Calibrated Incentive Contracts

This paper studies a dynamic agency problem which includes limited liability, moral hazard, and adverse selection. The paper develops a robust approach to dynamic contracting based on calibrating the incentive properties of simple benchmark contracts that are attractive but infeasible, due to limited liability constraints. The resulting dynamic contracts are detail‐free and satisfy robust performance bounds independently of the underlying process for returns, which need not be i.i.d. or even ergodic.     

Robust Predictions for Bilateral Contracting with Externalities

The paper studies bilateral contracting between one principal and N agents when each agent's utility depends on the principal's unobservable contracts with other agents. We show that allowing deviations to menu contracts from which the principal chooses bounds equilibrium outcomes in a wide class of bilateral contracting games without imposing ad hoc restrictions on the agents' beliefs. This bound yields, for example, competitive convergence as N →∞ in environments in which an appropriately‐defined notion of competitive equilibrium exists. We also examine the additional restrictions arising in two common bilateral contracting games: the “offer game” in which the principal makes simultaneous offers to the agents, and the “bidding game” in which the agents make simultaneous offers to the principal.     

Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy

Branch selection is a key decision in a cadet's military career. Cadets at USMA can increase their branch priorities at a fraction of slots by extending their service agreement. This real‐life matching problem fills an important gap in the market design literature, providing strong empirical legitimacy to a series of elegant theoretical works on matching with contracts. Although priorities fail a key substitutes condition, the agent‐optimal stable mechanism is well defined, and in contrast to the current USMA mechanism it is fair, stable, strategy‐proof, and respects improvements in cadet priorities. Adoption of this mechanism benefits cadets and the Army. This new application shows that the matching with contracts model is practically relevant beyond traditional domains that satisfy the substitutes condition.     

A Theory of the Firm with Non‐binding Employment Contracts

This paper examines an employment relation in which individual workers enjoy some bargaining power vis‐a‐vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non‐binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationary equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over‐employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a, b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark‐up over the reservation wage.     

Relational Contracts and the Nature of Market Interactions

We provide evidence that long‐term relationships between trading parties emerge endogenously in the absence of third party enforcement of contracts and are associated with a fundamental change in the nature of market interactions. Without third party enforcement, the vast majority of trades are initiated with private offers and the parties share the gains from trade equally. Low effort or bad quality is penalized by the termination of the relationship, wielding a powerful effect on contract enforcement. Successful long‐term relations exhibit generous rent sharing and high effort (quality) from the very beginning of the relationship. In the absence of third‐party enforcement, markets resemble a collection of bilateral trading islands rather than a competitive market. If contracts are third party enforceable, rent sharing and long‐term relations are absent and the vast majority of trades are initiated with public offers. Most trades take place in one‐shot transactions and the contracting parties are indifferent with regard to the identity of their trading partner.     

Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence

We develop and estimate a model of dynamic interactions in which commitment is limited and contracts are incomplete to explain the patterns of income and consumption growth in village economies of less developed countries. Households can insure each other through both formal contracts and informal agreements, that is, self‐enforcing agreements specifying voluntary transfers. This theoretical setting nests the case of complete markets and the case where only informal agreements are available. We derive a system of nonlinear equations for income and consumption growth. A key prediction of our model is that both variables are affected by lagged consumption as a consequence of the interplay of formal and informal contracting possibilities. In a semiparametric setting, we prove identification, derive testable restrictions, and estimate the model with the use of data from Pakistani villages. Empirical results are consistent with the economic arguments. Incentive constraints due to self‐enforcement bind with positive probability and formal contracts are used to reduce this probability.     

Complexity as a Contract Design Factor: A Human‐to‐Human Experimental Study

Despite being theoretically suboptimal, simpler contracts (such as price‐only contracts and quantity discount contracts with limited number of price blocks) are commonly preferred in practice. Thus, exploring the tension between theory and practice regarding complexity and performance in contract design is especially relevant. Using human subject experiments, Kalkancı et al. (2011) showed that such simpler contracts perform effectively for a supplier interacting with a computerized buyer under asymmetric demand information. We use a similar set of experiments with the modification that a human supplier interacts with a human buyer. We show that human interactions strengthen the supplier's preference for simpler contracts. We find that suppliers have fairness concerns even when they interact with computerized buyers. These fairness concerns tend to be even stronger when suppliers interact with human buyers, particularly when the complexity of the contract is low. We also find that suppliers are more prone to random decision errors (i.e., bounded rationality) when interacting with human buyers. In the absence of social preferences, Kalkancı et al. identified reinforcement and bounded rationality as key biases that impact suppliers' decisions. In human‐to‐human experiments, we find evidence for social preference effects. However, these effects may be secondary to bounded rationality.     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Incentive issues in performance-based outsourcing contracts in the UK defence industry: a simulation study

Traditional outsourcing literature has claimed gains for the customer in terms of quality and costs. However, such gains are illusory in outsourcing of high-risk, complex tasks. The use of contracts and governance mechanisms for handling complex procurements is essential in obtaining rewards from outsourcing. Powerful incentives and risks are normally used in industrial service contracts to transfer risks to measure compliance with performance measures. The availability contracts for complex engineering services provision are forms of outsourcing contracts that transfer resources from government to external service providers on a substantial scale. The change moves the contractor role from creating resources to managing resources. Such role change mandates collaboration with customers and suppliers in supply/value chains. The management task is then perceived in terms of linking and optimising alignments rather than increasing service levels. Incentive design is one mechanism for linking the coordination of resources required in availability contracting to the business model. This article studies the impacts of agreed contract type and incentive mechanism on the customer and service provider profits using agent-based discrete event simulation model under multiple risk sharing scenarios.     

Mechanism Design With Renegotiation and Costly Messages

According to standard theory, the set of implementable efficient outcome functions is greatly reduced if the mechanism or contract can be renegotiated ex post. In some cases, contracts can achieve nothing and so, for example, the hold‐up problem may be severe. This paper shows that if the mechanism is designed in such a way that sending a message involves a small cost, then renegotiation essentially does not restrict the set of efficient implementable functions. Given a weak preference‐reversal condition, any Pareto‐efficient, bounded social choice function can be implemented in subgame‐perfect equilibrium in a renegotiation‐proof manner, for any strictly positive message cost. The key point is that messages themselves can act as punishments.     

A Portfolio Approach to Procurement Contracts

The purpose of this paper is to develop a general framework for supply contracts in which portfolios of contracts can be analyzed and optimized. We focus on a multi‐period environment with convex contract, spot market, and inventory holding costs. We specialize the model to the case of a portfolio consisting of option contracts. We characterize the optimal replenishment policy and show that it has a simple structure. Namely, the use of every different option contract and the spot market is dictated by a modified base‐stock policy. In addition, we derive conditions to determine when an option is relatively attractive compared to other options or the spot market. Finally, we present our computational study, where we report the sensitivity of the results to the parameters of the model. Our experiments indicate that portfolio contracts not only increase the manufacturer's expected profit, but can also reduce its financial risk.     

Willingness to Pay for Shifting Inventory Risk: The Role of Contractual Form

In order to reduce their inventory risk, firms can attempt to contract with their suppliers for shorter supply lead‐times, with their buyers for longer demand lead‐times, or both. We designed a controlled laboratory experiment to study contracts that shift a focal firm's inventory risk to its supply chain partners and address two questions. First, is it more effective if the cost of shifting inventory risk is framed as a fixed fee or in per‐unit cost terms? We find that, generally, our participants are willing to pay more to avoid supply–demand mismatches than the expected costs from such mismatches. This tendency to overpay is mitigated under fixed fee schemes. Second, does it matter whether the option to reduce inventory risk is the outcome of either increased responsiveness from the upstream supplier or advanced demand information from the downstream buyer? Our results suggest that this difference, when only a matter of framing, has no significant effect on willingness‐to‐pay.     

AMBIVALENT INVESTMENT AND THE HOLD‐UP PROBLEM

In this paper we add to the foundations of incomplete contracting literature. We study the hold‐up problem with ambivalent investment, where investment benefits the investing party if ex post the right decision is undertaken but harms the investing party if the wrong decision is made. In this context, we show that the power of contracts to provide investment incentives depends on three factors: the commitment value of contracts, the amount of quasirents that the investing party can expect in the case of out‐of‐contract renegotiation, and the degree of ambivalence of investment. First, contracts provide first‐best investment incentives when parties can commit to a contract regardless of the type of investment. Second, with sufficiently ambivalent investment, if parties cannot commit not to renegotiate a contract and if the investing party's bargaining power is intermediate, contracts cannot improve investment incentives above those provided by no contract. In contrast, a simple buyer or seller option contract is optimal when the investing party's bargaining power is extreme. (JEL: D23, K12, L22)     

基于需求信息更新和短缺量延期供给的易逝品供应链期权契约研究

为了降低供给与需求的不匹配,引入期权契约讨论三阶段生产和订购策略:零售商在第1阶段发出固定订单;然后在第1阶段和第2阶段之间更新需求预测,并在第2阶段调整固定订购量同时购买期权;第3阶段满足市场需求,对销售季末短缺量以执行期权和紧急订购相结合的方式实行延期供给。契约参数包含期权购买价格、执行价格和延期供给对应的批发价,三者线性相关;期权契约下,制造商不存在投机动力。根据易逝品的特征,对生产和订购模型进行仿真计算和分析,结果表明:供应链及其成员的利润都得到帕累托改进,系统利润增量的分配随期权购买价格发生变化。     

Life‐Cycle Channel Coordination Issues in Launching an Innovative Durable Product

We analyze the dynamic strategic interactions between a manufacturer and a retailer in a decentralized distribution channel used to launch an innovative durable product (IDP). The underlying retail demand for the IDP is influenced by word‐of‐mouth from past adopters and follows a Bass‐type diffusion process. The word‐of‐mouth influence creates a trade‐off between immediate and future sales and profits, resulting in a multi‐period dynamic supply chain coordination problem. Our analysis shows that while in some environments, the manufacturer is better off with a far‐sighted retailer, there are also environments in which the manufacturer is better off with a myopic retailer. We characterize equilibrium dynamic pricing strategies and the resulting sales and profit trajectories. We demonstrate that revenue‐sharing contracts can coordinate the IDP's supply chain with both far‐sighted and myopic retailers throughout the entire planning horizon and arbitrarily allocate the channel profit.     

Definable and Contractible Contracts

This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player's contract. We provide a complete characterization of the set of allocations supportable as pure‐strategy Bayesian equilibria of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

Supply Chain Contract Design: Impact of Bounded Rationality and Individual Heterogeneity

In this article, we model various forms of non‐optimizing behavior in a newsvendor setting, including biases such as recency, reinforcement, demand chasing, and anchoring, as well as unsystematic decision errors. We assume that a newsvendor may evaluate decisions by examining both past outcomes and future expected payoffs. Our model is motivated by laboratory observations under several types of supply chain contracts. Ordering decisions are found to follow multi‐modal distributions that are dependent on contract structures and incentives. We differ from previous research by using statistics to determine which behavioral factors are applicable to each decision maker. A great deal of heterogeneity was discovered, indicating the importance of calibrating a contract to the individual. Our analysis also shows that the profit performance and the effectiveness of co‐ordinating contracts can be affected by non‐optimizing behaviors significantly. We conclude that, in addition to the aggregate order quantities, the decision distributions should be considered in designing contracts.     

不对称信息下考虑产能约束的供应链合同设计

本文针对由产能约束品牌制造商和零售商组成的供应链系统,考虑市场上消费者对产品的异质性偏好,以及品牌制造商和零售商之间存在信息不对称,研究品牌制造商最优合同设计与零售商定价策略,考察产能约束与不对称信息对产品定价和供应双方合作的影响。研究发现：受到产能约束的品牌制造商有三种合同策略,即低价合同、固定价格合同以及高价合同等三种合同,在低价合同下品牌制造商可以充分利用其产能约束,而在后两种合同下产品有可能滞销;不对称信息会导致"批发价格+一次性转移支付"合同不能完美协调供应链。当品牌制造商和零售商进行信息共享谈判时,若二者在高价合同下进行合作,则品牌制造商与零售商在一定条件下可以达成信息共享谈判,实现"双赢"。     

Dynamic Pricing,Production, and Channel Coordination with Stochastic Learning

We consider a decentralized two‐period supply chain in which a manufacturer produces a product with benefits of cost learning, and sells it through a retailer facing a price‐dependent demand. The manufacturer's second‐period production cost declines linearly in the first‐period production, but with a random learning rate. The manufacturer may or may not have the inventory carryover option. We formulate the resulting problems as two‐period Stackelberg games and obtain their feedback equilibrium solutions explicitly. We then examine the impact of mean learning rate and learning rate variability on the pricing strategies of the channel members, on the manufacturer's production decisions, and on the retailer's procurement decisions. We show that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We obtain revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Finally, we demonstrate the robustness of our results by examining a model in which cost learning takes place continuously.