模糊多目标半定规划的最优性条件

将模糊集理论应用到多目标半定规划中来,提出了有约束的模糊多目标半定规划模型,并首次给出了其最优有效解的定义.通过构造确定的隶属度函数,将以矩阵为决策变量的模糊多目标半定规划转化为一种目标函数的某些分量由约束函数决定的确定性多目标半定规划,并证明了前者最优有效解与后者有效解的一致性.在此基础之上,讨论了二者的最优性条件.     

多目标优化问题McRow最优解的刻画

基于多目标优化问题的McRow模型,该文确定了W-鲁棒有效解(也称为McRow最优解)与弱有效解、有效解以及真有效解的关系.首先, 针对确定多目标优化问题,研究了W-鲁棒有效解与各种精确解的关系.随后,针对随机多目标优化问题,引进McRow最优解的概念,给出了它与其余各种解的关系.算例表明,利用McRow模型所得到的解更具有鲁棒性.     

多目标规划ak—较多有效解类的若干性质

在（１）中,作者提出多目标规划的较多有效解和较多最优解概念,并研究了它们的基本性质,文（３）则讨论ｋ－较多最优解的若干性质。文（４）利用较多序类进一步引进多目标规划问题的ａｋ－较多有效解,并证明了这类解的最优性必要条件。本文再给出多目标规划问题的ａｋ－较多最优解的概念,并讨论了多目标规划ａｋ－较多有效解和ａｋ－较多最优解的若干重要性质。     

多目标规划αk-较多有效解类的若干性质

在［１］中,作者提出多目标规划的较多有效解和较多最优解概念,并研究了它们的基本性质．文［３］则讨论了ｋ－较多最优解的若干性质．文［４］利用较多序类进一步引进多目标规划问题的αｋ－较多有效解,并证明了这类解的最优性必要条件．本文再给出多目标规划问题的αｋ－较多最优解的概念,并讨论了多目标规划αｋ－较多有效解和αｋ－较多最优解的若干重要性质．     

多目标模糊系数规划

在单目标模糊系数规划的理论基础上，对多目标模糊系数规划进行讨论，在以目标间的协调程度尽可能大为最优性条件的要求下提出多目标模糊系数规划最优解的定义，并给出一种可行的求解方法。     

拟凸多目标优化问题近似解的最优性条件

研究了拟凸多目标优化问题近似弱有效解、近似有效解的最优性条件.首先,在已有拟凸函数次微分的基础上引进4种近似次微分的概念,并给出它们之间的关系.然后,将4种近似次微分的概念应用到拟凸多目标优化问题中,给出了拟凸多目标优化问题近似弱有效解和近似有效解的充分条件和必要条件,并给出实例加以说明.     

多目标规划的鞍点准则

本文给出多目标规划有效解适应鞍点准则的一个新的判别法 ,它不使用凸性的几何术语及凸分析中的概念。最后给出单目标规划的一个相应的判别法     

求多目标优化问题Pareto最优解集的方法

主要讨论了无约束多目标优化问题Pareto最优解集的求解方法,其中问题的目标函数是C1连续函数.给出了Pareto最优解集的一个充要条件,定义了α强有效解,并结合区间分析的方法,建立了求解无约束多目标优化问题Pareto最优解集的区间算法,理论分析和数值结果均表明该算法是可靠和有效的.     

多目标决策问题的广义折衷解研究

引进决策偏好参数，提出了多目标决策问题的广义折衷解概念，然后探讨了广义折衷解的性质，最后也给出其数学规划的求解方法。     

基于直觉模糊规划的多目标投资组合选择模型

将直觉模糊集合的概念引入投资组合模型中,并将多目标投资组合模型中的收益、方差和偏度三个目标模糊化,用隶属函数与非隶属函数作为新的目标函数.针对该模糊多目标投资组合模型,提出了一个动态遗传算法,算例给出了该模型的一个实例的最优解.     

On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.     

Multiobjective management of mining under water hazard by game theory

The management of an aquifer is studied under the assumption that the solution of the multiobjective programming model describing the management problem should satisfy a certain set of axioms. It is shown that a certain class of multiobjective problems may be solved by a game-theoretical concept leading to a single objective quasiconvex programming problem. The method is generalization of Nash's cooperative game theoretical model, and may lean on Zeuther's bargaining process. The methodology is applied to the Transdanubian Karstic region in Hungary where three objectives are present: mining costs, water supply and environmental protection. Results are compared with the solution previously obtained by compromise programming with an l₁-norm. It is found that results obtained by the two methods are comparable.     

Intergenerational risk sharing in closing pension funds

We model intergenerational risk sharing in closing funded pension plans. Specifically, we consider a setting in which in each period, the pension fund’s investment and indexation policy is the outcome of a bargaining process between representatives of the then living generations. Because some generations might be under- or overrepresented in the board, we use the asymmetric Nash bargaining solution to allow for differences in bargaining powers. In a numerical study, we compare the welfare that the generations derive from the outcome of this repeated bargaining to the welfare that they would derive if a social planner’s optimal policy would instead be implemented. We find that as compared to the social optimum, older generations benefit substantially from the repeated bargaining, even if all generations are equally well-represented in the board. If older generations are relatively over-represented, as is sometimes argued, these effects are attenuated.     

基于合作博弈纳什议价的几种网络定价结构模型比较

本文基于目前的网络资费模式,提炼出三种网络定价结构模型,研究本地网络服务提供商(ISP)及用户之间的利润分配.首先,利用一个简化的网络业务质量(Qos)保证模型构造目标函数,说明合作博弈得到的解比非合作博弈情形下更优,合作博弈时得到纳什议价解与双方的相对议价权力有关.然后,从社会结构理论角度,说明议价权力取决于网络结构类型以及局中人在结构中所处的位置.相对议价权力大,获益较多;相对议价权力小,获益较少.最后,通过实例分析得到三种网络定价结构模型下的纳什议价解.结果表明,本地网络服务提供商的合并、收购、互联有利于提高其相对议价权力,从而获益增加.     

A characterization of a limit solution for finite horizon bargaining problems

We investigate a two-person random proposer bargaining game with a deadline. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcomes as the number of bargaining periods goes to infinity while the deadline is kept fixed. This limit is close to the discrete Raiffa solution when the time horizon is very short. If the deadline goes to infinity the limit outcome converges to the time preference Nash solution. Regarding this limit as a bargaining solution under deadline, we provide an axiomatic characterization.     

NEGOTIATING OVER EXTERNALITIES

We present a simple model in which two perfectly informed, risk neutral agents will not negotiate an efficient agreement to lessen the effects of an externality and for which the outcome of negotiation depends on the legal assignment of property rights. The model permits agents to pre-commit themselves to refuse to negotiate particular agenda issues. The result is obtained because we prove that one player is always made strictly worse off from the addition of side-payments to a bargaining game. Along the way, we devise a supporting hyperplane for the n-person Nash bargaining game solution. We also display a simple game which establishes that our main result holds true—for at least some games—for an array of alternative bargaining game solutions such as that of Raiffa, Kalai, and Smorodinski.     

A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes.     

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。     

Solutions for some bargaining games under the Harsanyi-Selten solution theory,part I: Theoretical preliminaries

Part I of this paper discusses the problem of how to model bargaining behavior, and outlines a few basic ideas of the Harsanyi-Selten solution theory. In particular, we discuss removal of imperfect equilibrium points from the game by using the uniformly perturbed game form. We also describe definition of the solution in terms of payoff-dominance and risk-dominance relations, and in terms of the net strategic distances, between the primitive equilibrium points. Part II of the paper will discuss the actual solutions our theory provides for some important classes of bargaining games.     

On optimal reinsurance treaties in cooperative game under heterogeneous beliefs

In this paper, we study the optimal reinsurance policies as the result of a two-person cooperative game. We assume that both the insurer and the reinsurer are risk averse and expected-utility maximizers. In addition, we assume that they “agree to disagree” on the distribution of the underlying losses in the contract negotiation.In our analysis, we consider two scenarios. In the first one, the reinsurance premium is fully negotiable, whereas in the second one, the premium is determined by the reinsurer using the expected value premium principle. For both scenarios, we first derive the set of Pareto-optimal reinsurance contracts and then identify the reinsurance contract corresponding to the Nash bargaining solution as well as that corresponding to the Kalai–Smorodinsky bargaining solution.