How Incentives Increase Inequality

Abstract. We determine the optimal level of bonuses in the case of Co‐production between an agent and multiusers. There is Co‐production when the outcome is the result of both the agent's effort and the user's effort and type. Paying bonuses to the agent encourages him to vary his effort according to the user he meets. This variety in the agent's effort results in an increase in inequality. Hence, the optimal level of bonuses is muted when the principal cares about equality among users. This is typically the case in education or health.     

A Model of Delegated Project Choice

We present a model in which a principal delegates the choice of project to an agent with different preferences. The principal determines the set of projects from which the agent may choose. The principal can verify the characteristics of the project chosen by the agent, but does not know which other projects were available to the agent. We consider situations where the collection of available projects is exogenous to the agent but uncertain, where the agent must invest effort to discover a project, where the principal can pay the agent to choose a desirable project, and where the principal can adopt more complex schemes than simple permission sets.     

Procurement Contracts in the Presence of Endogenous Disruption Risk

We consider a manufacturer facing an unreliable supplier with high or low type on initial reliability. The private reliability can be enhanced through process improvement initiated by either manufacturer (manufacturer‐initiated improvement, MI) or supplier (supplier‐initiated improvement, SI). We derive optimal procurement contracts for both mechanisms and find that the moral hazard does not necessarily generate more profit for high‐type supplier. Furthermore, information asymmetry causes a greater possibility of not ordering from low type in SI than MI. For low type, when an upward effort distortion appears in both mechanisms, a decreased (increased) unit penalty should be imposed in MI (SI) compared with symmetric information case. Although possibly efficient effort from the supplier could yield greater channel profit in SI, several scenarios violate this expectation. However, the manufacturer's expected profit in MI is no less than that in SI. When MI is extended to MSI where both manufacturer and supplier can exert effort, the expected profits of two parties are equal to those in SI. We further extend SI to SID, where both process improvement and dual‐sourcing are available. The manufacturer considers the trade‐off between the benefit from diversification and the loss from dual information rent to decide to choose SID or MI. By comparing SID with pure dual‐sourcing, we find that supplier's process improvement could either accelerate or retard the exercise of dual‐sourcing.     

不同渠道权力结构和信息结构下供应链定价和销售努力决策

本文针对零售商销售努力和销售价格影响需求情况下的制造商-零售商两级供应链,研究不同渠道权力结构和信息结构下供应链的分散决策。基于博弈理论和建模方法,对几种权力结构和信息结构情景建立相应模型,通过理论与数值分析对不同博弈均衡进行比较。研究表明,随着零售商势力逐步增强制造商利润会逐步恶化;但零售商势力增强能否带来更多利润,取决于需求对价格和销售努力的敏感度、销售努力成本以及信息结构。占优一方可以通过获取对方更多信息来改善自己处境。若占优零售商不得不依赖于对制造商成本先验分布进行决策,当估计的均值大于真实成本时,适度的方差对零售商更有利。最后,讨论了销售努力成本分担的合作机制,针对非合作博弈给出了帕累托改进的合约区间和 Nash讨价还价均衡。     

Incentives in a Stage‐Gate Process

Many large organizations use a stage‐gate process to manage new product development projects. In a typical stage‐gate process project managers learn about potential ideas from research and exert effort in development while senior executives make intervening go/no‐go decisions. This decentralized decision making results in an agency problem because the idea quality in early stages is unknown to the executive and the project manager must exert unobservable development effort in later stages. In light of these challenges, how should the firm structure incentives to ensure that project managers reveal relevant information and invest the appropriate effort to create value? In this study, we develop a model of adverse selection in research and moral hazard in development with a go/no‐go decision at the intervening gate. Our results show that the principal's uncertainty regarding early‐stage idea quality—a term we refer to as idea risk—alters the effect of late‐stage development risk. The presence of idea risk can alter the incentives offered to the agent and may lead the principal to reject projects that otherwise seem favorable in terms of positive net present value. A simulation of early‐stage ideas, found through search on a complex landscape, shows that the firm can mitigate the negative effects of idea risk by encouraging breadth of search and high tolerance for failure.     

Spatial Transmission Models: A Taxonomy and Framework

Within risk analysis and, more broadly, the decision behind the choice of which modeling technique to use to study the spread of disease, epidemics, fires, technology, rumors, or, more generally, spatial dynamics, is not well documented. While individual models are well defined and the modeling techniques are well understood by practitioners, there is little deliberate choice made as to the type of model to be used, with modelers using techniques that are well accepted in the field, sometimes with little thought as to whether alternative modeling techniques could or should be used. In this article, we divide modeling techniques for spatial transmission into four main categories: population‐level models, where a macro‐level estimate of the infected population is required; cellular models, where the transmission takes place between connected domains, but is restricted to a fixed topology of neighboring cells; network models, where host‐to‐host transmission routes are modeled, either as planar spatial graphs or where shortcuts can take place as in social networks; and, finally, agent‐based models that model the local transmission between agents, either as host‐to‐host geographical contacts, or by modeling the movement of the disease vector, with dynamic movement of hosts and vectors possible, on a Euclidian space or a more complex space deformed by the existence of information about the topology of the landscape. We summarize these techniques by introducing a taxonomy classifying these modeling approaches. Finally, we present a framework for choosing the most appropriate spatial modeling method, highlighting the links between seemingly disparate methodologies, bearing in mind that the choice of technique rests with the subject expert.     

Impartial Nominations for a Prize

A group of peers must choose one of them to receive a prize; everyone cares only about winning, not about who gets the prize if someone else. An award rule is impartial if one's message never influences whether or not one wins the prize. We explore the consequences of impartiality when each agent nominates a single (other) agent for the prize. On the positive side, we construct impartial nomination rules where both the influence of individual messages and the requirements to win the prize are not very different across agents. Partition the agents in two or more districts, each of size at least 3, and call an agent a local winner if he is nominated by a majority of members of his own district; the rule selects a local winner with the largest support from nonlocal winners, or a fixed default agent in case there is no local winner. On the negative side, impartiality implies that ballots cannot be processed anonymously as in plurality voting. Moreover, we cannot simultaneously guarantee that the winner always gets at least one nomination, and that an agent nominated by everyone else always wins.     

The Manufacturer's Incentive to Reduce Lead Times

Although, ceteris paribus, reducing lead times may be desirable from an overall system perspective, an upstream party (e.g., a manufacturer) may have strong disincentives to offer shorter lead times, even if this came at no cost. We consider a setting in which the downstream party has the ability to exert a costly effort to increase demand (e.g., through sales promotions, advertising, etc.) during the selling season, and compare two situations: one where there is zero lead time (i.e., all demand can be satisfied after observing the demand realization), and one where orders need to be made before demand is realized. We identify two interacting effects that may inhibit shorter lead times. A so‐called “safety stock effect” can be observed when a lower risk of stocking out under short lead times induces the downstream party to alter her order quantity. A second effect, termed as “effort effect,” arises if shorter lead times impact the downstream party's optimal sales effort, and, as a consequence, lead to different order quantities. We provide a formal characterization of both effects, insight into how these effects interact, and show under which conditions the manufacturer has an incentive to offer shorter lead times.     

A Framework for Hazardous Materials Transport Risk Assessment

In this paper, we provide a framework for quantitative risk assessment in hazardous materials transport. We first outline a basic model where population centers are approximated by points on a plane with the assumption that in the case of an incident all residents in a population center will experience the same consequences. Different versions of this model have been used by other authors in the literature. This model may be valid if the hazardous materials route goes by small population centers. Then we extend this basic model to assess risks of shipping hazardous materials through large population centers that cannot be modeled as single points on a plane. In the extended model, large population centers are treated as two-dimensional objects on the plane, which allows for a more accurate treatment of consequences than the basic model. To the extent of our knowledge the extended model is novel. We provide numerical examples for both the basic and the extended models, and finish by discussing limitations of the suggested risk assessment framework.     

Emotions and the optimality of uneven tournaments

Standard results from tournament theory show that an employer should avoid organizing uneven tournaments in which workers are characterized by different cost functions. In this paper, we introduce a concept of emotions that workers have when comparing their own performance with the performances of their co-workers. We can show that under emotional workers the employer may prefer uneven tournaments to even ones. In that case, the employer benefits from both positive and negative emotions. Moreover, the behavior of emotional workers fits well with experimental findings on uneven tournaments where players choose excessive effort levels.     

复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同

本文着重研究复杂不确定环境下如何设计最优合同,以激励代理人减少项目持续期限。在代理问题中,以往的数量研究大多使用随机变量刻画项目参数和代理人的努力程度。但是,在某些情况下,项目参数和代理人的努力程度不能被历史数据获得,而必须由专家进行估计。运用不确定变量刻画专家对这些参数的估计,并且证明这样做是合理的。通过应用不确定理论,提出复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同模型。之后,为了解决这个问题,给出了该模型的确定性形式。此外,对是否考虑代理人不确定努力的最优合同进行了比较。结果显示,当其他条件相同时,委托人在考虑代理人不确定努力程度的合同中得到的期望收益不低于在没有考虑代理人不确定努力程度的合同中到的期望收益。最后,为了更好地展示模型的应用,给出了一个数值例子并进行了相关讨论。     

两种订货模式下订购和促销联合优化策略

本文基于CVaR决策准则,通过构建需求依赖于促销的一般需求模型,其中包括加法和乘法需求模型作为特例,考察了一次订货和允许紧急订货两种模式下风险厌恶零售商关于促销和库存的联合优化问题。讨论了紧急订购成本、风险厌恶以及市场需求变动对最优策略的影响,并对两种模式下零售商的最优策略和收益进行了比较分析,结果表明:在两种订货模式下,零售商的最优订购量和促销努力均随风险厌恶程度的增大而降低;紧急订货模式下的促销努力和实现的收益大于一次订货模式,且在加法需求模型下,紧急订货模式下的初次订购量小于一次订货模式的最优订购量。运用随机变量一阶和二阶交替随机占优的概念刻画了市场需求变动下零售商如何调整最优策略的充分条件。最后实施数值实验验证了理论分析结果。     

Dependency of Crop Production between Global Breadbaskets: A Copula Approach for the Assessment of Global and Regional Risk Pools

As recent events have shown, simultaneous crop losses in different parts of the world can cause serious risks to global food security. However, to date, little is known about the spatial dependency of lower than expected crop yields from global breadbaskets. This especially applies in the case of extreme events, i.e., where one or more breadbaskets are experiencing far below average yields. Without such information, risk management approaches cannot be applied and vulnerability to extremes may remain high or even increase in the future around the world. We tackle both issues from an empirical perspective focusing on wheat yield. Interdependencies between historically observed wheat yield deviations in five breadbaskets (United States, Argentina, India, China, and Australia) are estimated via copula approaches that can incorporate increasing tail dependencies. In doing so, we are able to attach probabilities to interregional as well as global yield losses. To address the robustness of our results, we apply three different methods for constructing multivariate copulas: vine copulas, ordered coupling using a minimax approach, and hierarchical structuring. We found interdependencies between states within breadbaskets that led us to the conclusion that risk pooling for extremes is less favorable on the regional level. However, notwithstanding evidence of global climatic teleconnections that may influence crop production, we also demonstrate empirically that wheat production losses are independent between global breadbaskets, which strengthens the case for interregional risk pooling strategies. We argue that through interregional risk pooling, postdisaster liabilities of governments and international donors could be decreased.     

Large Risks,Limited Liability,and Dynamic Moral Hazard

We study a continuous‐time principal–agent model in which a risk‐neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsizing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.     

Persistent Private Information

This paper studies the design of optimal contracts in dynamic environments where agents have private information that is persistent. In particular, I focus on a continuous‐time version of a benchmark insurance problem where a risk‐averse agent would like to borrow from a risk‐neutral lender to stabilize his utility. The agent privately observes a persistent state variable, typically either income or a taste shock, and he makes reports to the principal. I give verifiable sufficient conditions showing that incentive‐compatible contracts can be written recursively, conditioning on the report and two additional state variables: the agent's promised utility and promised marginal utility of the private state. I then study two examples where the optimal contracts can be solved in closed form, showing how persistence alters the nature of the contract. Unlike the previous discrete‐time models with independent and identically distributed (i.i.d.) private information, the agent's consumption under the contract may grow over time. Furthermore, in my setting the efficiency losses due to private information increase with the persistence of the private information, and the distortions vanish as I approximate an i.i.d. environment.     

Methods to Approximate Joint Uncertainty and Variability in Risk

As interest in quantitative analysis of joint uncertainty and interindividual variability (JUV) in risk grows, so does the need for related computational shortcuts. To quantify JUV in risk, Monte Carlo methods typically require nested sampling of JUV in distributed inputs, which is cumbersome and time-consuming. Two approximation methods proposed here allow simpler and more rapid analysis. The first consists of new upper-bound JUV estimators that involve only uncertainty or variability, not both, and so never require nested sampling to calculate. The second is a discrete-probability-calculus procedure that uses only the mean and one upper-tail mean for each input in order to estimate mean and upper-bound risk, which procedure is simpler and more intuitive than similar ones in use. Application of these methods is illustrated in an assessment of cancer risk from residential exposures to chloroform in Kanawah Valley, West Virginia. Because each of the multiple exposure pathways considered in this assessment had separate modeled sources of uncertainty and variability, the assessment illustrates a realistic case where a standard Monte Carlo approach to JUV analysis requires nested sampling. In the illustration, the first proposed method quantified JUV in cancer risk much more efficiently than corresponding nested Monte Carlo calculations. The second proposed method also nearly duplicated JUV-related and other estimates of risk obtained using Monte Carlo methods. Both methods were thus found adequate to obtain basic risk estimates accounting for JUV in a realistically complex risk assessment. These methods make routine JUV analysis more convenient and practical.     

Skill Management in Large‐Scale Service Marketplaces

Large‐scale, web‐based service marketplaces have recently emerged as a new resource for customers who need quick resolutions for their short‐term problems. Due to the temporary nature of the relations between customers and service providers (agents) in these marketplaces, customers may not have an opportunity to assess the ability of an agent before their service completion. On the other hand, the moderating firm has a more sustained relationship with agents, and thus it can provide customers with more information about the abilities of agents through skill screening mechanisms. In this study, we consider a marketplace where the moderating firm can run two skills tests on agents to assess if their skills are above certain thresholds. Our main objective is to evaluate the effectiveness of skill screening as a revenue maximization tool. We, specifically, analyze how much benefit the firm obtains after each additional skill test. We find that skill screening leads to negligible revenue improvements in marketplaces where agent skills are highly compatible and the average service times are similar for all customers. As the compatibility of agent skills weakens or the customers start to vary in their processing time needs, we show that the firm starts to experience sizable improvements in revenue from skill screening. Apparently, the firm can reap the most of these substantial benefits when it runs only one test. For instance, in marketplaces where agents posses uncorrelated skills, the second skill test only brings an additional 2% improvement in revenue. Accounting for possible skill screening costs, we then show the optimality of offering only one test when the compatibility between agent skills is sufficiently low. The results of this study also have important implications in terms of the right level of intervention in the marketplaces we study.     

Generalized median graphs and applications

We study the so-called Generalized Median graph problem where the task is to construct a prototype (i.e., a ‘model’) from an input set of graphs. While our primary motivation comes from an important biological imaging application, the problem effectively captures many vision (e.g., object recognition) and learning problems, where graphs are increasingly being adopted as a powerful representation tool. Existing techniques for his problem are evolutionary search based; in this paper, we propose a polynomial time algorithm based on a linear programming formulation. We propose an additional algorithm based on a bi-level method to obtain solutions arbitrarily close to the optimal in (worst case) non-polynomial time. Within this new framework, one can optimize edit distance functions that capture similarity by considering vertex labels as well as he graph structure simultaneously. We first discuss experimental evaluations in context of molecular image analysis problems—he methods will provide the basis for building a topological map of all 23 pairs of the human chromosome. Later, we include (a) applications to other biomedical problems and (b) evaluations on a public pattern recognition graph database. This work was supported by NSF grants CCF-0546509, IIS-0713489, and NIH grant GM 072131-23. The second author was also supported in part by the Department of Biostatistics and Medical Informatics, UW-Madison and UW ICTR, funded through an NIH Clinical and Translational Science Award (CTSA), grant number 1 UL1 RR025011.     

Motivating Retail Marketing Effort: Optimal Contract Design

We study a distribution channel where a manufacturer relies on a sales agent for selling the product, and for investing in the most appropriate marketing effort. The agent's effort is hard to monitor. In addition, the cost of effort is the agent's private information. These impose challenges to the manufacturer in its endeavor to influence the agent's marketing effort provisions and to allocate profit between the two parties. We propose two contract forms. The franchise fee contract is a two‐part price schedule specifying a variable wholesale price and a fixed franchise fee. The retail price maintenance contract links the allowed retail price that the agent charges customers with total payment to the manufacturer and sales level. Under information asymmetry, for implementing either contract form, the manufacturer needs to offer a menu of contracts, hoping to invoke the “revelation principle” when the agent picks a certain contract from that menu. We show that the two contract forms perform differently, and each party's preference toward a particular contract form is linked with the total reservation profit level and/or the sales agent's cost type. We provide managerial guidelines for the manufacturer in selecting a better contract form under different conditions.     

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.