On coordination of supply chain based on information asymmetry of effort level and fuzzy market environment

The agent’s private information contributes greatly to a person to make principal decision in the supply of a chain coordination. Therefore, it is a great issue for him to design an effective incentive mechanism in order to get the true information from the agent in his principle making. Assuming that the demand depend upon an agent’s effort level and the fuzzy market condition, the author in this paper researches and analyzes the principle-agent problem under fuzzy information asymmetry condition by using the theory of principal-agent as well as incentive mechanism.     

股权激励下的高管冒险决策与最优或有薪酬

股权类薪酬可导致高管冒险决策,而“内部债”是解决这个问题的可行方案。或有薪酬作为一种新型的“内部债”模式得到了实务界的重视,但如何设计或有薪酬以缓解股权激励下的高管冒险决策尚无理论研究。本文利用动态规划方法,得到高管薪酬价值及企业证券价值的显式解;构建委托代理模型,给出薪酬合同激励相容的一个充分条件;并给出了最优合同的数值结果及定量分析。分析表明:与单纯的股权薪酬相比,或有薪酬有效缓解了高管的冒险决策,促使其顾及社会总福利、注重企业长期发展。     

Dominant strategy mechanisms for contract auctions with risk aversion and moral hazard

Within the class dominant strategy incentive compatible mechanisms, we show that there exists an optimal contracting mechanism for the principal for a version of the incomplete information principal-agent problem in which several agents compete for a contract and the principal selects an agent via a contract auction. In our auction model, we assume that the principal and the agents are risk averse, and we allow for uncountably many agent types. We also assume that the principal's probability measure over type profiles in such that correlation between agent's types is possible. Thus, we do not require that agents' types be independently distributed. Finally, we impose limited liability constraints upon the set of contracts. Due to the nature of the individual rationality and incentive compatibility constraints, the existence problem is nonstandard and novel existence arguments are required. We prove existence using a measurable selection result and a new notion of compactness called K-compactness.     

A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems

This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information, in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as a fuzzy variable. What’s more, a bilevel fuzzy optimal nonlinear taxation model is developed with the purpose of maximizing the expected social welfare and the monopolist’s expected welfare under the incentive feasible mechanism. The equivalent model for the bilevel fuzzy optimal nonlinear taxation model is presented and Pontryagin maximum principle is adopted to obtain the necessary conditions of the solutions for the fuzzy optimal nonlinear taxation problems. Finally, one numerical example is given to illustrate the effectiveness of the proposed model, the results demonstrate that the consumer’s purchased quantity not only relates with the consumer’s taste, but also depends on the structure of the social welfare.     

Optimal incentive contracts under relative income concerns

We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral biases: envy, jealousy, or admiration toward the other coworkers’ compensation. We assume workers care about their relative position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303–328, 1987). We model team production by agents in which each agent’s effort generates an observable signal and depends on efforts of other agents. One of the important findings is that an agent’s optimal effort is negatively impacted by the behavioral biases in other agents’ judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica 69(1):1–35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits high pay-for-performance sensitivity.     

基于委托—代理下的模糊报童问题

在委托-代理关系中.代理人的私人信息对委托人的决策会产生重要影响.因此,为了获取代理人的真实信息.设计一个有效的激励机制是委托人的核心问题.本文基于需求依赖于代理人的努力水平和模糊市场条件的假设,利用委托一代理相关理论,探讨了模糊报童问题的激励机制问题.首先讨论了委托人最优产量的确定问题.然后分别给出了可观测和不可观测两种努力水平下的最优激励机制,最后分析了模糊市场条件对委托一代理双方利益的影响.     

带有解聘补偿机制的过度自信高管动态激励契约设计研究

考虑具有双边道德风险的委托代理问题,将解聘补偿和过度自信同时引入公司高管的激励契约,构建带有解聘补偿机制的过度自信高管动态激励模型,研究委托人解聘倾向对过度自信高管激励合同设计的影响。结果表明:委托人解聘倾向与高管的过度自信水平呈U型关系,高管代理人努力水平与高管的过度自信水平呈倒U型关系,适度的自信水平能够降低委托人的解聘倾向以及提高高管的努力水平;在引入解聘机制的情境下,解聘补偿能够有效抑制委托人的道德风险,降低委托人的解聘倾向,增加高管两期的努力水平;随着聘期的增加,高管第二期的努力水平低于第一期,委托人第二期的解聘倾向高于第一期;两个合同期内的补偿机制相互影响,表现在第二期的解聘补偿提高了委托人第一期的解聘倾向,导致高管第一期努力水平的下降,而第一期的解聘补偿提高了高管在第二期继续留任的可能性,从而增加了高管和委托人在第二期的期望收益。研究结论对我国企业高管薪酬改革以及长期激励合同设计具有一定的理论参考价值。     

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.     

The principal-agent problem with adaptive players

In this study we show predictions made by the standard principal-agent theory may not hold when knowlege assumptions are relaxed. Conventional principal-agent models assume players are completely rational: they know their own and other player's utilities and probabilities of all states of nature. In reality, players must make decisions without such knowledge.We define a simple version of the principal-agent game and examine it using object-oriented computer simulation. Player learning is modeled with a statistical learning model. Our results show that even this simple game combined with standard learning assumptions results in complex behavior. Expectations of both the principal and the agents are crucial in determining the system outcomes. Expectations and lack of prior knowledge make it possible for the principal to converge on suboptimal behavior or not converge on a consistent behavior at all. The same attributes in the agents make it possible for the principal to drive expectations down and thus get higher effort for lower reward.This study contributes a more robust understanding of the principal-agent model and its application to incentive design.     

An inexact-restoration method for nonlinear bilevel programming problems

We present a new algorithm for solving bilevel programming problems without reformulating them as single-level nonlinear programming problems. This strategy allows one to take profit of the structure of the lower level optimization problems without using non-differentiable methods. The algorithm is based on the inexact-restoration technique. Under some assumptions on the problem we prove global convergence to feasible points that satisfy the approximate gradient projection (AGP) optimality condition. Computational experiments are presented that encourage the use of this method for general bilevel problems. This work was supported by PRONEX-Optimization (PRONEX—CNPq/FAPERJ E-26/171.164/2003—APQ1), FAPESP (Grants 06/53768-0 and 05-56773-1) and CNPq.     

Strong-Weak Nonlinear Bilevel Problems: Existence of Solutions in a Sequential Setting

The paper deals with a strong-weak nonlinear bilevel problem which generalizes the well-known weak and strong ones. In general, the study of the existence of solutions to such a problem is a difficult task. So that, for a strong-weak nonlinear bilevel problem, we first give a regularization based on the use of strict ??-solutions of the lower level problem. Then, via this regularization and under sufficient conditions, we show that the problem admits at least one solution. The obtained result is an extension and an improvement of some recent results appeared recently in the literature for both weak nonlinear bilevel programming problems and linear finite dimensional case.     

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.     

Test problem construction for linear bilevel programming problems

A method of constructing test problems for linear bilevel programming problems is presented. The method selects a vertex of the feasible region, far away from the solution of the relaxed linear programming problem, as the global solution of the bilevel problem. A predetermined number of constraints are systematically selected to be assigned to the lower problem. The proposed method requires only local vertex search and solutions to linear programs.     

Analysis of various optimal contracts in the problem of stimulation of agents by a principal in a model with two agents

This work is devoted to one section of a game theory popular in recent years, the theory of contracts and the problem of an agent and a principal. A principal tries to stimulate agents into making a number of contracts with clients using his resources in order to maximize his profits as a result. At the same time, the principal has limited information about the agents. He knows only the results he has obtained; he does not know their type or the efforts made. The strategy of the principal is an incentive scheme that shows the agent’s reward depending on his results. In turn, the agents try to maximize their benefits while having the right to turn down a contract. We do not consider models with random events, and we restrict ourselves to the deterministic case. The model thus does not fall under the heading of a moral hazard but is related to a situation of unfavorable selection.     

The influence of face-to-face communication: a principal-agent experiment

The principal-agent problem is an interesting problem involved in many everyday relationships, such as the one between company owners and their delegates. Our experiment simulates such a relationship, whereby the task of participating pairs is to negotiate labor contracts. Our aim is to find the effects of face-to-face communication and negotiation on contract framing. We argue that including pre-play communication into the principal-agent problem leads to a significant improvement of agent’s effort and results in changes of the compensation scheme. We show that incentives are not the only possibility to induce high effort. We use content analysis of the video-taped negotiations to find some characteristics of the communication process.     

An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems

This paper considers a class of bilevel linear programming problems in which the coefficients of both objective functions are fuzzy random variables. The main idea of this paper is to introduce the Pareto optimal solution in a multi-objective bilevel programming problem as a solution for a fuzzy random bilevel programming problem. To this end, a stochastic interval bilevel linear programming problem is first introduced in terms of α-cuts of fuzzy random variables. On the basis of an order relation of interval numbers and the expectation optimization model, the stochastic interval bilevel linear programming problem can be transformed into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In order to compare different optimal solutions depending on different cuts, two criterions are given to provide the preferable optimal solutions for the upper and lower level decision makers respectively. Finally, a production planning problem is given to demonstrate the feasibility of the proposed approach.     

A dual-relax penalty function approach for solving nonlinear bilevel programming with linear lower level problem

The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.     

A penalty function method for solving inverse optimal value problem

In order to consider the inverse optimal value problem under more general conditions, we transform the inverse optimal value problem into a corresponding nonlinear bilevel programming problem equivalently. Using the Kuhn–Tucker optimality condition of the lower level problem, we transform the nonlinear bilevel programming into a normal nonlinear programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Then we give via an exact penalty method an existence theorem of solutions and propose an algorithm for the inverse optimal value problem, also analysis the convergence of the proposed algorithm. The numerical result shows that the algorithm can solve a wider class of inverse optimal value problem.     

求解弱线性双层规划问题的一种全局优化方法

双层规划在经济、交通、生态、工程等领域有着广泛而重要的应用.目前对双层规划的研究主要是基于强双层规划和弱双层规划.然而,针对弱双层规划的求解方法却鲜有研究.研究求解弱线性双层规划问题的一种全局优化方法,首先给出弱线性双层规划问题与其松弛问题在最优解上的关系,然后利用线性规划的对偶理论和罚函数方法,讨论该松弛问题和它的罚问题之间的关系.进一步设计了一种求解弱线性双层规划问题的全局优化方法,该方法的优势在于它仅仅需要求解若干个线性规划问题就可以获得原问题的全局最优解.最后,用一个简单算例说明了所提出的方法是可行的.     

Is bilevel programming a special case of a mathematical program with complementarity constraints?

Bilevel programming problems are often reformulated using the Karush–Kuhn–Tucker conditions for the lower level problem resulting in a mathematical program with complementarity constraints(MPCC). Clearly, both problems are closely related. But the answer to the question posed is “No” even in the case when the lower level programming problem is a parametric convex optimization problem. This is not obvious and concerns local optimal solutions. We show that global optimal solutions of the MPCC correspond to global optimal solutions of the bilevel problem provided the lower-level problem satisfies the Slater’s constraint qualification. We also show by examples that this correspondence can fail if the Slater’s constraint qualification fails to hold at lower-level. When we consider the local solutions, the relationship between the bilevel problem and its corresponding MPCC is more complicated. We also demonstrate the issues relating to a local minimum through examples.