Hierarchical hypergames and Bayesian games: A generalization of the theoretical comparison of hypergames and Bayesian games considering hierarchy of perceptions

This paper discusses the relationship of two independently developed models of games with incomplete information, hierarchical hypergames and Bayesian games. It can be considered as a generalization of the previous study on the theoretical comparison of simple hypergames and Bayesian games (Sasaki and Kijima, 2012) by taking into account hierarchy of perceptions, i.e., an agent’s perception about the other agents’ perceptions, and so on. The authors first introduce the general way of transformation of any hierarchical hypergames into corresponding Bayesian games, which was called as the Bayesian representation of hierarchical hypergames. The authors then show that some equilibrium concepts for hierarchical hypergames can be associated with those for Bayesian games and discuss implications of the results.     

多冲突环境下的两人一阶超对策交互集结模型

针对不确定多冲突环境,建立了多个两人一阶超对策的交互集结模型。基于单一局中人在多个超对策中所认知的对策模型,结合该局中人所受到的资源约束及其对另一局中人资源约束的认知,建立该局中人在多冲突环境中所认知的多个对策的集结模型,在所有局中人所认知的对策集结模型基础上得到多个一阶超对策的交互集结模型;给出了超对策交互集结模型的稳定性分析过程。最后,通过一个军事例子说明了模型的实用有效性。     

Basketball scoring in NBA games: An example of complexity

Abstract Scoring in a basketball game is a highly dynamic, non-linear process. NBA teams try to be more and more competitive each season. For instance, they incorporate into their rosters the best players in the world. This and other mechanisms concur to make the scoring process in NBA games exciting and rarely predictable. This paper is to study the behavior of timing and scoring in basketball games. The authors analyze all the games in five NBA regular seasons (2005–06, 2006–07, 2007–08, 2008–09, 2009–10), for a total of 6150 games. Scoring does not behave uniformly; therefore, the authors also analyze the distributions of the differences in points in the basketball games. To further analyze the behavior of the tail of the distribution, the authors also carry out a semilog-plot and a log-log plot to verify whether this trend approaches a Poisson distribution or a PL. This paper reveals different areas of behavior related to the score, with specific instances of time that could be considered tipping points of the game. The presence of these critical points suggests that there are phase transitions where the dynamic scoring of the games varies significantly.     

The well-posedness for generalized fuzzy games

This paper establishes the stable results for generalized fuzzy games by using a nonlinear scalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.     

基于认知差异的恐怖主义袭击误对策分析

恐怖袭击事件中博弈双方高度不对称和存在认知差异,误对策方法提供了合适的分析框架.本文运用误对策分析方法剖析了恐怖袭击事件中政府反恐力量与恐怖分子的认知差异,并分析了不同情境下策略冲突的平衡结局.由于双方认知偏差可能导致不存在纯策略纳什均衡,而混合均衡进一步加大了策略的不确定性,安全策略采取"安全第一"的原则使决策者避免最大风险,相对于纳什均衡更合适作为存在认知差异的误对策问题的均衡分析方法.在实践操作角度上,恐怖袭击二阶误对策模型的平衡结局为恐怖分子发动的恐怖袭击行动将被挫败,因此提出提高反恐效能的政策建议,即发动社会民众提供反恐情报和预警线索,提高民众反恐意识.     

Optimal substructure of set-valued solutions of normal-form games and coordination

A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses on the minimal of such stable subspaces, this paper argues that non-minimal stable subspaces represent well the multi-agent situations to which neither Nash equilibrium nor rationalizability may be applied with satisfaction. As a theoretical support, the authors prove the optimal substructure of stable subspaces regarding the restriction of a game. It is further argued that the optimal substructure characterizes hierarchical diversity of coordination and interim phases in learning.     

Cooperative games on convex geometries with a coalition structure

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure,which can be seen as an extension of cooperative games with a coalition structure.For this kind of games,the cooperation among unions and within each union will be the convex sets,i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively.The explicit form of the generalized Owen value for this kind of games is given,which can be seen as an extension of the Owen value.Furthermore,two special cases of this kind of games are researched.The corresponding payoff indices are also studied.Finally,an illustrative example is given.     

基于联盟结构合作博弈的Selectope解集

定义了基于联盟结构合作博弈的Selectope解集形式: 首先将大联盟的收益在结构联盟间进行支付; 其次在结构联盟内对局中人进行支付. 将定义的Selectope解集与Pulido定义在联盟结构上的Weber集进行了比较, 得出Weber集总是包含在定义的Selectope解集中, 而这一结论与定义在可行联盟上的Weber集和Selectope解集的关系是一致的; 最后, 证明了基于联盟结构博弈的Selectope解集等价于定义在一种特定的可行联盟结构上的Selectope解集形式.     

具有Choquet积分形式的模糊合作对策

结合模糊数的限制运算，探讨了一类具有模糊支付的模糊合作对策--Choquet积分形式的模糊合作对策，研究了其单调性和连续性。具有模糊支付的模糊合作对策是凸模糊合作对策时，研究了Choquet积分形式的模糊合作对策的模糊核心和模糊Shapley值，并探讨了两者之间的关系，有趣的是这种关系与经典情形相一致。需要指出的是，所给有关模糊合作对策的定义都是对经典情形的推广。最后通过一个算例来说明其应用。     

无圈超图对策上的有效平均树解

在超图对策中,平均树解(简称AT值)是一类重要的分支有效解.本文在大联盟能够形成的假设下,基于单而芳等(2017)和Béal等(2018)在无圈图对策上提出的有效平均树解,进一步提出了无圈超图对策上基于平均树解的一类有效解.该有效解先给每个参与者进行AT值分配,再将大联盟收益超出分支收益之和的剩余部分平均分配给每个参与者.首先,证明了该有效解可以由有效性、分支公平性和分支内盈余等分性这三个公理所唯一刻画.其次,通过算例分析了该有效解.通过与其他值比较发现,对处于关键位置的参与者,在该解下会获得更多的收益.     

重复博弈的两段式分析法

提出了用于研究重复博弈的两段式分析法，该方法把无名氏定理的本质提取出来，即是否存在一个具有足以威胁参与人的后续博弈，两段式分析法既能适用于有限重复博弈也适用于无限重复博弈，利用两段式分析法，对不同的重复博弈无名氏定理进行了综合，从而可以看出不同的无名氏定理之间具有一致性，反过来也验证了论文提出的两段式分析法对重复博弈的实用性。     

基于超对策偏好认知信息沟的均衡结局鲁棒性分析

建立了反映超对策结局偏好认知不确定性的信息沟模型,对超对策均衡结局进行了鲁棒性分析。对于给定的不确定参数,通过在初始偏好认知向量的基础上迭代定义一序列新的偏好向量集合,构建超对策偏好认知信息沟模型。基于信息沟模型,通过确定使初始偏好认知下的超对策均衡结局集保持不变的最大不确定参数来讨论超对策均衡结局的鲁棒性。最后,一个军事例子说明了分析方法的实用有效性。     

The Extension of Hypergame Analysis and Its Application

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基于PSO神经网络的进化博弈研究

针对进化博弈中博弈人是有限理性的,提出了一种基于粒子群神经网络的进化博弈决策机制。该机制将神经网络技术引入到进化博弈中,并采用粒子群优化算法(PSO算法)来训练神经网络,因而可利用神经网络来模拟博弈人在进化过程中的学习和策略调整。利用该机制分别对有限理性条件下的鹰-鸽博弈和重复囚徒困境博弈进行了研究。实验表明:PSO神经网络可以准确地模拟进化博弈中博弈人的动态学习与决策过程,能有效地指导博弈人的策略选取,是进化博弈分析的有力工具。     

模糊合作对策上的Banzhaf函数

通过对经典合作对策上Banzhaf函数的描述,给出了模糊合作对策上Banzhaf函数的定义.讨论了两类模糊合作对策上Banzhaf函数的存在性和唯一性,并给出了它们的具体表达形式.探讨了所给Banzhaf函数的模糊零元,个人理性,单调性,非负性.研究了模糊联盟与其模糊支撑关于Banzhaf函数之间的关系,最后通过算例来说明所给模糊合作对策上的Banzhaf指标.     

本质博弈与Nash平衡点集的本质连通区

1962年吴文俊和江嘉禾对n人非合作有限博弈引进了本质平衡点和本质博弈的概念,并证明了每一个有限博弈都能够被本质博弈任意逼近.1963年江嘉禾对n人非合作有限博弈引进了平衡点集本质连通区的概念,并证明了每一个有限博弈都存在至少一个平衡点集的本质连通区.这些是中国数学家对博弈论的重要贡献.     

模糊合作对策在凸几何上的Shapley函数

首先给出了模糊合作对策在凸几何上的定义。通过相应的公理体系,论述了模糊合作对策在凸几何上的Shapley函数。为了更好了解此类模糊合作对策,研究了两类特殊模糊合作对策在凸几何上的Shapley函数,并证明了其存在性和唯一性,拓展了模糊合作对策的研究范围。最后通过算例分析来具体说明局中人在此类模糊合作对策上的收益值。     

准拟阵合作对策的τ值

考虑合作对策中联盟结构受到拟阵限制的情形,探讨准拟阵合作分配的理性和公平原则的公理化.利用经典合作对策τ值思想,构造了准拟阵合作对策τ值,并证明其满足理性和公平原则.最后将该方法与拟阵合作对策Shapley值在个体理性方面做了比较.     

Vector space structure of finite evolutionary games and its application to strategy profile convergence

A vector space structure is proposed for the set of finite games with fixed numbers of players and strategies for each players.Two statical equivalences are used to reduce the dimension of finite games.Under the vector space structure the subspaces of exact and weighted potential games are investigated.Formulas are provided to calculate them.Then the finite evolutionary games(EGs)are considered.Strategy profile dynamics is obtained using different strategy updating rules(SURs).Certain SURs,which assure the convergence of trajectories to pure Nash equilibriums,are investigated.Using the vector space structure,the projection of finite games to the subspace of exact(or weighted)potential games is considered,and a simple formula is given to calculate the projection.The convergence of near potential games to anε-equilibrium is studied.Further more,the Lyapunov function of EGs is defined and its application to the convergence of EGs is presented.Finally,the near potential function for an EG is defined,and it is proved that if the near potential function of an EG is a Lyapunov function,the EG will converge to a pure Nash equilibrium.Some examples are presented to illustrate the results.     

带层次结构效用可转移合作对策的多步Shapley值

作为一种局中人结盟形式,层次结构比联盟结构更具一般性.本文致力于给出带层次结构效用可转移合作对策的多步Shapley值,具体给出了其分配过程及公理化刻画.另外,作为一个等价分配过程,本文还证明了它等价于一个特殊效用可转移合作对策的加权Shapley值.研究结果扩展了带联盟结构效用可转移合作对策的两步Shapley值,可为研究其它带结盟限制合作对策的解提供借鉴.