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。     

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。     

无界域上非凸二次规划存在最优解的充分必要条件及判别方法

本给出了无界域上不定二次规划存在最优解的充分必要条件及判别方法,而且还给出通过解一系统线性规划来判别是否存在最优解的方法。     

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。     

求解线性矩阵方程的初等变换法

[1]给出了线性矩阵方程AXB=C有解的简单判别法则，本则应用初等变换，给出矩阵方程     

包络排除方法及奇解排除定理

讨论包络和奇解的判断问题,通过分析c-判别曲线上切线斜率的存在性,明确p-判别曲线中p的含义,得出通解曲线族中的曲线只有在c-判别曲线上每一点处存在切线斜率时,c-判别曲线才有可能是包络,否则c-判别曲线必定不是包络,另外在求奇解时,p-判别曲线中的p必须等于p-判别曲线的斜率,否则p-判别曲线必定不是奇解.     

线性规划多重最优解判别准则刍议

本构造了一些线性规划问题来探讨多重最优解的判别准则，补充了现行献中关于多重最优解判别准则描述的不足，并指出多重最优解判别准则在出现退化解时可能失效的例外情况。     

一类贝叶斯判别问题的渐近解

本文给出了母体具有有界的高维密度函数且密度函数未知的贝叶斯判别问题的渐近解,指出了渐近解平均风险的收敛性。     

多重纳什均衡解的粒子群优化算法

提出了一种求解双矩阵对策多重纳什均衡解的粒子群优化算法。该算法通过随机初始点以及迭代粒子的归一化,保证粒子群始终保持在对策的可行策略空间内,避免了在随机搜索中产生无效的粒子,提高了粒子群优化算法求解纳什均衡解的计算性能。最后给出了几个数值例子,说明了粒子群优化算法的高效性。     

两阶段主从博弈均衡解的存在性

首先给出带参数的纳什均衡问题Γ(x),在此基础上给出了具有带参数的纳什均衡约束的两阶段主从博弈问题G.可以证明带参数的纳什均衡点是存在的,即无论领导者选择何种策略,跟随者的最佳回应集都是非空的.最后推出了关于两阶段主从博弈均衡点的存在性定理.     

Computing equilibria of Cournot oligopoly models with mixed-integer quantities

We consider Cournot oligopoly models in which some variables represent indivisible quantities. These models can be addressed by computing equilibria of Nash equilibrium problems in which the players solve mixed-integer nonlinear problems. In the literature there are no methods to compute equilibria of this type of Nash games. We propose a Jacobi-type method for computing solutions of Nash equilibrium problems with mixed-integer variables. This algorithm is a generalization of a recently proposed method for the solution of discrete so-called “2-groups partitionable” Nash equilibrium problems. We prove that our algorithm converges in a finite number of iterations to approximate equilibria under reasonable conditions. Moreover, we give conditions for the existence of approximate equilibria. Finally, we give numerical results to show the effectiveness of the proposed method.     

Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality

We define the concept of reproducible map and show that, whenever the constraint map defining the quasivariational inequality (QVI) is reproducible then one can characterize the whole solution set of the QVI as a union of solution sets of some variational inequalities (VI). By exploiting this property, we give sufficient conditions to compute any solution of a generalized Nash equilibrium problem (GNEP) by solving a suitable VI. Finally, we define the class of pseudo-Nash equilibrium problems, which are (not necessarily convex) GNEPs whose solutions can be computed by solving suitable Nash equilibrium problems.     

基于模糊数的政府与绿色制造商博弈分析

近年来环境问题已经成为人们迫切需要解决的重要问题,促使制造商采取绿色制造模式也是各国政府正在面临的一大难题。因此文章结合三角模糊数与博弈理论建立了政府与绿色制造商的模糊博弈模型,将博弈结果分为纯策略和混合策略两类,并讨论了各种情形下政府与绿色制造商的不同策略以及影响因素,分析了最优博弈结果以及相应的管理策略,为绿色制造模式的顺利实施提供了相关建议。研究结果表明,政府的补贴和惩罚等策略在绿色制造模式的采取方面起着举足轻重的作用。最后利用三角结构元法对算例分纯策略和混合策略两种情况进行分析求解,从而验证了结论的正确性和可行性。     

Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets

Consider the N-person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization policy. In this paper, we focus on the robust Nash equilibrium problem in which each player’s cost function is quadratic, and the uncertainty sets for the opponents’ strategies and the cost matrices are represented by means of Euclidean and Frobenius norms, respectively. Then, we show that the robust Nash equilibrium problem can be reformulated as a semidefinite complementarity problem (SDCP), by utilizing the semidefinite programming (SDP) reformulation technique in robust optimization. We also give some numerical example to illustrate the behavior of robust Nash equilibria.     

Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints

The equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalization of Nash equilibrium problem (NEP) and the mathematical program with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a special class of EPECs where a common parametric P-matrix linear complementarity system is contained in all players?? strategy sets. After reformulating the EPEC as an equivalent nonsmooth NEP, we use a smoothing method to construct a sequence of smoothed NEPs that approximate the original problem. We consider two solution concepts, global Nash equilibrium and stationary Nash equilibrium, and establish some results about the convergence of approximate Nash equilibria. Moreover we show some illustrative numerical examples.     

Partial penalization for the solution of generalized Nash equilibrium problems

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.     

A two-person non-zero-sum game model of the world oil market

The world oil market is modelled as a two-person non-zero-sum game in normal form with each player having a continuum of strategies. The two players are the oil importing nations (OPIC) and the oil exporting nations (OPEC). The game is solved in the noncooperative sense using the equilibrium point solution concept due to Nash. The Nash equilibrium point solution yields an analytic expression for the optimal price per barrel of oil for OPEC and the optimal level of imports of oil for OPIC assuming noncooperation between the players. The cooperative solution to the game is also investigated using the von Neumann-Morgenstern negotiation set solution and Nash's bargaining point solution. Again, we give analytic expressions for the optimal price of a barrel of oil and the optimal level of imports of oil assuming that the players cooperate (negotiate, bargain, etc., for a binding agreement) in arriving at a solution.     

A note on correlated equilibrium

The set of correlated equilibria for a bimatrix game is a closed, bounded, convex set containing the set of Nash equilibria. We show that every extreme point of a maximal Nash set is an extreme point of the above convex set. We also give an example to show that this result is not true in the payoff space, i.e. there are games where no Nash equilibrium payoff is an extreme point of the set of correlated equilibrium payoffs.