Measuring the interactions among variables of functions over the unit hypercube

By considering a least squares approximation of a given square integrable function f:n[0,1]→R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory.     

关于拓扑对策中的I2(κ)(∈)I(κ)问题

证明了如果空间类K为D-空间类或闭遗传不可约空间类,则I（K）包含K.这一结果对于K为D空间类和闭遗传不可约空间类,肯定地回答了I（K）是否包含I^2（K）问题.     

Optimal convergence in naming game with geography-based negotiation on small-world networks

We propose a negotiation strategy to address the effect of geography on the dynamics of naming games over small-world networks. Communication and negotiation frequencies between two agents are determined by their geographical distance in terms of a parameter characterizing the correlation between interaction strength and the distance. A finding is that there exists an optimal parameter value leading to fastest convergence to global consensus on naming. Numerical computations and a theoretical analysis are provided to substantiate our findings.     

A general framework for cooperation under uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the associated cooperative games are totally balanced. Finally, we consider several example situations.     

不确定性条件下市场特征与市场信息的价值

通过建立一个博弈模型,研究在不确定性条件下,市场特征和市场信息对企业利润的影响.在一定条件下,预测越精确,信息越有价值;而在其他情况下则相反.产品替代程度越高,或市场预期需求越大,都将对企业利润产生积极影响.     

基于利益相关者合作博弈的决策优化与收益分配

企业剩余既是利益相关合作的成果也是争夺的对象。本首先用TOPSIS方法描述利益相关参与企业群体决策，并对决策群体给出的多种方案进行优化的过程。然后运用Shapley值，计算优化方案中不同利益相关合作的影响指数，再通过评估获得不同利益相关的分配收益。     

广告分担、价格折扣与供应链的纵向合作广告

研究了生产商和零售商的纵向合作广告问题。分别在广告分担和价格折扣策略下，探讨了双方的均衡结果和利润。当生产商的边际利润较小时，生产商的最优决策是不采取任何一种策略。当生产商的边际利润达到一定范围时，广告分担策略是双方共同的最优选择。而无论在什么样的条件内，价格折扣策略都不会使双方同时满意。为了增加双方的收益，供应链成员应该在广告上集成决策。最后给出了系统集成的可行最优解的范围和Nash讨价还价解。     

一类多步矩阵对策上的计策问题

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.     

中国现行财政体制下“买税”行为的博弈分析

博弈论为理论依据,通过对高、低两种任务下买税利益团体和上级监管部门的利益偏好和行为特征进行建模对比分析,考察影响其行为的各种因素,从经济学角度探求引起“买税”行为的根源,并试着给出建议.