Cores,aggressiveness and the breakdown of cooperation in economic games

The paper develops the use of the core as a solution concept in game theory in two interrelated directions. In the first place, an indicator of aggressiveness of claims is introduced in a modified definition of the core. The modified core may be smaller than the usual core, and may fail to exist if aggressiveness increases beyond some critical level. In the second place the article gives a formulation of a mixed cooperative/non-cooperative game, in which the game will be played cooperatively within coalitions, but non-cooperatively as between coalitions. A mixed cooperative/non-cooperative solution obtains if the grand coalition of all players fail to materialize because the various claims are incompatible. The two directions referred to are interrelated because the level of aggressiveness may be decisive for whether or not the grand coalition, and possibly other coalitions, will break down. The final section of the paper draws some general conclusions and relates the approach to other ideas in the literature.     

Cooperative Outcomes through Noncooperative Games

This paper shows the equivalence between the stable solution set of any cooperative game in characteristic form (G1) and the subgame perfect Nash equilibria in pure strategies of a certain noncooperative game (G2). Players of G1 are named "agents." G2 is played by different players ("principals") who compete in wages to attract agents. The equivalence result holds when there are enough principals (if the game is superadditive, two principals suffice). Finally, another related cooperative game (G3) is constructed with both principals and agents as players. For G2 and G3 the same result is then proven, for any number of principals. Journal of Economic Literature Classification Numbers: C71 and C72.     

The (Price) Core of a Bertrand–Edgeworth Economy

In this paper, a solution concept from cooperative game theory is applied to a special kind of oligopolistic markets. Traditionally, oligopoly theory uses non-cooperative game theory. The cooperative solution concept, the Price Core, has been specially developed for this paper. In contrast to the Core, in the Price Core, different consumers may pay different prices for the same commodity. An example shows that the set of competitive allocations may be a proper subset of the Core and that the Core may be a proper subset of the Price Core. Received July 24, 2001; revised version received February 25, 2002 Published online: December 5, 2002     

营销渠道的冲突与协调研究——基于我国食品制造商和直接零售商合作博弈的实证分析

当渠道的非合作导致的冲突被逐渐认识到时，渠道成员就会有意识地开展合作。那么，合作是否确实减少了冲突，增进了协调呢？本文利用博弈理论提出六个假设，然后用现代计量方法进行实证检验，最后得出以下结论：渠道合作博弈优于非合作博弈，渠道成员间倾向于合作博弈，合作博弈下的营销渠道纵向成员（参与方）选择为地位相当者，渠道合作博弈中普遍存在隐性冲突，其程度与成员影响力的运用有关，合作博弈下的渠道成员普遍比较协调，营销渠道成员合作的协调及持续协调与诚信公平相关。     

Cooperative vs non-cooperative truels: little agreement, but does that matter?

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, over one round or n rounds. Representative solution concepts (Nash and subgame-perfect equilibrium; two notions of core) are compared, and little agreement is found among them. Although it might be desirable to subsume these different solutions within a common framework, such unification seems unlikely since they are grounded in fundamentally different notions of stability.     

简论科学发展观的价值内涵

科学发展观对当今中国社会发展的主体和动力、衡量发展的根本标准、实现路径和实施手段等问题都做出了科学的回答,包含着极其深刻的价值意蕴。要全面把握科学发展观的科学内涵和精神实质,就必须深刻领悟科学发展观的价值内涵。     

Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents

This paper extends the notions of superadditivity and convexity to stochastic cooperative games. It is shown that convex games are superadditive and have nonempty cores, and that these results also hold in the context of NTU games. Furthermore, a subclass of stochastic cooperative games to which one can associate a deterministic cooperative game is considered. It is shown that such a stochastic cooperative game satisfies properties like nonemptiness of the core, superadditivity, and convexity if and only if the corresponding deterministic game satisfies these properties.Journal of Economic LiteratureClassification Number: C71.     

Cooperation by Asymmetric Agents in a Joint Project

The object of study is cooperation in joint projects where agents may have different desired sophistication levels for the project and where some of the agents may have low budgets. In this context, questions concerning the optimal realizable sophistication level and the distribution of the related costs among the participants are tackled. A related cooperative game, the enterprise game, and a non‐cooperative game, the contribution game, are both helpful. It turns out that there is an interesting relation between the core of the convex enterprise game and the set of strong Nash equilibria of the contribution game. Special attention is paid to a new rule inspired by the Baker–Thompson rule in the airport landing fee literature. For this rule, the project is split up in a sequence of subprojects where the involved participants pay amounts which are, roughly speaking, equal, but not more than their budgets allow. The resulting payoff distribution turns out to be a core element of the related enterprise game.     

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication.     

Cooperative economic growth

We comparatively study optimal economic growth in a simple endogenous growth model and under two different games, i.e., dynamic sequential game and cooperative stochastic differential game, between a representative household and a typical self-interested politician. Sequential equilibrium solution is derived by applying Backward Induction Principle and corresponding optimal economic growth rate is endogenously determined. Moreover, cooperative equilibrium solution is established with group rationality, individual rationality and sub-game consistency requirements fulfilled, and it is further confirmed that the representative household will save more, and the self-interested politician will tax less, thereby leading to much faster economic growth, when compared to those of the sequential equilibrium solution.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Connecting the cooperative and competitive structures of the multiple-partners assignment game

Multiple-partners assignment game is the name used by Sotomayor [The multiple partners game, in: M. Majumdar (Ed.), Equilibrium and Dynamics: Essays in Honor of David Gale, The Macmillan Press Ltd., New York, 1992; The lattice structure of the set of stable outcomes of the multiple partners assignment game, Int. J. Game Theory 28 (1999) 567-583] to describe the cooperative structure of the many-to-many matching market with additively separable utilities. Stability concept is proved to be different from the core concept. An economic structure is proposed where the concept of competitive equilibrium payoff is introduced in connection to the equilibrium concept from standard microeconomic theory. The paper examines how this equilibrium concept compares with the cooperative equilibrium concept. Properties of interest to the cooperative and competitive markets are derived.     

Games superheroes play: Teaching game theory with comic book favorites

The valuable insights of game theory sometimes remain out of reach for students who are overwhelmed by the subject's complexity. Comic book applications of game theory, with superheroes as players, can facilitate enthusiasm and classroom interaction to enhance the learning of game theory. Drawing from content in superhero movies and books, the authors construct games to illustrate pure-strategy Nash equilibrium, Bayes-Nash equilibrium, mixed strategies, sub-game perfection, and perfect Bayesian equilibrium. To help instructors build students' skills in finding and interpreting game solutions, they translate comic book scenarios into specific game forms; however, not all scenarios are obvious so they suggest instructors help students develop their own game-theoretic judgments to determine what game forms, payoffs, and solution concepts might be appropriate for understanding a situation.     

Coalition Formation and Potential Games

In this paper we study the formation of coalition structures in situations described by a cooperative game. Players choose independently which coalition they want to join. The payoffs to the players are determined by an allocation rule on the underlying game and the coalition structure that results from the strategies of the players according to some formation rule. We study two well-known coalition structure formation rules and show that for both formation rules there exists a unique component-efficient allocation rule that results in a potential game. Journal of Economic Literature Classification Numbers: C71, C72.     

Cooperative and non-cooperative management of the Northeast Atlantic cod fishery

The fishery for Northeast Atlantic cod (Gadus morhua) in the Barents Sea is one of the most valuable fisheries in the North Atlantic. After the introduction of Extended Fisheries Jurisdiction, cod is a shared stock between Norway and Russia. Overfishing of quotas has been a concern for a number of years. The purpose of this article is to analyse cooperative and non-cooperative management of the Northeast Atlantic cod fishery. This will be done in a game theoretic context, based on different assumptions regarding important variables such as cost of effort and initial stock size. The game theoretic analysis will be based on an empirical bioeconomic model developed and estimated by Hannesson (Mar Policy 31:698–705, 2007; J Bioecon forthcoming). The case of cooperative management is analysed for different cost parameters and starting values of the stock. An interesting result is that the optimal policy gives rise to pulse fishing. As this involves effort (and harvests) varying from year to year, potentially imposing substantial social costs on the industry in years when the fishery is closed, a policy of constant effort is also considered. Finally, non-cooperative management is analysed.     

生育和经济社会的协调发展

有三个相关的生育问题需要作些深入研究,第一个是究竟我国当前生育是在什么水平?第二个是假如总和生育率的水平是1.8,这个水平能在今后三十年保持不变吗?第三个是假如未来三十年总和生育率过高或过低于1.8是不是会不利于人口与经济社会的协调发展?第一个问题应该可以用现有的但没有发表的生育数据作更深入分析和举办一次追踪调查去了解妇女生育的历史,追踪同样样本妇女的妊娠结果(活产、死产、流产)和出生儿童的性别。第二个问题的答案是否定的,因为世界上还没有一个国家能够不鼓励生育而能保持正在下降的出生水平。我国社会具备了生育水平继续下降的一切条件,特别是小家庭社会制度的普及更在促进生育水平下降。第三个问题用人口预测的方法比较未来不同生育水平对人口发展的影响,显示出不同预测的人口总数和年龄结构相差不大,无法得出过高和过低于1.8生育水平的未来人口会不利于人口与经济社会的协调发展的结论。     

The social cost problem,rights, and the (non)empty core

We revisit the “Coase theorem” through the lens of a cooperative game model which takes into account the assignment of rights among agents involved in a problem of social cost. We consider the case where one polluter interacts with many potential victims. Given an assignment or a mapping of rights, we represent a social cost problem by a cooperative game. A solution consists in a payoff vector. We introduce three properties for a mapping of rights. First, core compatibility indicates that the core of the associated cooperative games is nonempty. Second, Kaldor‐Hicks core compatibility indicates that there is a payoff vector in the core where victims are fully compensated for the damage once the negotiations are completed. Third, no veto power for a victim says that no victim has the power to veto an agreement signed by the rest of the society. We then demonstrate two main results. First, core compatibility is satisfied if and only if the rights are assigned either to the polluter or to the entire set of victims. Second, there is no mapping of rights satisfying Kaldor‐Hicks core compatibility and no veto power for a victim.     

The impact of lifestyle health risk on the bottom line: a case study

As the Lifestyle Advantage study continues, HPS expects to follow the utilization trends for a consistent group of participants and nonparticipants, maintaining full confidentiality. Several key issues will be addressed in the process: As the participation rate increases, will the claims payment gap between participants and nonparticipants be reduced? Can a company hope to see a return on an investment in a health promotion program? If so, over what period of time? Finding answers to these questions will contribute to the larger issues of long-term health care cost containment and health care reform.     

企业理论之新解释:一个基于知识管理的模型

企业理论研究往往关注三个基本问题:"企业为什么存在、企业和市场的边界是什么";"为什么企业会有所不同,是什么原因导致了这种不同";以及这些理论如何被应用于企业以获得持久的竞争优势.本文力图在这三个方面作出理论探索:一是从知识管理的角度回答企业理论的几个基本问题;二是建立一个基于知识传输的模型,并基于这个模型提出了四个可以检验的命题;三是讨论该模型对战略管理实践的启示.     

集体信誉的理论分析——组织内部逆向选择问题

建立在重复博弈模型上的逆向选择问题称为信誉理论,该理论主要研究博弈参与者如何通过树立信誉实现在非合作博弈中的合作均衡。传统的信誉理论涉及的多是个体的信誉问题,但是当个体信息无法传递时,个体信誉便无法发挥作用。此时,公众通常会对拥有相同标识的集体形成一个整体判断,与个体利益相关的是他们拥有的集体信誉。本文考察了集团内部存在不同类型个体时集体信誉维护的问题,本文称为内部逆向选择问题。我们发现,由于个体利益与集体利益的差异,导致集体信誉的激励作用要弱于传统的个体信誉的作用。此外,由于集体利益与社会利益的不一致,最终即使可以有效激励集团成员最大限度地维护集体利益,如果公众信念更新相对麻木,仍会造成经济运行无效率。