指派问题的纳什均衡解

为弥补传统指派问题解不符合个体理性的不足,提出指派问题的纳什均衡解,并证明有限指派问题有且仅有纯纳什均衡解。相比传统的指派问题解,纯纳什均衡符合Pareto最优,是个体理性视角下的最优解。在此基础上,给出一个综合考虑个体理性与集体理性的求解方法。     

双人静态博弈纯战略纳什均衡存在性判别

本文给出了双人有限静态博弈纯战略纳什均衡存在性的一种判别方法。并且，在纳什均衡存在的条件下，本判别法将给出纳什均衡解及解的唯一性判别。     

基于随机反应均衡的供应链激励机制设计

随机反应均衡是在有限理性条件下对纳什均衡的拓展。本文将随机反应均衡引入到供应链激励机制设计的模型中，建立依据反应函数的概率选择分析框架，修正依赖于决策者完全理性的激励相容和参与约束。通过理论分析和数值算例研究发现，随着供应商理性程度的不同，最优机制设计的形式发生变化，且对供应链渠道绩效产生显著影响。零售商和供应链渠道的期望利润随着供应商理性程度的提高而增加，而供应商的期望利润在其理性程度极低或极高时均较少。     

基于差异化产品动态寡头博弈的系统动力学分析

以寡头企业具有有限理性和简单理性的产量调整行为和非线性成本函数为基础,论证了当横向产品差异度在一定范围内时,纳什均衡可作为稳定的动态均衡而实现.当超过一定范围时,利用数值模拟可观测到系统出现的周期性和混沌的复杂现象.在企业具有二次成本的假设条件下,研究了产品差异程度对纳什均衡稳定性的影响,得到了产品差异度越大,或市场竞争程度越低,系统的纳什均衡越不稳定的结论,表明了经济周期波动产生于非线性系统的内生性.与线性成本的对比说明,非线性成本缩小了纳什均衡的稳定域,增加了寡头市场的复杂性.研究也表明规模不经济的寡头厂商想通过增加产品差异度来减少竞争是有一定难度的.     

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.     

一种n人静态博弈纯策略纳什均衡存在性判别法

本首先给出了n人静态博弈纯策略纳什均衡存在的充要条件。然后给出n人静态博弈纯策略纳什均衡存在性的一种判别方法。最后在判别纯策略纳什均衡存在的条件下，给出判定该静态博弈存在多少纯策略纳什均衡以及哪些纯策略组合是纯策略纳什均衡(解)的方法。     

检测水平有限和外部损失分担下的供应链质量控制模型研究

在制造商生产水平和品牌商检测水平共同决定产品质量的供应链系统中,构建了基于品牌商检测水平有限和制造商分担外部损失比例的质量控制模型,得出了不同参数关系下的供应链质量控制博弈的纳什均衡解,刻画了纯战略和混合战略均衡的形成机制,分析了混合策略均衡解与品牌商检测水平和制造商分担外部损失比例这两个参数之间的互动协调策略,并找出了重复博弈下品牌商采取冷酷战略时最优检测概率的影响因素。     

棚户区改造的PPP模式研究:基于演化博弈视角

随着棚户区改造工作的大规模推进,传统棚改模式面临着融资困难等问题.在现有研究基础上,提出棚户区改造的PPP模式,该模式有助于解决传统模式的资金问题,提高棚户区改造的质量,同时在有限理性基础上构建以政府和企业为主体的演化博弈模型,分析在PPP模式下双方的稳定均衡策略.运用MATLAB仿真分析,通过改变参数模拟不同因素变化,探讨不同条件下的稳定演化均衡.根据稳定演化均衡结果提出改进棚户区改造PPP模式的对策建议.     

运输问题的合作对策求解方法

产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。     

我国民办高校可持续发展的数量分析

民办高校作为我国高等教育的一种新的办学模式，对于教育供给不足的我国，这种新的办学模式的出现，将给我国高等教育带来积极影响。然而，对于刚刚起步的民办高等教育，由于办学和管理经验不足，仍存在一些制约其持续发展的不利因素。据此，本运用数量分析方法来探讨民办高校可持续发展的对策。全分四部分，在第二部分探讨民办高校办学、学生进民办高校学习的优化目标模型分析，进而比较两优化解的差异及经济意义。在第三部分中，本运用均衡分析理论来论述不同素质学生的就业与民办高校科学管理的关系，并导出现行民办高校的宽出政策的危害性。最后，本围绕实现我国民办高校可持续发展问题提出四方面对策建议。     

Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

In this paper, we extend the notion of diagonally strictly concave functions and use it to provide a sufficient condition for uniqueness of Nash equilibrium in some concave games. We then provide an alternative proof of the existence and uniqueness of Nash equilibrium for a network resource allocation game arising from the so-called Kelly mechanism by verifying the new sufficient condition. We then establish that the equilibrium resulting from the differential pricing in the Kelly mechanism is related to a normalised Nash equilibrium of a game with coupled strategy space.     

COMPETITION AND COOPERATION IN A DYNAMICAL MODEL OF NATURAL RESOURCES

Abstract In this paper, we propose a model describing the commercial exploitation of a common renewable resource by a population of strategically interacting agents. Players can cooperate or compete; cooperators maximize the payoff of their group while defectors maximize their own profit. The partition of the players into two groups, defectors and cooperators, results from the players' choices, so it is not predetermined. This partition is decided as a Nash equilibrium of a static game. It is shown that different types of players can exist in an equilibrium; more precisely, depending on the parameter values such as resource stock, cost, and so on, there might be equilibria only with defectors, cooperators, or with a combination of cooperators and defectors. In any case the total harvest depends on the renewable resource stock, so it influences agents' positions. It is assumed that at each time period the agents harvest according to Nash equilibrium, which can be combined with a dynamic model describing the evolution of fish population. A complete analysis of the equilibria is presented and their stability is analysed. The effect of the different Nash equilibria on the stability of the fish stock, showing that full cooperation is the most stable case, is examined.     

基于MAS协作机制的动态计算资源调度模型

针对网格环境的自治性、动态性、分布性和异构性等特征.提出基于多智能体系统(Mutil Agent System,MAS)博弈协作的资源动态分配和任务调度模型,建立了能够反映供求关系的网格资源调度模型和任务求解算法,证明了资源分配博弈中Nash均衡点的存在性、唯一性和Nash均衡解,该方法能够利用消费者agent的学习和协商能力,考虑和引入消费者的心理行为,使得消费者的资源申请和任务调度具有较高的合理性和有效性.实验结果表明,资源调度算法不但可以有效减少不必要的延迟,而且在响应时间的平滑性、吞吐率及资源利用率方面比传统算法要好,从而使得整个资源的供需合理、负载均衡.     

Complex dynamics and multistability with increasing rationality in market games

In this work we study oligopoly models in which firms adopt decision mechanisms based on best response techniques with different rationality degrees. Firms are also assumed to face resource or financial constraints in adjusting their production levels, so that, from time to time, they can only increase or decrease their strategy by a bounded quantity. We consider different families of oligopolies of generic sizes, characterized by heterogeneous compositions with respect to the rationality degrees of firms. We analytically study the local stability of the equilibrium depending on the oligopoly size and composition and through numerical simulations we investigate the possible dynamics arising when trajectories do not converge toward the equilibrium. We show that in this case complex dynamics can arise, and this is due to both the loss of stability of the equilibrium and to the emergence of multiple attractors, with the stable steady state coexisting with a different, periodic or chaotic, attractor. In particular, we show that multistability phenomena occur when the overall degree of rationality of the oligopoly is increased. Finally, we investigate the effect of non-convergent dynamics on the realized profits.     

Game Theoretic Analysis of a Distribution System with Customer Market Search

Consider a distribution system with one supplier and two retailers. When a stockout occurs at one retailer customers may go to the other retailer. We study a single period model in which the supplier may have infinite or finite capacity. In the latter case, if the total quantity ordered (claimed) by the retailers exceeds the supplier’s capacity, an allocation policy is involved to assign the limited capacity to the retailers. We analyze the inventory control decisions for the retailers using a game theoretical approach. The necessary and sufficient conditions are derived for the existence of a unique Nash equilibrium. A computational procedure is also proposed to calculate the Nash equilibrium. In case the Nash equilibrium does not exist, we use the concept of Stackelberg game to develop optimal strategies for both the leader and the follower. The work was partially supported by the National Textile Center of the US Department of Commerce under Grant No. I01-S01. The second author is supported in part by NSF under DMI-0196084 and DMI-0200306.     

Asymptotic Analysis of Linear Feedback Nash Equilibria in Nonzero-Sum Linear-Quadratic Differential Games

In this paper, we discuss nonzero-sum linear-quadratic differential games. For this kind of games, the Nash equilibria for different kinds of information structures were first studied by Starr and Ho. Most of the literature on the topic of nonzero-sum linear-quadratic differential games is concerned with games of fixed, finite duration; i.e., games are studied over a finite time horizon t _f. In this paper, we study the behavior of feedback Nash equilibria for t _f.In the case of memoryless perfect-state information, we study the so-called feedback Nash equilibrium. Contrary to the open-loop case, we note that the coupled Riccati equations for the feedback Nash equilibrium are inherently nonlinear. Therefore, we limit the dynamic analysis to the scalar case. For the special case that all parameters are scalar, a detailed dynamical analysis is given for the quadratic system of coupled Riccati equations. We show that the asymptotic behavior of the solutions of the Riccati equations depends strongly on the specified terminal values. Finally, we show that, although the feedback Nash equilibrium over any fixed finite horizon is generically unique, there can exist several different feedback Nash equilibria in stationary strategies for the infinite-horizon problem, even when we restrict our attention to Nash equilibria that are stable in the dynamical sense.     

无限阶段网络博弈中合作解的策略稳定性

合作博弈的经典合作解不满足时间一致性, 并缺乏策略稳定性. 本文研究无限阶段网络博弈合作解的策略稳定性理论. 首先建立时间一致的分配补偿程序实现合作解的动态分配, 然后建立针对联盟的惩罚策略, 给出合作解能够被强Nash均衡策略支撑的充分性条件, 最后证明了博弈中的惩罚策略局势是强Nash均衡, 从而保证了合作解的策略稳定性. 作为应用, 考察了重复囚徒困境网络博弈中Shapley值的策略稳定性.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

On Cournot–Bertrand competition with differentiated products

In this paper, we present a game theoretic framework for Cournot–Bertrand competition based on a nonlinear price function. The competition is between two firms and is assumed to take place in terms of pricing decision and quantity produced. However, the proposed objective function has not been used in literature before, yet the throughput obtained in this paper generalizes some of the existing results in literature. The competitive interaction between firms is described and analyzed using best-reply reaction, proposed adaptive adjustment and bounded rationality approach. The condition of stability of Nash equilibrium (NE) is induced by these approaches. Interestingly, we prove that there exists exactly a unique NE. Furthermore, it is noticed that when firms adopt best-reply and the proposed adaptive adjustment, the firms’ strategic variables become asymptotically stable. On the contrary, when the bounded rationality is used both quantity and price behave chaotically due to bifurcation occurred.