包括两步策略函数估计，基于矩的马尔可夫均衡（MME）和聚合博弈。关于政策函数估计，在一定条件下，无论市场上有多少企业，只要包含足够数量的矩，都可以将公共政策函数估计为企业自身状态和竞争者状态多项式项（矩）之和的函数。对于MME，本研究表明，当矩数达到一定水平且满足正则性条件时，MME等价于Markov完美均衡。对于聚集对策，本文建立了任何满足支付函数对称性和连续性条件的对策都可以表示为多维广义聚集对策。这通过引入多维聚合扩展了之前关于广义（完全）聚合博弈的研究。

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引用次数: 0

A nonatomic game involving incomplete information and general ambiguity attitudes 一种包含不完全信息和一般模棱两可态度的非原子博弈

IF 0.7 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-11 DOI: 10.1016/j.mathsocsci.2025.102435

Jian Yang

We consider a nonatomic game involving incomplete information. On top of a player’s own action and the joint distribution of other players’ traits and actions, also influencing the player’s return is a state of the world that incorporates uncertain factors external to all players. Non-exact knowledge about the latter is embedded in a player’s signal. When other players adopt strategies that amount to signal-based action distributions, a given player’s action would be guided by her own preference on the vector made up of the distributions on returns that she anticipates to encounter under all potential states allowed by her signal. There can be two equilibrium notions; namely, the action- and distribution-based ones that depend on whether a player controls individual actions or merely their distributions. Besides the existence of equilibria, we also study relationships between the two equilibrium notions for various special cases. Furthermore, the nonatomic game is shown to approximate its finite counterparts.

我们考虑一个包含不完全信息的非原子博弈。除了玩家自己的行动以及其他玩家特征和行动的共同分布之外，影响玩家返回的还有包含所有玩家外部不确定因素的世界状态。关于后者的不精确的知识嵌入在玩家的信号中。当其他玩家采用的策略相当于基于信号的行动分布时，给定玩家的行动将受到其自身偏好向量的引导，该向量由其在信号允许的所有潜在状态下预期遇到的收益分布组成。有两种平衡概念；也就是说，基于行动和分布的模式取决于玩家是控制个人行动还是仅仅控制其分布。除了均衡的存在性外，我们还研究了各种特殊情况下这两个均衡概念之间的关系。进一步，证明了非原子对策近似于有限对策。

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 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-01 DOI: 10.1016/j.mathsocsci.2025.102430

Rajendra P. Kundu, Siddhi Gyan Pandey

We propose a game theoretic model for multiplexity in signed networks through strategic interactions amongst

n

players who are linked to each other in an existing signed network of friendships and enmities

g

, 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

i

and

j

determine the nature of the tie between them in

G (g)

, which is the new layer of the signed multiplex. We investigate how properties of structural balance in the existing signed social network

g

influence balance in the new signed network

G (g)

, identifying conditions on the existing network that yield a structurally balanced new layer of the multiplex.

我们提出了签名网络中多重性的博弈论模型，通过在现有的友谊和敌人的签名网络中相互联系的n个参与者之间的战略互动，形成了参与者在彼此配对互动时所面临的激励结构。这些互动以完全信息同步移动合作游戏的形式出现，其中网络效应创造了合作动机，因为存在共同的朋友和敌人。参与者i和j之间的策略交互中的纯策略纳什均衡集决定了他们在G(G)中的联系性质，G(G)是有符号复用的新层。我们研究了现有签名社会网络g中结构平衡的性质如何影响新签名网络g (g)中的平衡，确定了现有网络上产生结构平衡的新多层的条件。

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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 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-01 DOI: 10.1016/j.mathsocsci.2025.102432

Wei Bi , Huiyun Ding

This paper studies jump bidding in a war of attrition, where a bidder makes a costly preemptive commitment to deter opponents. We identify a Double-Edged Sword Effect: while jump bidding increases early-stage costs for the jump bidder, it enhances her ability to deter high-valuation opponents in later stages. The bidder jump bids when she believes that her opponent is likely to have a high valuation and not quit soon, such as when the valuation distribution is convex or bounded away from zero. Although jump bidding may result in inefficient allocation, it reduces total attrition costs and can improve overall welfare ex ante.

本文研究了消耗战中的跳标问题，在这种情况下，竞标者做出代价高昂的先发制人承诺来威慑对手。我们发现了一种双刃剑效应：虽然跳跃式竞价增加了跳跃式竞价者的早期成本，但它增强了跳跃式竞价者在后期阻止高估值对手的能力。当竞标者认为对手的估值可能很高且不会很快退出时，比如估值分布是凸的或有界远离零时，竞标者就会跳投。跳跃竞价虽然会导致分配效率低下，但降低了总损耗成本，提高了事前的整体福利。

引用次数: 0

Deposit insurance in a sequential-service constrained environment 顺序服务受限环境中的存款保险

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-01 DOI: 10.1016/j.mathsocsci.2025.102434

Fernando Barros Jr. , Samuel Cruz , Bruno R. Delalibera , Diego Silva

We study the effect of a deposit insurance scheme (DIS) in an economy with multiple isolated banks. Participant banks fund the scheme, which follows a pre-determined insurance payment scheme. An external player transfers insurance benefits to all banks where depositors are running. The total insurance payment depends on resources collected by the external authority and the number of eligible queues to receive the insurance benefit. We discuss the effect of DIS on the optimal payment contract. More specifically, we analyze the existence of bank-run equilibria and whether the optimal payment contract is incentive-compatible. We find that DIS prevents bank-run equilibria at the same time that it may expose the environment to contagion. We also see that the insurance policy relaxes the truth-telling condition for general parameters.

我们研究了存款保险计划（DIS）在一个有多个孤立银行的经济体中的效果。参与银行为该计划提供资金，该计划遵循预先确定的保险支付计划。外部参与者将保险收益转移到存款人所在的所有银行。保险支付总额取决于外部机构收集的资源和获得保险福利的合格队列的数量。讨论了DIS对最优支付契约的影响。更具体地说，我们分析了银行挤兑均衡的存在性以及最优支付契约是否激励相容。我们发现，DIS在防止银行挤兑均衡的同时，也可能使环境暴露于传染。我们还看到保险单放宽了一般参数的真实条件。

引用次数: 0

Cost structures and innovation incentives 成本结构与创新激励

IF 0.5 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences

Pub Date : 2025-07-01 DOI: 10.1016/j.mathsocsci.2025.102436

Suryaprakash Mishra

In a Cournot oligopoly set up with constant marginal cost and linear demand, innovation is rewarding, i.e., profit enhancing. We show that the same may not be true when marginal costs are increasing. In contrast to the standard results, we show the possibilities of conditional innovation/technological retrogression (henceforth retrogression) by firms: when the number firms

n = 1

or 2 innovation is undertaken by firms unconditionally and with certainty while for

n > 3

there exists an innovation–neutral technology line dividing the regions of innovation and retrogression. We bring forth the unconventional but interesting relationship between the intensity of competition and welfare –

\forall n > 3

competition decreases welfare and thus leads to Pareto deterioration while the lack thereof enhances welfare and results in Pareto improvement. We suggest ‘monitored competition’ as in restricted entry to encourage innovation, as a potential policy instrument.

在边际成本不变、需求线性的古诺寡头垄断中，创新是有益的，即利润增加。我们表明，当边际成本增加时，情况可能并非如此。与标准结果相比，我们展示了企业条件创新/技术倒退（以下简称倒退）的可能性：当企业数量n=1或2时，企业无条件地、确定地进行创新，而当企业数量n= gt；3时，存在一条创新中性的技术线将创新和倒退区域分开。我们提出了竞争强度与福利之间非传统但有趣的关系——∀n>；3竞争会降低福利，从而导致帕累托恶化，而缺乏竞争会提高福利，并导致帕累托改善。我们建议将“监管竞争”作为一种潜在的政策工具，如限制进入以鼓励创新。

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