碳排放税收政策下供应链网络成员企业行为研究

针对三种碳税决策框架:分权碳税框架、集权碳税框架——固定阀值、集权碳税框架——弹性阀值,分别分析三种碳排放税收政策决策框架下供应链网络中成员企业收益的变化以及各企业间的交互行为,给出了各成员企业的均衡条件,并将其转化为变分不等式问题,建立碳排放税收政策下供应链网络成员企业博弈模型,并提出基于欧拉算法的模型求解方法。最后结合算例分析碳排放税收政策下供应链网络成员企业关于生产决策、分销决策、碳排放量的反应,研究为达到预期的环境目标,政府相关部门如何调整单位碳排放税,同时,根据成员企业相关经济指标的均衡结果,政府相关部门又如何调整碳排放的环境目标。     

A dynamic analysis of corporate investments and emission tax policy in an oligopoly market with network externality

We investigate the product innovation, green R&D investments and the emission tax policy in an oligopoly market with network externality. It is shown that an appropriate tax policy should be deployed to effectively control pollution and motivate innovation. At the early stage of the market, the emission tax should gradually reduce to motivate firms to achieve optimal investments. Later at the mature stage, the emission tax policy should carefully consider both the market competition and green technology levels.     

Necessary optimality conditions for a special class of bilevel programming problems with unique lower level solution

We consider a bilevel programming problem in Banach spaces whose lower level solution is unique for any choice of the upper level variable. A condition is presented which ensures that the lower level solution mapping is directionally differentiable, and a formula is constructed which can be used to compute this directional derivative. Afterwards, we apply these results in order to obtain first-order necessary optimality conditions for the bilevel programming problem. It is shown that these optimality conditions imply that a certain mathematical program with complementarity constraints in Banach spaces has the optimal solution zero. We state the weak and strong stationarity conditions of this problem as well as corresponding constraint qualifications in order to derive applicable necessary optimality conditions for the original bilevel programming problem. Finally, we use the theory to state new necessary optimality conditions for certain classes of semidefinite bilevel programming problems and present an example in terms of bilevel optimal control.     

A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming

In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given.     

A robust approach for modeling limited observability in bilevel optimization

Many applications of bilevel optimization contain a leader facing a follower whose reaction deviates from the one expected by the leader due to some kind of bounded rationality. We consider bilinear bilevel problems with follower's response uncertainty due to limited observability regarding the leader's decision and exploit robust optimization to model the decision making of the follower. We show that the robust counterpart of the lower level allows to tackle the problem via the lower level's KKT conditions.     

Optimality Conditions for Multiobjective Optimization Problem Constrained by Parameterized Variational Inequalities

We study a multiobjective optimality problem constrained by parameterized variational inequalities. By separation theorem for convex sets, we translate the multiobjective optimality problem into single objective optimality problem, and obtain the first-order optimality conditions of this problem. Under the calmness conditions, an efficient upper estimate of coderivative for a composite set-valued mapping is derived. At last, we apply that result to the multiobjective bilevel programming problem and MPEC with Nash equilibrium constraints.     

A Bridge Between Bilevel Programs and Nash Games

We study connections between optimistic bilevel programming problems and generalized Nash equilibrium problems. We remark that, with respect to bilevel problems, we consider the general case in which the lower level program is not assumed to have a unique solution. Inspired by the optimal value approach, we propose a Nash game that, transforming the so-called implicit value function constraint into an explicitly defined constraint function, incorporates some taste of hierarchy and turns out to be related to the bilevel programming problem. We provide a complete theoretical analysis of the relationship between the vertical bilevel problem and our “uneven” horizontal model: in particular, we define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of our game. Furthermore, by referring to some applications in economics, we show that our “uneven” horizontal model, in some sense, lies between the vertical bilevel model and a “pure” horizontal game.     

The bilevel programming problem: reformulations, constraint qualifications and optimality conditions

We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially calm without any restrictive assumption. Finally, we consider the bilevel demand adjustment problem in transportation, and show how KKT type optimality conditions can be obtained under the partial calmness, using the differential calculus of Mordukhovich.     

带有限反馈下层的二层规划问题的部分合作模型

对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.     

Bilevel programming problems with simple convex lower level

This article is dedicated to the study of bilevel optimal control problems equipped with a fully convex lower level of special structure. In order to construct necessary optimality conditions, we consider a general bilevel programming problem in Banach spaces possessing operator constraints, which is a generalization of the original bilevel optimal control problem. We derive necessary optimality conditions for the latter problem using the lower level optimal value function, ideas from DC-programming and partial penalization. Afterwards, we apply our results to the original optimal control problem to obtain necessary optimality conditions of Pontryagin-type. Along the way, we derive a handy formula, which might be used to compute the subdifferential of the optimal value function which corresponds to the lower level parametric optimal control problem.     

An Objective Penalty Function of Bilevel Programming

Penalty methods are very efficient in finding an optimal solution to constrained optimization problems. In this paper, we present an objective penalty function with two penalty parameters for inequality constrained bilevel programming under the convexity assumption to the lower level problem. Under some conditions, an optimal solution to a bilevel programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the objective penalty function, an algorithm is developed to obtain an optimal solution to the original bilevel programming, with its convergence proved under some conditions.     

技术创新、溢出效应与最优环境政策组合

构建环境政策内生的三阶段博弈模型,分析存在技术溢出效应时,环境政策组合工具对企业绿色技术创新的影响。研究发现,排污税和研发补贴有利于企业进行绿色技术创新,两者组合可以实现社会福利最大化。社会最优排污税税率低于排污对社会的边际破坏程度,并随着均衡产量的增加而提高。在技术溢出效应较高时,政府采取排污税和补贴的组合工具,而当技术溢出效应较低时,政府采取排污税和研发税的组合工具。当排污税税率外生给定时,竞争创新情况下的政府补贴要高于协同创新情况下的政府补贴。政府应结合行业技术溢出特征,采取相应的税收与补贴结合的政策工具,并在知识产权保护的基础上,促进企业集群协同绿色技术创新。     

关于二层规划的逼近问题

下层问题以上层决策变量作为参数,而上层是以下层问题的最优值作为响应 的一类最优化问题——二层规划问题。我们给出了由一系列此类二层规划去逼近原二层规划的逼近法,得到了这种逼近的一些有趣的结果.     

一种双层规划的光滑化目标罚函数算法

论文研究了一种双层规划的光滑化目标罚函数算法,在一些条件下,证明了光滑化罚优化问题等价于原双层规划问题,而且,当下层规划问题是凸规划问题时, 给出了一个求解算法和收敛性证明.     

Optimality conditions for mixed discrete bilevel optimization problems

In this article, we consider bilevel optimization problems with discrete lower level and continuous upper level problems. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. In the case where the lower level is a parametric linear problem, the bilevel problem is transformed into a continuous one. After that, we are able to discuss local optimality conditions using tools of variational analysis for each of the different approaches. Finally, we consider a simple application of our results namely the bilevel programming problem with the minimum spanning tree problem in the lower level.     

On Bilevel Programs with a Convex Lower-Level Problem Violating Slater’s Constraint Qualification

This paper focuses on bilevel programs with a convex lower-level problem violating Slater’s constraint qualification. We relax the constrained domain of the lower-level problem. Then, an approximate solution of the original bilevel program can be obtained by solving this perturbed bilevel program. As the lower-level problem of the perturbed bilevel program satisfies Slater’s constraint qualification, it can be reformulated as a mathematical program with complementarity constraints which can be solved by standard algorithms. The lower convergence properties of the constraint set mapping and the solution set mapping of the lower-level problem of the perturbed bilevel program are expanded. We show that the solutions of a sequence of the perturbed bilevel programs are convergent to that of the original bilevel program under some appropriate conditions. And this convergence result is applied to simple trilevel programs.     

CVaR准则下的双层报童问题模型研究

本文以供应商为领导层,零售商为从属层。基于CVaR(Conditional Value-at- Risk)准则,建立了两个双层报童问题模型.对于零售商,在兼顾其利润收益的同时,使用了CVaR风险计量方法对其风险进行了有效监控.然后根据模型中下层规划的特点及已有结论将双层规划模型转换成单层规划进行求解,数值计算结果表明模型是有意义的.     

Weak and strong stationarity in generalized bilevel programming and bilevel optimal control

In this article, we consider a general bilevel programming problem in reflexive Banach spaces with a convex lower level problem. In order to derive necessary optimality conditions for the bilevel problem, it is transferred to a mathematical program with complementarity constraints (MPCC). We introduce a notion of weak stationarity and exploit the concept of strong stationarity for MPCCs in reflexive Banach spaces, recently developed by the second author, and we apply these concepts to the reformulated bilevel programming problem. Constraint qualifications are presented, which ensure that local optimal solutions satisfy the weak and strong stationarity conditions. Finally, we discuss a certain bilevel optimal control problem by means of the developed theory. Its weak and strong stationarity conditions of Pontryagin-type and some controllability assumptions ensuring strong stationarity of any local optimal solution are presented.     

Organizational strategy and tacit collusion in oligopoly with agency

We study a model that integrates organizational structure and agency withdynamic price competition in oligopoly. Workers in different levels of the organizational structure have asymmetric information and heterogeneous objectives; i.e., there are agency conflicts within the firm. The organizational strategy of the firm is to determinesequentially the decision power relating to price and non-price competition instruments at each level. We examine the equilibrium organizational and competitive strategy of firms in a duopoly, and characterize the extent of noncooperative tacit collusion (with respect to price and non-price competition) that is feasible. We identify two sets of sufficient conditions that guarantee, (i) the monopoly solution is sustainable at any discount factor (rate of impatience of the workers), or (ii) the monopoly solution is not sustainable for any level of the discount factor. Interestingly, tacit collusion may be feasible when either the agency problem is non-existentor very severe; i.e., firm profits in equilibrium may be non-monotone in the extent of the agency conflict. Our analysis indicates that intrafirm learning and agency will have a stronger impact on feasible tacit collusion in markets where non-price competition plays a strong role. Moreover, there is an intimate connection between the firm's organizational strategy and the extent of tacit collusion with the (industry) business cycle.     

Public Disclosure Programs vs. traditional approaches for environmental regulation: Green goodwill and the policies of the firm

A Public Disclosure Program (PDP) is compared to a traditional environmental regulation (exemplified by a tax/subsidy) in a simple dynamic framework. A PDP aims at revealing the environmental record of firms to the public. This information affects its image (goodwill or brand equity), and ultimately its profit. A firm polluting less than its prescribed target would win consumer’s sympathy and raise its goodwill, whereas it is the other way around when the firm exceeds its emissions quota. The evolution of this goodwill is assumed to depend also on green activities or advertising expenditures. Within this framework, we analyze how a PDP affects the firm’s optimal policies regarding emissions, pricing and advertising as compared to a traditional regulation. We show that advertising acts as a complementary device to pricing and that emissions are increasing in goodwill. The role of a standard or target level for emissions turns out to be totally different under both policy regimes. In the case of a tax/subsidy approach, this target level only acts as constant who increases or decreases profit by a fixed amount, but it does not affect the policy of the firm. On the contrary, if a PDP is implemented, the target value for emissions enters in an important way in the goodwill accumulation mechanism and determines how the firm reacts to the regulation and what is the time path for the economic and environmental variables. Moreover, this value is also crucial to determine the possibility that a PDP is profit improving. A policy implication of this fact is that regulators should be particularly careful in fixing the emission standard when a PDP is applied. The theoretical results are complemented with a numerical illustration.