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将求解一般0-1策略对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程组的问题.作为一种特殊而重要的情形,利用Pascal矩阵,Newton矩阵(对角元素为Newton二项式系数的对角矩阵)和Pascal-Newton矩阵(Pascal矩阵和Newton矩阵的逆阵的乘积)将求解对称0-1对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程的问题,并给出第二问题的反问题(由完全混合Nash均衡求解对称0-1对策族)的求解方法.同时,给出了一些算例来说明对应问题的算法. 相似文献
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本文介绍一类新的均衡问题--带有三元函数的广义半均衡问题.借助于辅助原理法提出了求解此类问题的一个三步预测-校正迭代法,并分析了算法的收敛性. 相似文献
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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. 相似文献
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Nash均衡点是非合作对策分析中的一个重要概念,本文基于冲突分析理论中的一些概念,提出一个考虑局中人二步行为的Nash均衡概念.并使用F-H稳定性分析方法求解这扩展的Nash平衡点,最后,基于这二步Nash均衡的概念对囚犯难题进行实证分析,并利用此概念解决了"囚犯难题"的悖论. 相似文献
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《数学物理学报(A辑)》2015,(4)
利用广义Wiener-Hopf方程技巧构造了求解广义混合均衡问题、无限个非扩张映射的不动点问题及变分不等式问题的公共元的迭代算法,并在Hilbert空间中获得了两个强收敛定理.最后利用这些新算法研究了几类优化问题.以上方法和结果不同于前人并且推广了Shi和Noor的结果. 相似文献
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运用广义最大元方法在非传递性偏好下给出了博弈均衡的存在性定理,推广了一些经典的博弈均衡存在性定理.在文中介绍策略式博弈的Nash均衡具有宽泛的条件,在微观经济理论中有广泛的应用. 相似文献
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本文研究了一个求解广义圆锥互补问题的无导数光滑算法.利用光滑函数将广义圆锥互补问题等价转化成一个光滑方程组,然后再利用牛顿法求解此方程组.该算法采用了一种新的非单调无导数线搜索技术,并且在适当条件下具有全局和局部二次收敛性质.数值实验结果表明算法是非常有效的. 相似文献
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Masao Fukushima 《Computational Management Science》2011,8(3):201-218
The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem, in which each
player’s strategy set may depend on the rival players’ strategies. The GNEP has recently drawn much attention because of its
capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international
pollution control. However, a GNEP usually has multiple or even infinitely many solutions, and it is not a trivial matter
to choose a meaningful solution from those equilibria. The purpose of this paper is two-fold. First we present an incremental
penalty method for the broad class of GNEPs and show that it can find a GNE under suitable conditions. Next, we formally define
the restricted GNE for the GNEPs with shared constraints and propose a controlled penalty method, which includes the incremental
penalty method as a subprocedure, to compute a restricted GNE. Numerical examples are provided to illustrate the proposed
approach. 相似文献
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The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP),in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications.However,the convergent solution algorithms are extremely scare in the literature.In this paper,we present an incremental penalty method for the GNEP,and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs.We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach. 相似文献
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This paper deals with the generalized Nash equilibrium problem (GNEP), i.e. a noncooperative game in which the strategy set
of each player, as well as his payoff function, depends on the strategies of all players. We consider an equivalent optimization
reformulation of GNEP using a regularized Nikaido–Isoda function so that solutions of GNEP coincide with global minima of
the optimization problem. We then propose a derivative-free descent type method with inexact line search to solve the equivalent
optimization problem and we prove that our algorithm is globally convergent. The convergence analysis is not based on conditions
guaranteeing that every stationary point of the optimization problem is a solution of GNEP. Finally, we present the performance
of our algorithm on some examples. 相似文献
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In this paper we reformulate the generalized Nash equilibrium problem (GNEP) as a nonsmooth Nash equilibrium problem by means
of a partial penalization of the difficult coupling constraints. We then propose a suitable method for the solution of the
penalized problem and we study classes of GNEPs for which the penalty approach is guaranteed to converge to a solution. In
particular, we are able to prove convergence for an interesting class of GNEPs for which convergence results were previously
unknown. 相似文献
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The generalized Nash equilibrium problem (GNEP) is a noncooperative game in which the strategy set of each player, as well as his payoff function, depend on the rival players strategies. As a generalization of the standard Nash equilibrium problem (NEP), the GNEP has recently drawn much attention due to its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. In this paper, we propose an improved two-step (a prediction step and a correction step) method for solving the quasi-variational inequality (QVI) formulation of the GNEP. Per iteration, we first do a projection onto the feasible set defined by the current iterate (prediction) to get a trial point; then, we perform another projection step (correction) to obtain the new iterate. Under certain assumptions, we prove the global convergence of the new algorithm. We also present some numerical results to illustrate the ability of our method, which indicate that our method outperforms the most recent projection-like methods of Zhang et al. (2010). 相似文献
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' 1 IntroductionWe collsider the fOllowi11g bilevel programndng problen1:max f(x, y),(BP) s.t.x E X = {z E RnIAx = b,x 2 0}, (1)y e Y(x).whereY(x) = {argmaxdTyIDx Gy 5 g, y 2 0}, (2)and b E R", d, y E Rr, g E Rs, A, D.and G are m x n1 s x n aild 8 x r matrices respectively. If itis not very difficult to eva1uate f(and/or Vf) at all iteration points, there are many algorithmeavailable fOr solving problem (BP) (see [1,2,3etc1). However, in some problems (see [4]), f(x, y)is too com… 相似文献
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Minglu Ye 《Optimization》2017,66(7):1119-1134
The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method. 相似文献
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H. Bustince A. Jurio A. Pradera R. Mesiar G. Beliakov 《European Journal of Operational Research》2013
In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines. 相似文献
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We consider an optimization reformulation approach for the generalized Nash equilibrium problem (GNEP) that uses the regularized
gap function of a quasi-variational inequality (QVI). The regularized gap function for QVI is in general not differentiable,
but only directionally differentiable. Moreover, a simple condition has yet to be established, under which any stationary
point of the regularized gap function solves the QVI. We tackle these issues for the GNEP in which the shared constraints
are given by linear equalities, while the individual constraints are given by convex inequalities. First, we formulate the
minimization problem involving the regularized gap function and show the equivalence to GNEP. Next, we establish the differentiability
of the regularized gap function and show that any stationary point of the minimization problem solves the original GNEP under
some suitable assumptions. Then, by using a barrier technique, we propose an algorithm that sequentially solves minimization
problems obtained from GNEPs with the shared equality constraints only. Further, we discuss the case of shared inequality
constraints and present an algorithm that utilizes the transformation of the inequality constraints to equality constraints
by means of slack variables. We present some results of numerical experiments to illustrate the proposed approach. 相似文献