Optimal Menu Of Contracts Research Articles

Supply chain contract design considering carbon tax policy under demand information asymmetry

AbstractOur paper constructs a low‐carbon supply chain (LSC) with a single manufacturer producing low‐carbon products and a single retailer. Assume that the retailer possesses private demand information and consider two cases: The manufacturer or the retailer determines the low‐carbon product's retail price. By constructing principal‐agent models, we obtain the optimal menu of contracts in each case. The impacts of the carbon tax rate and information asymmetry on LSC members' equilibrium solutions and expected profits are discussed. The results show that, given certain conditions, both the LSC members may obtain more expected profits under information asymmetry by introducing appropriate contracts.

Designing menus of contracts efficiently: The power of randomization

We study hidden-action principal-agent problems in which a principal commits to an outcome-dependent payment scheme (called contract) so as to incentivize the agent to take a costly, unobservable action leading to favorable outcomes. In particular, we focus on Bayesian settings where the agent has private information. This is collectively encoded by the agent's type, which is unknown to the principal but randomly drawn according to a finitely-supported, commonly-known probability distribution. In our model, the agent's type determines both the probability distribution over outcomes and the cost associated with each agent's action. In Bayesian principal-agent problems, the principal may be better off by committing to a menu of contracts specifying a contract for each agent's type, rather than committing to a single contract. This induces a two-stage process that resembles interactions studied in classical mechanism design: after the principal has committed to a menu, the agent first reports a type to the principal, and, then, the latter puts in place the contract in the menu that corresponds to the reported type. Thus, the principal's computational problem boils down to designing a menu of contracts that incentivizes the agent to report their true type and maximizes expected utility.Previous works showed that, in Bayesian principal-agent problems, computing an optimal menu of contracts or an optimal (single) contract is APX-hard, which is in sharp contrast from what happens in non-Bayesian settings, where an optimal contract can be computed efficiently. Crucially, previous works focus on menus of deterministic contracts. Surprisingly, in this paper, we show that, if one instead considers menus of randomized contracts defined as probability distributions over payment vectors, then an “almost-optimal” menu can be computed in polynomial time. Indeed, the problem of computing a principal-optimal menu of randomized contracts may not admit a maximum, but only a supremum. Nevertheless, we show how to design a polynomial-time algorithm that guarantees the principal with an expected utility arbitrarily close to the supremum. Besides this main result, we also close several gaps in the computational complexity analysis of the problem of computing menus of deterministic contracts. In particular, we prove that the problem cannot be approximated up to within any multiplicative factor and it does not admit an additive FPTAS unless P = NP, even in basic instances with a constant number of actions and only four outcomes. This considerably extends previously-known negative results. Then, we show that our hardness result is tight, by providing an additive PTAS that works in instances with a constant number of outcomes. We complete our analysis by showing that an optimal menu of deterministic contracts can be computed in polynomial time when either there are only two outcomes or there is a constant number of types.

Supply chain contracting considering the cost structure between capacity and quality under information asymmetry

This paper studies the supply chain contracting problem to ensure on-time delivery of high-quality products from the supplier to the buyer. The notions of complements and substitutes are utilized to describe the correlation among the supplier’s production cost, production capacity, and product quality, i.e., the cost structure between capacity and quality. A principal-agent model is proposed to solve the supply chain contracting considering the cost structure between capacity and quality under information asymmetry. We derive the conditions for complements and substitutes and the optimal menu of contracts. Our results indicate that the cost structure plays an important role in supply chain contracting.

Rationalizable Screening and Disclosure Under Unawareness

This paper analyzes a principal-agent procurement problem in which the principal is unaware of events affecting the agent's marginal costs. Since she does not conceive of all relevant events, her planned menu of contracts may be suboptimal. Communication arises naturally as some types of the agent may have an incentive to make the principal aware of some of those events before a contract menu is offered. The menu must not only reflect the principal's change in awareness, however: She also learns about the agent's types, as not all of them may have incentives to raise her awareness. We capture this reasoning through an extensive-form version of cautious rationalizability with beliefs on marginal cost types restricted to logconcavity and reverse Bayesianism (Karni and Viero, 2013). We show that if initially the principal is only unaware of some low marginal cost types, she is not made aware of all types and there is bunching at the top. If the principal is only unaware of some high marginal cost types, then she becomes aware of all types. Thus, the principal is happily made aware of inefficiencies but kept tacitly in the dark about some efficiencies. In any case, the principal offers an optimal menu of contracts for all types of which she is or has become aware. The possibility of disclosure improves ex post social welfare but does not always eradicate welfare frictions due to asymmetric awareness.

Efficiency Wage (and Slavery) Efficiency: in Theory and in Time

The formal differentiation of (i) pain incentives from ordinary rewards, (ii) of effortful from careful production and (iii) of diligent from slothful workers under labor market imperfect competition ultimately suggests that the optimal menu of contracts associates inducements to production kinds following the preference triggered by slothful workers: effortful production with pain incentives and careful production with ordinary rewards. The efficiency of the efficiency wage as interpreted by the sociological theory is therefore discerned to arise under a particular production kind and so is that of slavery its dual (undoubtedly illicit). More broadly, the confusion of the two production kinds under market and state capitalism respectively contributes to the Phillips curve and price rigidity, in the misapplication of ordinary rewards to effortful production. State capitalism jurisprudentially eliminates the risks of dismissal and redundancy and thereby lastly causes effortful production to enter stagnation.

Limited liability and non-responsiveness in agency models

This paper analyzes the optimal menu of contracts offered by a risk-neutral principal to a risk-averse agent under moral hazard, adverse selection, and limited liability. We show that a limited liability constraint causes pooling of the most efficient agent types. We also find sufficient conditions under which full pooling is optimal, regardless of the agent's risk aversion or type distribution. Our model suggests that offering a single contract is often optimal in environments with moral hazard, adverse selection, and in which the principal faces a limited liability constraint.

The management of talent: Optimal contracting for selection and incentives

AbstractOptimally reallocating human capital to tasks is key for an organization to successfully navigate a transition. We study how to design employment contracts to allocate employees to different valuable projects within an organization given two simultaneous challenges: The employees have private information about their cost of effort, and they exert unobservable effort. The optimal contract menu pairs a higher probability of assignment to a valuable project with a lower bonus in case of success. In limited cases, a fixed salary may be offered to employees with high effort cost. We link our results to job design features encountered in practice.

The Impact of Cost Information Sharing on Procurement Contract Design

In this paper, we provides contract design mechanisms and analysis for manufacturers to manage decentralized supply chain. Suppose the manufacturer’s final product consists of components, each produced by a different supplier, and the manufacturer first purchases components from suppliers, then assembles them into final product and meet demands aftermarket realization. While supply chain’s internal cooperation always benefits both, suppliers are often reluctant to proactively share their own production cost structure, otherwise manufacturers may depress purchase prices, which may reduce supplier’s profit. Manufacturers on the other hand, prefers to be informed of true cost information in order to gain greater revenues. We takes manufacturer’s perspective and design the optimal contract menu for suppliers, both to enable suppliers to disclose private cost information and to maximize the benefits. We start by modeling the original problem and find that the original problem is a complex multidimensional optimization problem. We then examine the nature of the original problem solving and devise the solution algorithm to arrive at the optimal contract menu. This algorithm reduces the complexity of the original question from o(2 n ) to o(n). We further investigate the influence mechanism of model parameters on the results and find that when market demand increases or the selling price of the final product increases, value of private information increases significantly. However, if market demand uncertainty increases, the value of information may increase or decrease for both sides.

Value of audit for supply chains with hidden action and information

Outsourcing can provide firms with a competitive advantage by realizing the benefits of suppliers’ low labor, better quality and improved innovation. Yet, the supply chain managers have several concerns about outsourcing which are mainly due to lack of critical information regarding the actions of their suppliers. In this paper, we study the effectiveness of auditing the supplier’s hidden actions for the buyer (principal) when the supplier (agent) is privately informed about the extent of the supply risk. In order to accomplish this, we first extend the standard principal-agent model by considering a case in which the agent’s hidden action affects the extent of information asymmetry between principal and agent. By comparing the agency costs associated with the optimal menu of contracts with and without audit, we then completely characterize the value of audit from the perspectives of both buyer and supplier as well as total supply chain. First, the analysis of value of audit from the buyer’s perspective shows that the buyer can strictly benefit from auditing the supplier’s actions. Second, we find that not only the buyer but also the supplier can strictly benefit from an audit. Third, the audit enables the buyer to customize her contract offerings based on the reliability of the supplier. Finally, by analyzing the impact of problem parameters on the value of the audit, we identify the conditions under which an audit would be beneficial for individual supply chain parties as well as the overall supply chain.

Bank Monitoring Incentives Under Moral Hazard and Adverse Selection

In this paper, we extend the optimal securitization model of Pages [41] and Possamai and Pages [42] between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitanic, Wan and Yang [12], we characterize explicitly and rigorously the so-called credible set of the continuation and temptation values of the bank, and obtain the value function of the investor as well as the optimal contracts through a recursive system of first-order variational inequalities with gradient constraints. We provide a detailed discussion of the properties of the optimal menu of contracts.

Robust pooling for contracting models with asymmetric information

We consider a principal-agent contracting model between a seller and a buyer with single-dimensional private information. The buyer’s type follows a continuous distribution on a bounded interval. We present a new modelling approach where the seller offers a menu of finitely many contracts to the buyer. The approach distinguishes itself from existing methods by pooling the buyer types using a partition. That is, the seller first chooses the number of contracts offered and then partitions the set of buyer types into subintervals. All types in a subinterval are pooled and offered the same contract by the design of our menu.We call this approach robust pooling and apply it to a utility maximisation problem adapted from the literature. For this problem we are able to express structural results as a function of a single new parameter, which remarkably does not depend on all instance parameters. We determine the optimal partition and the corresponding optimal menu of contracts. This results in new insights into the (sub)optimality of the equidistant partition. For example, the equidistant partition is optimal for a family of instances. Finally, we derive performance guarantees for the equidistant and optimal partitions for a given number of contracts. For the considered problem the robust pooling approach has good performances when using only a few contracts.

The Cost of a Bad Hire: On the Optimality of Pay to Quit Programs

Optimally reallocating human capital to tasks is key for an organization to successfully navigate a transition. We study how to design employment contracts to allocate employees to different valuable projects within an organization given two simultaneous challenges: The employees have private information about their own cost of effort, and they exert unobservable effort. The organization has two types of valuable projects, high and low impact, only the former of which requires effort. It would like to assign only an employee with low effort cost to the high-impact project. We characterize the optimal contract and show how it separates the employee types. The optimal contract menu pairs a higher probability of assignment to the high-impact project with a lower bonus in case of success. A fixed salary may also be used for the employees with high cost of effort, but only in limited cases. We link our results to job design features encountered in practice.

Two-echelon supply chain coordination under information asymmetry with multiple types

We analyse a principal-agent contracting model with asymmetric information between a supplier and a retailer. Both the supplier and the retailer have the classical non-linear economic ordering cost functions consisting of ordering and holding costs. We assume that the retailer has the market power to enforce any order quantity. Furthermore, the retailer has private holding costs. The supplier wants to minimise his expected costs by offering a menu of contracts with side payments as an incentive mechanism. We consider a general number of discrete single-dimensional retailer types with type-dependent default options. A natural and common model formulation is non-convex, but we present an equivalent convex formulation. Hence, the contracting model can be solved efficiently for a general number of retailer types. We also derive structural properties of the optimal menu of contracts. In particular, we completely characterise the optimum for two retailer types and provide a minimal list of candidate contracts for three types. We show that the retailer’s lying behaviour is more complex than simply lying to have higher costs. Finally, we prove a sufficient condition to guarantee unique contracts in the optimal solution for a general number of retailer types.

Supply chain contracts for capacity decisions under symmetric and asymmetric information

Production capacity decision under random demand is an important factor that significantly effects supply chain profits. It is realized in decentralized supply chains that the suppliers build capacity levels that are less than optimal for the total supply chain, since the supplier incurs all the cost and bears all the risk for the built capacity. To improve the supply chain performance, we analyze supply chain contracts considering capacity decisions in a two-party supply chain composed of a single manufacturer and a single supplier. We analyze and compare four well-known contracts, namely, simple wholesale price only contract, linear contract, cost sharing contract and revenue sharing contract under symmetric and asymmetric information about the supplier’s capacity building cost. The choice of the contract and determining the optimal contract parameters might be difficult for the manufacturer, especially if he has incomplete information about the supplier. In the asymmetric information models, we analyze the screening problem of the manufacturer when designing a menu of contracts without exact knowledge of the supplier’s capacity cost. We determine the optimal menu of contracts designed for both high and low cost suppliers and analyze their results through numerical experiments. Focusing on the capacity decisions under random demand, we aim to answer the three questions: (i) Which contracts coordinate the supply chain; (ii) Which contracts allow for any division of the supply chains profit among the firms; and (iii) Which contracts are worth adopting. We find the optimal contract parameters, determine the respective profits obtained by the supply chain members, and find which contracts would be better to use for the companies depending on the system parameters in different settings by analyzing and comparing the efficiencies of the contracts.

BEHAVIORAL ASPECTS OF REGULATOR DECISIONS

The findings of many behavioral economics studies have led many experts to share the view that the effects of limited rationality can be solved through the proper development of the menu options available to the consumer. The devising of such a menu rests on the shoulders of regulators. However, the question arises as to how regulators themselves, in turn, are limitedly rational, and how much they are motivated to provide an optimal menu of contracts that ensures maximum social welfare, given that designing such a menu is costly. This paper systematizes the main manifestations of limited rationality which can influence decision-making by regulators. An attempt is made to answer two questions: is there a need and possibility to take into account the limited rationality of civil servants in modeling the actions of the regulator and are special practical measures required to correct for the identified effects.

Outsource planning with asymmetric supply cost information through a menu of option contracts

AbstractThis paper investigates a supply contract design by a dominant manufacturer who faces a stochastic demand during a selling season. The manufacturer has several estimations of the supplier's cost with corresponding probabilities, that is, asymmetric cost information. The manufacturer designs a menu of call option contracts that include three variables: a supply order, an option, and an exercise price. We determine the optimal negative correlation between option and exercise prices as well as closed‐form formulas for the optimal supply orders. The results show that in the optimal menu of contracts either the option or the exercise price may be omitted from the menu, whereas the supply orders should always be customized for each supplier type. We show that in this problem, optimal profit assignment between contract partners under put and bidirectional option contracts is the same as call option contract studied. Numerical analysis including managerial insights is presented.

Adverse Selection and Moral Hazard with Multidimensional Types

This paper studies a contracting problem where agents’ cost of actions is private information. With two actions, this leads to a two-dimensional screening problem with moral hazard. There is a natural one-dimensional ordering of types when there is both adverse selection and moral hazard. Regardless of the number of types, an optimal menu of contracts either pools every type together or offers a menu of two contracts. Any incentive-compatible menu of contracts has to satisfy pairwise single-crossing properties in incentivized actions and ex-ante utilities. The principal can no longer sell the firm to the agent.

Additionality When REDD Contracts Must be Self-Enforcing

This paper examines self-enforcing contracts as a financial mechanism for reducing carbon emissions from deforestation and forest degradation when the opportunity cost of the land (i.e., landholder type) is private information and is imperfectly correlated over time (i.e., partially persistent types). Because self-enforcement limits the feasible incentives, the conservation levels are constrained by the surplus created. Regardless of the degree of persistence of such opportunity costs across contracting periods, a first-best self-enforcing contract can deliver “additional” carbon sequestration beyond the business as usual scenario only if the value of forest conservation is sufficiently high. Otherwise, self-enforcing contracts can induce some, suboptimal level of carbon sequestration. The degree of persistence of opportunity costs across periods does not affect the amount of total payments provided in the optimal menu of contracts, but greater persistence of opportunity cost types leads to contracts that feature more of the total payment as a bonus in contracts for landholders with a high opportunity cost for their land and more of the total payment as an upfront fixed payment for landholders with a low opportunity cost.

Welfare improving discrimination based on cognitive limitations

This paper is concerned with the situation in which a profit-maximizing monopolist faces consumers that are heterogeneous in two dimensions: their taste for quality and their level of cognitive limitations. The behavioral phenomenon considered here is the attraction effect when choices are made across categories. Using the standard second-degree price discrimination model, the optimal menu of contracts is characterized. Discriminating consumers based on their taste and cognitive limitations allows the monopolist to partially relax the incentive compatibility constraints. The decrease in distortion caused by the reduction of information rents moves the economy towards the efficient outcome. The optimal contract does not only increase the monopolist׳s profit but also improves the aggregate welfare of the economy. Furthermore, it provides a possible explanation for the apparent puzzle why one may observe that the same quality products are priced differently under different labels.

Contracting under asymmetric customer returns information and market valuation with advertising-dependent demand

We consider a contract design problem when the customer returns rate is private information to the retailer. Assuming that the retailer is a listed firm and cares about her market value, in the advertising-dependent demand setting, we derive the optimal menu of contracts and investigate the impact of the retailer's market value concern on the optimal contract parameters, as well as on the supply chain performance. It is shown that retailer's market value concern mitigates ordering quantity and advertising investment distortions caused by information asymmetry. Although this concern increases the manufacturer's expected payoff and the supply chains expected payoff, it may benefit or hurt the retailer depending on some specific conditions. [Received 15 September 2013; Revised 8 April 2014; Accepted 5 May 2014]