内生网络环境下具有异质连接费用的局部策略互动

考察内生网络环境下局中人之间的局部策略互动, 网络中的局中人只与直接邻居进行协同对策. 网络生成的过程中, 建立连接的费用是异质的~(具有两种水平), 与采取有效行动的局中人建立连接时执行高水平费用, 与采取风险占优行动的局中人建立连接时执行低水平费用. 在异质连接费用的情形下, 首次较为完整地给出了均衡网络的结构特性和局中人的行动选择, 并分析了费用参数对均衡结果的影响.     

内生网络环境下2-步邻域内的局部策略互动及其仿真

考察内生网络环境下局中人与2-步邻域内的邻居进行的局部协同对策,较为完整地给出了均衡网络的结构特性,以及费用参数和互动半径对于均衡结构的影响. 基于 NetLogo仿真系统,编制了局部互动仿真模拟实验程序. 仿真结果显示,网络生成的动态进程对于网络均衡结果存在很大影响. 结果对于解决社会和经济领域中的互动问题可提供策略性指导.     

联盟剖分型单向流动态网络生成对策

通过定义联盟同质费用研究考察具有固定联盟剖分的单向流动态网络生成对策.局中人通过采取局部行动生成网络,行动的原则是最大化其所在联盟的整益.选择B&G函数作为局中人的基本支付函数,诱导产生联盟-局中人的B&G函数.在新的规则之下,分别给出了局部纳什网的存在性、结构特性及其动态生成进程的定理.     

基于再保险人分担理赔费用的保险欺诈博弈模型分析

本文首先建立了基于再保险人分担理赔费用的夸大风险损失的索赔欺诈博弈模型，然后分析了保险双方的博弈策略选择及其可能达到的均衡。研究表明，博弈模型存在某种形式的精炼贝叶斯纳什均衡，但如实告知一般不是保单持有人的精炼贝叶斯纳什均衡策略。而且，博弈模型不存在分离均衡，当费用自负率在一定范围内变化时，局中人将交替选用分离策略与合并策略。     

求解广义纳什均衡问题的增量罚算法

研究每个局中人的决策集都有可能与竞争者的决策集有关的广义纳什均衡问题.给出了该广义纳什均衡问题罚函数形式的再定式.通过分析其KKT点的特点,进一步给出了求解广义纳什均衡问题的增量罚算法.     

一类博弈排序问题的纳什均衡存在性证明

研究机器带有激活费用的博弈排序问题. 机器集由两类组成: 一类是速度为1、 激活费用为B的k_1台同型机; 另一类是速度为a(>1)、激活费用为aB的k_2台同型机, 其中k_1与k_2是任意正整数. 工件作为``局中人", 其目的是极小化自身的费用, 工件的费用是由其所在机器的负载和其所承担的激活费用组成, 其中工件承担的激活费用与工件的加工时间成正比. 针对不同的情况, 设计不同的算法, 并证明各算法得到的排序都是纳什均衡.     

基于训练和过滤的期望均衡及其实现路径

期望均衡是博弈局中人或局外人对于博弈均衡点的一致期望,强调互利共赢,它要求博弈群体的每个成员对期望均衡点有一个共同的预期.显然,基于纳什均衡的帕累托优化组合策略是一个比纳什均衡更有效的期望均衡.要实现期望均衡,可采用局中人参与的训练与学习使得群体的预期一致,也可采用第三方过滤器来达到期望目标.在期望均衡的概率分布下,个体行为的偏离不能比均衡态取得更多收益.否则,训练就是无效的,第三方过滤器就是不公平的.     

基于Selectope解集和局中人最大满意度的合作对策解的研究

针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。     

决策支持下的不完全偏好信息多目标对策

针对多目标对策的不完全偏好信息,将理性策略概念和偏好规划理论引入到多目标对策研究中,把两人的多目标对策考虑为两个局中人同时面临的两个多目标决策问题,偏好信息用可行权重限定集合进行建模.多目标对策模型分为对策模型和决策模型两部分.在对策模型中,利用理性和偏好的共同知识,获得理性策略集.在决策模型中,局中人将策略选择作为使用私人偏好信息的多目标决策问题.最后,通过实例验算表明所提方法的有效性.     

考虑边流量有限的网络路径博弈问题研究

考虑每条边有流量约束的网络路径博弈问题, 根据收益函数单调递增的特点分析其内在零和性质, 并建模为存在公共边的路径博弈模型。在寻找均衡解的过程中, 首先考虑非合作的情形, 在局中人风险中性的假设下, 给出了求Nash均衡流量分配的标号法并证明该均衡分配的唯一性。接着进一步考虑局中人合作的可能性, 给出模型求得所有局中人的整体最大收益, 并基于纳什谈判模型给出目标函数为凸函数的数学模型确定唯一收益分配方案。事实上, 该方案是对剩余价值的平均分配。最后给出一个算例, 验证本文理论和方法的可行性。关键词:流量约束; 均衡流量; 网络路径博弈; 收益分配     

Optimal strategic reasoning with McNaughton functions

The aim of the paper is to explore strategic reasoning in strategic games of two players with an uncountably infinite space of strategies the payoff of which is given by McNaughton functions—functions on the unit interval which are piecewise linear with integer coefficients. McNaughton functions are of a special interest for approximate reasoning as they correspond to formulas of infinitely valued Lukasiewicz logic. The paper is focused on existence and structure of Nash equilibria and algorithms for their computation. Although the existence of mixed strategy equilibria follows from a general theorem (Glicksberg, 1952) [5], nothing is known about their structure neither the theorem provides any method for computing them. The central problem of the article is to characterize the class of strategic games with McNaughton payoffs which have a finitely supported Nash equilibrium. We give a sufficient condition for finite equilibria and we propose an algorithm for recovering the corresponding equilibrium strategies. Our result easily generalizes to n-player strategic games which don't need to be strictly competitive with a payoff functions represented by piecewise linear functions with real coefficients. Our conjecture is that every game with McNaughton payoff allows for finitely supported equilibrium strategies, however we leave proving/disproving of this conjecture for future investigations.     

Random attractor for stochastic second-order non-autonomous stochastic lattice equations with dispersive term

In this paper, we consider the asymptotic behaviour of solutions to second-order non-autonomous stochastic lattice equations with dispersive term and additive white noises in the space of infinite sequences. We first transfer the stochastic lattice equations into random lattice equations, and prove the existence and uniqueness of solutions that generate a random dynamical system. Second, we prove the existence of a tempered random absorbing set and a random attractor for the system. Finally, we establish the upper semi-continuity of the random attractors as the coefficient of the white noise term tends to zero.     

A random attractor for a stochastic second order lattice system with random coupled coefficients

In this paper, we mainly focus on the asymptotic behavior of solutions to the second-order stochastic lattice equations with random coupled coefficients and multiplicative white noises in weighted spaces of infinite sequences. We first transfer stochastic lattice equations into random lattice equations and prove the existence and uniqueness of solutions which generate a random dynamical system. Second we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Then we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero. Finally we present the corresponding results for the system with additive white noises.     

On the existence of Nash equilibria in large games

We study the existence of Nash equilibria in games with an infinite number of players. We show that there exists a Nash equilibrium in mixed strategies in all normal form games such that pure strategy sets are compact metric spaces and utility functions are continuous. The player set can be any nonempty set.     

关于无限对策Nash平衡点集的本质连通区

证明了任意纯策略集是紧度量空间和支付函数连续的n人无限非合作对策存在 Nash平衡点集的本质连通区．     

Unified approach to approximate solutions in games and multiobjective programming

Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infinite alternative set, or an infinite set of criteria by a finite subset without losing all approximate solutions of the problem under consideration.This work was done during the period when the second author was Visiting Professor of the Italian National Research Council at the Mathematical Department of the University of Pavia, Pavia, Italy.     

Random attractor of stochastic Zakharov lattice system

In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random  asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system.     

Size direction games over the real line. II

Variants of two basic infinite games of perfect information are studied. A notion of continuous strategy for the playerS (Size) is shown to be related to a notion of convergence norm for sequences of reals. With each such norm, a variant of each of the basic games is associated in which the size player has to see that each play obeys the norm. Restriction to choose only rational numbers is also imposed onS. Some games are completely solved, and in this caseS has a winning strategy iff his set includes a perfect subset, andD has a winning strategy iffS's set is at most denumerable. Some other games, in whichS has to choose only rationals and obey a norm, induce a hierarchy structure on the class of nowhere dense perfect sets, that is embedded cofinally in the lattice of infinite sequences of integers modulo finite differences.     

正则对策的N-M稳定集及其唯一存在定理

研究了有非对称性和负传递性偏好的无限策略对策,提出了N-M稳定集和正则对策的概念,其中N-M稳定集是将合作对策中由Von Neumann 和Morgenstern给出的相应概念引入到策略对策中的.所谓正则对策是指其Nash均衡集中每条链关于一致偏好总有上界的无限策略对策.证明了每个正则对策都有唯一N-M稳定集. 此结果及其应用例子说明正则对策N-M稳定集的概念对于策略对策的纯Nash均衡的精炼起着重要作用.