代理人在职消费对动态多任务激励契约的影响

将代理人的在职消费行为引入到动态多任务委托代理框架中,构造了代理人在职消费行为下的两阶段多任务模型,分析了代理人在职消费行为对动态多任务激励契约的影响.研究结果表明:一是任务为两阶段时,无论代理人有无在职消费行为,代理人的努力程度随着时间均呈上升趋势,这就表明当委托人在设计契约时,如果委托人期望代理人在第一阶段的努力水平不低于第二阶段的努力水平,就需要适当提高第一阶段的业绩薪酬系数;二是代理人在职消费自利行为并不一定会提高自身的努力程度,需要依据在职消费行为对绩效的影响情形来具体分析;三是在两阶段内,代理人存在在职消费时,委托人可适当降低业绩薪酬系数.     

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.     

Optimal derivatives design for mean–variance agents under adverse selection

We consider a problem of derivatives design under asymmetry of information: the principal sells a contingent claim to an agent, the type of whom he does not know. More precisely, the principal designs a contingent claim and prices it for each possible agent type, in such a way that each agent picks the contingent claim and pays the price that the principal designed for him. We assume that the preferences of the agent depend linearly on the parameters which determine the agent’s type; this model is rich enough to accommodate quadratic utilities. The problem then is reformulated as an optimization problem, where the optimization is performed within a class of convex functions. We prove an existence result for the provide explicit examples in the case when the agent is fully characterized by a single parameter     

Optimal compensation with adverse selection and dynamic actions

We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal. Research supported in part by NSF grants DMS 04-03575 and 06-31298. We would like to express our gratitude to participants of the following seminars and conferences for useful comments and suggestions: UCLA (Econ Theory), Caltech (Econ Theory), Columbia (Probability), Princeton (Fin. Engineering), U. Texas at Austin (Math Finance), Banff Workshop on Optim. Problems in Fin. Econ, Kyoto U. (Economics), UC Irvine (Probability), Cornell (Fin. Engineering), Bachelier Seminar. Moreover, we are very grateful to the anonymous referee for helpful suggestions. The remaining errors are the authors’ sole responsibility.     

Solving nonlinear principal-agent problems using bilevel programming

While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent’s participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent’s incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevel programming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort.     

Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information

Screening contracts (or ‘menu of contracts’) are frequently used for aligning the incentives in supply chains with private information. In this context, it is assumed that all supply chain parties are strictly (expected) profit-maximizing. However, previous empirical work shows that this is a critical assumption. In fact, it seems that inequity adverse subjects are willing to invest money for achieving higher relative payoffs. Interestingly, the classical approach to design incentive compatible mechanisms gives the agent cheap leeway to increase relative pecuniary payoffs and thereby achieving more equitable profit allocations, because the agent is left (almost) indifferent between two contract alternatives. In other words, we argue (and actually observe in laboratory experiments) that this classical approach of contract design allows the agent to achieve more equitable outcomes at low cost. Since the agent’s better relative performance solely stems from reducing the principal’s payoffs, we observe a substantial negative impact on the overall supply chain performance. The present work relaxes the assumption of the profit-maximizing buyer (agent) in a serial supply chain for a lot sizing framework with asymmetrically distributed holding cost information and deterministic end-customer demand. The study provides researchers and managers an approach on how to account for disadvantageous inequity aversion (ie, the agent suffers from profits being lower than the principals profits) by designing a contract that anticipates such behaviour while providing a solution method for the resulting non-linear mathematical program. We denote the resulting contract as ‘behavioural robust’, since it limits the inefficiency losses that result if agents exhibit disadvantageous inequity aversion instead of being strictly profit-maximizing. A numerical study compares the advantages of the ‘behavioural robust’ contract against the classical screening contract. The results highlight that supply chain performance losses can be substantially reduced under the behavioural robust contract.     

Contingent payment auction mechanism in multidimensional procurement auctions

This paper considers the auctioning of an indivisible project among several suppliers who hold private information about their own efficiency type. Both quality and price need to be determined. Different from scoring auctions, we present a new method, i.e., contingent payment auction mechanism (CPAM), which can effectively deal with the optimal procurement strategy in multidimensional procurement auctions. CPAM can implement the optimal mechanism for the buyer and is thus optimal among all possible procurement strategies. CPAM implies that the buyer should first design and announce a contingent payment function that specifies a payment for each possible quality level before the bidding begins. Compared to scoring auctions, CPAM has some advantages. It does not require a special form of scoring rule and can be generalized in a more broad auction formats. Furthermore, it can help us to solve the ex post moral hazard problem. We consider two kinds of CPAM. For the CPAM I is sensitive to different auction formats, we come up with CPAM II which can improve the performance of CPAM I. Broadly speaking, CPAM integrates the idea of dimension reduction from scoring auction into that of incentive contract design from contract theory to solve the problem of ex post moral hazard.     

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.     

A game-theoretic model for repeated assignment problem between two selfish agents

This paper addresses a distributed system where a manager needs to assign a piece of equipment repeatedly between two selfish agents. On each day, each agent may encounter a task—routine or valuable—and can request the use of the manager's equipment to perform the task. Because the equipment benefits a valuable task more than a routine task, the manager wants to assign the equipment to a valuable task whenever possible. The two selfish agents, however, are only concerned with their own reward and do not have incentive to report their task types truthfully. To improve the system's overall performance, we design a token system such that an agent needs to spend tokens from his token bank to bid for the equipment. The two selfish agents become two players in a two-person non-zero-sum game. We find the Nash equilibrium of this game, and use numerical examples to illustrate the benefit of the token system.     

Framing contingencies in contracts

This paper develops a contracting model in which the principal frames the contract when the agent is unaware of some contingencies, yet is aware that she may be unaware. We call the contract vague if the agent is still unaware of some contingencies after understanding the contract. We show that the optimal contract is vague if and only if the principal exploits the agent. Applying the model to an insurance problem, we show the insuree is free from exploitation if she slightly underestimates the unforeseen calamities. In a contracting problem, whenever the contractor is unaware of the force majeure event, she is exploited by the employer.     

基于解聘补偿的股权激励模型研究

传统的委托代理模型存在激励的短期性与道德风险的单边性两方面的问题．通过引入解聘补偿机制,建立并分析了信息完全对称和不完全对称两种情况下的股权激励模型,研究了委托人解聘倾向对股权激励合同设计的影响机制．研究结果表明：在初始合同中引入解聘补偿,不仅可以有效缓解委托人的道德风险,而且可以进一步提升代理人的工作努力程度．     

动态多任务双边道德风险契约研究

针对管理活动的动态性与多任务性的特点,将解聘补偿与解聘倾向引入动态多任务契约设计中,构建了基于解聘补偿的动态多任务双边道德风险契约。通过数理推导分析的方法给出了最优契约设计,声誉效应和棘轮效应的度量,探讨了解聘倾向对于契约设计的影响。结果表明解聘倾向的引入对于委托人的道德风险约束是有效的,但是对于代理人的道德风险约束则取决于声誉效应与棘轮效应的大小。在第2期契约中,解聘倾向对固定支付的影响取决于代理人保留收入与解聘补偿的差额。而第1期的契约设计要受到解聘补偿,声誉效应与棘轮效应三者的综合影响。任务关联性对契约设计影响以及相应的实证分析是未来的研究方向。     

声誉效应与经理报酬契约的关系研究

探讨了声誉对经理报酬契约的影响 .首先 ,分析了经理效用函数的组成 ,将声誉这个隐性激励约束因素引入经理的效用函数 .随后 ,建立了信息不对称下经理的报酬激励模型 .分析了声誉系数对契约中各要素的影响 ,说明了所有者可以利用经理的声誉效应来设计更加有利的报酬契约 .文章最后给出了主要结论 .     

The Value of Preference Information in Agency Relationships

Standard models of agency theory often assume that the principal has complete information about the preferences of the agent. This paper starts from the assumption of incomplete information on the agent&2018;s preferences and models a situation where the principal can obtain additional preference information before concluding a contract with the agent. We introduce the concept of a Value of Preference Information (VPI), which describes the benefits to the principal from obtaining such information. This information can be obtained either before or after the principal knows the precise structure of the decision problems which will be delegated to the agent. Analytic and simulation techniques are used to study factors influencing the VPI in these two situations.     

具有私人信息的道德风险的委托—代理人模型的合约分析

本文对存在的不对称信息的环境下的具有私人信息道德风险的委托—代理人模型的合约问题进行了详细的讨论,并得出一些有新意的结论.此讨论问题的方法很值得推荐和推广,特别是在最优激励合同中,比如投资激励,管理机制中的激励,销售激励,保险激励等合同的设计,都可以借鉴此方法来研究和分析.     

A principal–agent problem with heterogeneous demand distributions for a carbon capture and storage system

Mechanism design problems optimize contract offerings from a principal to different types of agents who have private information about their demands for a product or a service. We study the implications of uncertainty in agents’ demands on the principal’s contracts. Specifically, we consider the setting where agents’ demands follow heterogeneous distributions and the principal offers a menu of contracts stipulating quantities and transfer payments for each demand distribution. We present analytical solutions for the special case when there are two distributions each taking two discrete values, as well as a method for deriving analytical solutions from numerical solutions. We describe one application of the model in carbon capture and storage systems to demonstrate various types of optimal solutions and to obtain managerial insights.     

Reinsurance contract design when the insurer is ambiguity-averse

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.     

Designing sniping agents

Sniping agents are increasingly being deployed to assist bidders in acquiring items in online auctions. This paper reviews the extant auction literature and proposes an overarching sniping agent design framework that could potentially increase the commercial viability of snipping agents. For better alignment between the functions of sniping agents and the needs of human bidders, we review existing literature based on three fundamentals: (1) knowledge about human bidder behavior, (2) awareness of the product(s) desired by a bidder, and (3) an understanding of the research on bidding agents and auction design. The output of this review is the explicit consideration of iterative combinatorial auction agent design, fuzzy set representation of the bidder’s preferences and dynamic derivation of bidding strategies according to the progress of ongoing auctions.     

Platform exploitation in the sharing economy

We model a revenue sharing contract between a sharing economy platform and a freelance service provider, where the latter hides revenue from the former by canceling some assignments and performing them for cash (“platform exploitation”). The platform counters this via costly, imperfect audits with endogenous success probability, and a variable payment. We show that at equilibrium, all agent types except the highest, indulge in revenue falsification. This problem is exacerbated by the principal's ability to extract restitution from the agent.     

A dynamic principal-agent problem as a feedback Stackelberg differential game

We consider situations in which a principal tries to induce an agent to spend effort on accumulating a state variable that affects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg differential game in which the players use feedback strategies. Whereas in general Stackelberg differential games with feedback strategy spaces the leader’s optimization problem has non-standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. A linear-quadratic example is used to illustrate our approach.