基于主体的博弈要素分析

从博弈基本理论的完美性出发,对博弈要素进行系统规范化是一个重要的课题.博弃由博弃主体、博弈语境和信号三个基本要素,而信息、理性、信念和效用则是博弈主体的根本属性.这些要素共同决定博弈主体在博弈中的行为.博弃主体具有效用最大化的倾向,但效用的评价却具有多样性.主体的策略空间和效用函数具有客观性,但主体对它们的认识却具有主观性.博弈主体的根本任务就是要通过对博弈语境的学习,使主观认识和客观事实不断接近,理性不断改善,最终获取较优的博弈效用.     

图化思维及其应用

引言与初中数学相比,高中数学课程无论在知识的深度、难度和广度上,还是在思维能力的要求上,对学生来说都是一次飞跃,这使得他们在高中学习过程中常常不能与教学要求相适应.特别     

考虑参照依赖的突发公共卫生事件预警信息公开策略研究

突发公共卫生事件预警信息公开是疫情防范关口前移尤为重要的一环。本研究基于有限理性假设，改变传统期望效用函数，引入参照依赖理论，刻画了更加符合应急场景的博弈方认知与决策规律。构建地方政府、中央政府、公众的演化博弈模型，通过复制动态方程描述不同主体交互行为。结果表明，中央政府监管与公众参与在促进地方政府预警信息公开上形成了互补嵌入；主体感知效用、信息公开成本等对系统演化驱动效果明显，各方对感知效用边际递减系数和厌恶损失规避系数比较敏感；适当增加中央政府监管成功率、提高地方政府风险研判水平、加强公众信息辨识准确程度均有助于促进突发传染病预警信息公开。本研究结果可指导政府风险决策并为其制定合理的权、责、利条款提供模型支撑。     

工程项目主体行为博弈分析

在工程项目建设过程中,项目主体扮演着重要的角色,同时相互之间构成了一定的经济伙伴关系.由于项目主体之间的信息存在不对称性,项目各主体为追求自身利益最大化相互之间形成了博弈关系.在分析项目主体之间的博弈关系的基础上,分别建立了一般项目和政府投资项目主体三方之间的行为博弈模型,分析了博弈混合策略纳什均衡解.最后从建立完善的建设管理制度、建立事先监督机制与事后惩罚机制、建立激励机制与约束机制等方面提出了规范项目主体行为的具体对策.     

博弈论中的一个优化控制模型

博弈中往往会出现个人理性和集体理性的预选，使得社会资源不能得到很好的利用。本以公共悲剧为例，通过引入“政府”作为局中人，建立了一个特殊的完全信息动态博弈模型——带有控制的博弈模型。试图解决个人理性和集体理性的预选，实现对博弈均衡结果的优化。     

基于学习的互利协调与互制均衡及其矢量分析

纳什均衡代表了博弈参与人如何博弈的一致性预测.但是,有限理性的博弈者一般不会在一次博弈中取得一致性预期,他们总是通过不断的重复学习,使得预期逐渐向均衡方向演化.对互利协调与互制均衡进行分析,并探讨协调和均衡的动态形成机理.互制均衡强调自我实现,倾向个体利益最优.互利协调在强调自我实现的基础上,注重双赢,引导合作.现代博弈学习理论正是从有限理性的实际出发,通过学习和进化,最终实现博弈的均衡或协调.这对于如何走出传统博弈的困境具有重要意义.     

在解题反思中进行深度学习

在数学学习中,解题是深度学习的重要途径.学生在解题过程中进行反思性学习是深度学习的有效方式.由于“反思”难以自发形成,故教师应在解题教学中发挥主导作用,努力将“反思”融入主体思维活动中.     

非对称信息证券交易的跨期动态博弈均衡解析

揭示了不对称信息条件下证券市场均衡的基本特征.Grossman和Stiglitz模型依据不知情交易者的弱理性,解析了证券交易的静态均衡状态.O'Hara模型增强了不知情交易者的理性,强调了市场均衡时的风险定价,但其命题的成立条件是相互矛盾的.认为不知情交易者信息收集和处理能力的提高会使决策更为理性,证券市场的均衡本质上是交易者的动态博弈均衡.依此思路,运用不完美信息的跨期动态博弈模型解析了非对称信息条件下证券交易者的精炼贝叶斯纳什均衡.结论显示出,市场失效的主要原因是交易者之间的信息分析能力不平衡,而不是信息不对称;市场流动性的决定因素不是信息不对称风险而是知情交易者与不知情交易者所研判的无风险收益率的差别.     

有限理性条件下演化博弈行为分析

基于博弈双方有限理性的假设,运用动力系统的相关理论和方法对一般2×2非对称演化博弈过程建立了动态复制方程,并对博弈双方在演化过程中的行为进行了分析,得出博弈双方交互系统均衡点及稳定性相应的结论及其全部动力学行为.     

基于博弈论的信息安全风险管理信念研究

信息安全风险管理的核心是采取一系列安全策略,用以防御威胁对信息系统造成安全事件的措施.本质上是威胁与防御的博弈,这种博弈是动态的、非合作的、不完全信息的,可用扩展博弈模型加以描述.通过对博弈中信念及其主体间概率的理解,分析博弈风险管理信念,特别是作为主体集的风险管理信念对防御的影响,提出基于测量的安全风险管理信念的可容忍威胁以及对威胁的防御机制,为网络安全风险管理的定量研究提供了一种新的途径.     

博弈训练及其对均衡的影响

训练和学习是博弈中的一对统一体.博弈学习是通过降低博弈语境的不确定性来提高博弈收益,而博弈训练则是针对博弈学习的一种策略.训练者通过可信的信号传递来影响对手的博弈学习结果,改变受训者的信念,从而提高博弈收益.博弈训练的目标可分为事实隐藏和事实揭示.在使用博弈训练时,应遵循"利已、利他、可信、可辩"的原则,从全局的角度审视整个博弈环境,选择利己利他的训练方法,最终取得较优的训练效果.     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Experimental results on ultimatum games with incomplete information

This paper is about experiments on two versions of ultimatum games with incomplete information, called the offer game and the demand game. We apply the strategy method, that is, each subject had to design a complete strategy in advance instead of reacting spontaneously to a situation which occurs in the game. Game theory predicts very similar outcomes for the offer and the demand games. Our experiments, however, show significant differences in behavior between both games. Using the strategy method, allows us to explore the motivations leading to those differences. Since each subject played the same version of the game eight rounds against changing anonymous opponents we can also study subjects' learning behavior. We propose a theory of boundedly rational behavior, called the “anticipation philosophy”, which is well supported by the experimental data.     

The principal-agent problem with evolutionary learning

We extend agency theory to incorporate bounded rationality of both principals and agents. In this study we define a simple version of the principal-agent game and examine it using object-oriented computer simulation. Player learning is simulated with a genetic algorithm model. Our results show that players of incentive games in highly uncertain environments may take on defensive strategies. These defensive strategies lead to equilibria which are inferior to Nash equilibria. If agents are risk averse, the principal may not be able to provide enough monetary compensation to encourage them to take risks. But principals may be able to improve system performance by identifying good performers and facilitating information exchange among agents.The authors would like to thank the anonymous referees for their helpful suggestions.     

The lattice structure of the set of stable outcomes of the multiple partners assignment game

The Multiple Partners assignment game is a natural extension of the Shapley and Shubik Assignment Game (Shapley and Shubik, 1972) to the case where the participants can form more than one partnership.  In Sotomayor (1992) the existence of stable outcomes was proved. For the sake of completeness the proof is reproduced in Appendix I. In this paper we show that, as in the Assignment Game, stable payoffs form a complete lattice and hence there exists a unique optimal stable payoff for each side of the market. We also observe a polarization of interests between the two sides of the matching, within the whole set of stable payoffs. Our proofs differ technically from the Shapley and Shubik's proofs since they depend on a central result (Theorem 1) which has no parallel in the Assignment model. Received: June 1996/Revised version: February 1999     

Characterization of the core in games with restricted cooperation

Games with restricted cooperation describe situations in which the players are not completely free in forming coalitions. The restrictions in coalition formation can be attributed to economic, hierarchical, political or ethical reasons. In order to manage these situations, the model includes a collection of coalitions which determines the feasible agreements among the agents. The purpose of this paper is to extend the characterization of the core of a cooperative game, made by Peleg [International Journal of Game Theory 15 (1986) 187–200; Handbook of Game Theory with Economic Applications, vol. I. Elsevier Science Publishers B.V., pp. 397–412] to the context of games with restricted cooperation. In order to make the approach as general as possible, we will consider classes of games with restricted cooperation in which the collection of feasible coalitions has a determined structure, and we will impose conditions on that structure to generalize the Peleg’s axiomatization.     

On implementation via demand commitment games

A simple version of the Demand Commitment Game is shown to implement the Shapley value as the unique subgame perfect equilibrium outcome for any n-person characteristic function game. This improves upon previous models devoted to this implementation problem in terms of one or more of the following: a) the range of characteristic function games addressed, b) the simplicity of the underlying noncooperative game (it is a finite horizon game where individuals make demands and form coalitions rather than make comprehensive allocation proposals and c) the general acceptability of the noncooperative equilibrium concept. A complete characterization of an equilibrium strategy generating the Shapley value outcomes is provided. Furthermore, for 3 player games, it is shown that the Demand Commitment Game can implement the core for games which need not be convex but have cores with nonempty interiors. Received March 1995/Final version February 1997     

博弈视角下闭环供应链契约协调机制研究

应用博弈论,在存在第三方回收商的闭环供应链中研究了供应链各个节点如何选择定价策略从而达到个体与整体系统利润最大化.在传统收入共享享契约协调机制的基础上进行了改进,从而使得各节点与整体供应链的利润都得到提高.最后,运用具体算例验证了算法的合理性.     

The potential of recreational mathematics to support the development of mathematical learning

ABSTRACT

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts. Recreational mathematics can be used in education for engagement and to develop mathematical skills, to maintain interest during procedural practice and to challenge and stretch students. It can also make cross-curricular links, including to history of mathematics. In undergraduate study, it can be used for engagement within standard curricula and for extra-curricular interest. Beyond this, there are opportunities to develop important graduate-level skills in problem-solving and communication. The development of a module ‘Game Theory and Recreational Mathematics’ is discussed. This provides an opportunity for fun and play, while developing graduate skills. It teaches some combinatorics, graph theory, game theory and algorithms/complexity, as well as scaffolding a Pólya-style problem-solving process. Assessment of problem-solving as a process via examination is outlined. Student feedback gives some indication that students appreciate the aims of the module, benefit from the explicit focus on problem-solving and understand the active nature of the learning.