Structure Of Optimal Contracts Research Articles

Technology licensing contract design considering royalty transparency and demand information asymmetry with downstream co-opetition

This paper studies how technology suppliers can optimally design licensing contracts when there is incomplete information on the licensee’s demand potential for the product in a high-technology supply chain. A licensing contract typically contains an up-front payment and royalties on product sales. The licensor decides to license one technology to a licensee, which designs products based on the supplier’s technology and outsources the product manufacturing to a competitive downstream manufacturer. We apply principal-agent models to formulate the licensor’s contracting problem while considering the transparency of the licensing royalty and find that under demand information asymmetry, the optimal contract structure changes with the demand potential. More specifically, both the separating and pooling strategies can be the optimal strategies for the licensor under the observable contract case. Conversely, under the unobservable case, only the separating strategy is the optimal licensing strategy. And the licensor can always charge zero royalty to a high-type design firm regardless of the menu strategy or the single contract. Furthermore, we examine the effect of licensing royalty transparency on licensing decisions and firms’ profits and highlight the effect of downstream competition on the licensor’s profit. Our results show that the licensor can be better off in the observable contract case. By contrast, the design firm may be better off in the unobservable contract case. We provide a rationale for the licensing contract design under demand information asymmetry and further shed light on the choice between public and secret licensing terms.

Risk-Averse Bargaining in a Stochastic Optimization Context

Problem definition: Bargaining situations are ubiquitous in economics and management. We consider the problem of bargaining for a fair ex ante distribution of random profits arising from a cooperative effort of a fixed set of risk-averse agents. Our approach integrates optimal managerial decision making into bargaining situations with random outcomes and explicitly models the impact of risk aversion. The proposed solution rests on a firm axiomatic foundation and yet allows to compute concrete bargaining solutions for a wide range of practically relevant problems. Methodology/results: We model risk preferences using coherent acceptability functionals and base our bargaining solution on a set of axioms that can be considered a natural extension of Nash bargaining to our setting. We show that the proposed axioms fully characterize a bargaining solution, which can be efficiently computed by solving a stochastic optimization problem. We characterize special cases where random payoffs of players are simple functions of overall project profit. In particular, we show that, for players with distortion risk functionals, the optimal bargaining solution can be represented by an exchange of standard options contracts with the project profit as the underlying asset. We illustrate the concepts in the paper with a detailed example of risk-averse households that jointly invest into a solar plant. Managerial implications: We demonstrate that there is no conflict of interest between players about management decisions and that risk aversion facilitates cooperation. Furthermore, our results on the structure of optimal contracts as a basket of option contracts provides valuable guidance for negotiators. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.1076 .

Comment on “Optimal Contract to Induce Continued Effort”

In this comment, we first use a counterexample to demonstrate that the optimal contract structure proposed in section 4 of the paper [Sun P, Tian F (2018) Optimal contract to induce continued effort. Management Sci. 64(9):4193–4217] can be wrong when the two players’ discount rates are different. We then specify correct optimal contract structures, which involve generalizing the contract space to allow random termination. Numerical study with a wide range of model parameters illustrates that such a random termination only occurs sparingly in optimal contracts. Moreover, the suboptimality gap, measured by the relative improvement of the optimal contract over the best contract without random termination, is extremely small. This paper was accepted by Manel Baucells, decision analysis.

Optimal Design of Uptime-Guarantee Maintenance Contracts

This paper analyzes the contracting of maintenance services provided by an original equipment manufacturer (OEM) to an operator for a device. The service provider can exert different levels of maintenance effort during the course of the contract and the device's reliability (uptime) is influenced by these levels. However, the service provider's effort level is non-contractible. We obtain the optimal design of performance-based maintenance contracts in this context by singling out a unique uptime-guarantee contract structure that contains profit-maximizing contracts in all situations. With the optimal contract structure, the service provider guarantees 100% uptime and compensates the operator's downtime at a higher unit rate than it charges him/her for maintenance services (with the factor of inverse expected downtime under no contract). This finding shows that some of the well-known performance-based contract structures used in practice (e.g., pay-for-performance contracts) can be sub-optimal for the OEMs. When the operator's revenue rate from the device is known to the service provider, the optimal contract compensates for any lost revenue due to downtime yet leaves the operator with zero expected profit from the contract. Under asymmetric information, we provide a closed-form formula for calculating the optimal compensation rate. We also demonstrate the advantages and limitations of offering menus of contracts to increase the service provider's expected profits.

Contract Design for the Stockist in Indian Distribution Networks

Problem definition: Stockists are the entity in the supply chain who deliver to the millions of small shops that account for over 90% of retail sales in India. The stockist purchases product from the manufacturer, develops retailer interest in carrying the product, solves the logistics problem of delivery to retailers, and manages retail credit and money collection. In return, the stockist is provided assistance by the manufacturer and paid an associated margin that is a percent of the product’s retail price. We observed relatively low distribution margins offered to the stockists in India that was a surprise given infrastructure and financing challenges. We noted that the low margins are enabled by the efficiency in product delivery and demand stimulation induced by the stockist. In this paper, we focus on the analysis of screening contracts offered by manufacturers to stockists. Methodology: We use a principal–agent model structure and model the routing cost, inventory cost, and demand impact of the stockist’s capability. We then use a substitutes or complements relationship between manufacturer assistance and stockist impact to understand the optimal contract structure—i.e., level of assistance and associated retail margin. We describe the economics associated with the stockist, provide data regarding the margins and assistance provided by the manufacturer, and use the model to understand their use in developing an effective supply chain. Results: Our model uses three parameters to show that a manufacture can adjust the level of spatial retailer intensity and thus the impact of the stockist in generating demand, the fraction of high-performing stockists associated with the manufacturer and the nature of the relationship between assistance provided and its impact on the stockist’s performance (i.e., complements or substitutes relationship), to attain superior performance. Academic/practical relevance: We parameterize data from Indian firms in the consumer goods industry to understand the observed assistance provided by the manufacturer to the stockist, and associated margins. We then use our model to understand actions taken by a manufacturer in the Indian market. Managerial implications: Our analysis provides a framework for manufacturers to design screening contracts for stockists who play a vital role in managing the fragmented retail markets in developing countries. The online supplement is available at https://doi.org/10.1287/msom.2018.0722 . This paper has been accepted for the Manufacturing & Service Operations Management Special Issue on Value Chain Innovations in Developing Economies.

Liability Structure in Small-Scale Finance: Evidence from a Natural Experiment

Microfinance, the provision of small individual and business loans, has witnessed dramatic growth, reaching over 150 million borrowers worldwide. Much of its success has been attributed to overcoming the challenges of information asymmetries in uncollateralized lending. Yet, very little is known about the optimal contract structure of such loans – there is substantial variation across lenders, even within a particular setting. This paper exploits a plausibly exogenous change in the liability structure offered by a microfinance program in India, which shifted from individual to group liability lending. We find compelling evidence that contract structure matters: for the same borrower, required monthly loan installments are 6 percent less likely to be missed under the group liability setting, relative to individual liability. In addition, compulsory savings deposits are 19 percent less likely to be missed under group liability contracts.

Designing structured supply contracts under demand and price uncertainty in an open supply chain

This paper develops an integrated model for analyzing and designing structured supply contracts from the perspectives of the buyer, the supplier, and the entire supply chain in an open supply chain. We first present a flexible framework that encapsulates a wide range of contracting types that have been studied previously. We then introduce the concept of relative contract value vis-a-vis a reference alternative, which facilitates addressing explicitly both the demand uncertainty and the price uncertainty within which real supply relationships operate. To guide practitioners in designing optimal supply contracts, we derive closed-form expressions for optimal contract structure, quantity commitment and flexibility, pricing, and sharing policy as well as the conditions to maximize total supply chain profitability associated with a contract. Our research demonstrates that structured contracts consisting of several fixed and/or flexible components are capable of maximizing total supply chain profit and allocating profit between contracting parties arbitrarily.

Licensing Contracts: Control Rights and Options

Research and development (RD the innovator may, under certain conditions, prefer to grant launch control rights or buy-out options to the marketer despite the fact that both terms restrict its downstream actions. We demonstrate that a menu of contracts is not necessary to address the adverse selection problem as the menu can be replicated by a single option contract. We show that timing, through renegotiation or delayed contracting, as well as the careful allocation of control rights and options can have a significant influence on the value of collaborative R&D. We provide recommendations on the optimal contract structure and timing based on two project characteristics, novelty of the R&D process and market-potential variability.

Optimal support strategy for mechanical systems under contract realm

Purpose– Original equipment manufacturers (OEMs) start providing support to products that helped them in sustaining their business worldwide. The customers are entering into contracts with the OEM, to get the required level of performance but at minimum possible cost. It required the work distribution between OEM/service provider and the client, and may formalize through contract. The contract structure depends upon the number of player involved (customer, OEM and third party) and the support activity. The different contract alternatives can be formulated and the best one may be selected on the basis of minimum Life cycle cost. The paper aims to discuss these issues.Design/methodology/approach– In this work, mathematical models are developed; which are implemented on a real life problem. The developed models are optimized in context to preventive maintenance schedule.Findings– In this research, important issues are listed; research steps and mathematical models are presented. The problem has been identified from the literature perspective for mechanical systems. A methodology for formulating and selecting the optimal contract structure is also proposed. The model has been implemented on a real life problem, in which the OEMs provide support to their make installed at Compressed Natural Gas workstation in National Capital Region, India.Originality/value– The research results of this paper will contribute both academic and empirical value.

Risk Management Under a Prudential Policy

In this paper, we study the structure of optimal contracts in a banking system when there is no risk of moral hazard. We consider a risk management problem under a policy that reduces the excessive risk taking behavior by making all banks bear part of the risk that they transfer to other parties in the market. First, we characterize the optimal solutions to the risk management problem, and, second, we find a necessary and sufficient condition under which the “risk of the tail events” will not be transferred. In particular, we will study the problem using two known risk measures, Value at Risk and Conditional Value at Risk, and will show that in these cases the optimal solutions are in the form of stop-loss policies.

Analysis of legal and economic aspects of precipitation weather derivatives for Serbian agricultural sector

Weather derivatives are not present in Serbia nor in the neighboring countries and have no significant application in the European Union, either. Weather derivatives originated in the USA, where the market for these instruments is most developed, in terms of both economy and law. However, positive effects of their application, through the decrease of influence of unfavorable weather conditions on agricultural crops, are a good basis for their further study. The most common reasons for their absence from our financial market are their complexity and the inexistence of prerequisites for their introduction. This paper analyses legal and economic aspects of weather derivatives, as forms of financial derivatives, as well as weather derivative contracts concluded with the aim of hedging against precipitation exposure. The goal of the analysis is to find an optimal contract structure, but also the conditions that have to be met in order for its signing to be economically justified for both contractual parties, as well as the creation of preconditions for this weather derivative contract to be the instrument of trade on the financial market. The paper also analyses normative frameworks for the conclusion of these derivative contracts, as well as the necessity to educate market participants, which refers both to agricultural producers and financial institutions. Furthermore, it emphasizes the difference in relation to the classical contract of insurance against drought risk.

Licensing Contracts: Control Rights, Options, and Timing

Research and development (R&D) collaborations, common in high-tech industries, are challenging to manage because of technical and market risks as well as incentive problems. We investigate how control rights, options, payment terms, and timing allow the innovator to capture maximum value from its R&D collaborations with a marketer. Our study reveals a counterintuitive result; the innovator may, under certain conditions, prefer to grant launch control rights or buyout options to the marketer despite the fact that both terms restrict its downstream actions. We demonstrate that a menu of contracts is not necessary to address the adverse selection problem because the menu can be replicated by a single option contract. We show that timing, through renegotiation or delayed contracting, as well as the careful allocation of control rights and options can have a significant influence on the value of collaborative R&D. We provide recommendations on the optimal contract structure and timing based on two project characteristics, novelty of the R&D process and market-potential variability. This paper was accepted by David Hsu, entrepreneurship and innovation.

Liability Structure in Small-Scale Finance: Evidence from a Natural Experiment

Microfinance, the provision of small individual and business loans, has experienced dramatic growth, reaching over 150 million borrowers worldwide. Much of the success of microfinance has been attributed to attempts to overcome the challenges of information asymmetries in uncollateralized lending. However, very little is known about the optimal contract structure of these loans, and there is substantial variation across lenders, even within a particular setting. This paper exploits a plausibly exogenous change in the liability structure offered by a microfinance program in India, which shifted from individual to group liability lending. We find evidence that the lending model matters: for the same borrower, the required monthly loan installments are 11 percent less likely to be missed under the group liability setting in comparison with individual liability. In addition, compulsory savings deposits are 20 percent less likely to be missed under group liability contracts.

Mediated contracts and mechanism design

Abstract The framework of incentive compatible finite direct coordination mechanisms in the sense of Myerson (1982) [5] is isomorphic to a framework of incentive compatible stochastic mediated contracts in the sense of Rahman and Obara (2010) [11] and Rahman (2009) [10] . The equivalence follows because the framework of Myerson (1982) [5] allows for a correlation between recommendations and transfers. The literature has hitherto not recognized the importance of this correlation for the structure of optimal contracts and for extending the revelation principle to address agency (moral hazard) problems.

Optimal incentive contracts under inequity aversion

We analyze the classic moral hazard problem with the additional assumption that agents are inequity averse. The presence of inequity aversion alters the structure of optimal contracts. When the concern for equity becomes more important, there is convergence towards linear sharing rules. The sufficient statistics result is violated. Depending on the environment, contracts may be either overdetermined, i.e. include non-informative performance measures, or incomplete, i.e. neglect informative performance measures. Finally, our model delivers a simple rationale for team based incentives, implying wage compression.

Milestone Payments or Royalties? Contract Design for R&D Licensing

We study how innovators can optimally design licensing contracts when there is incomplete information on the licensee's valuation of the innovation, and limited control over the licensee's development efforts. A licensing contract typically contains an up-front payment, milestone payments at successful completion of a project phase, and royalties on sales. We use principal-agent models to formulate the licensor's contracting problem, and we find that under adverse selection, the optimal contract structure changes with the licensee's valuation of the innovation. As the licensee's valuation increases, the licensor's optimal level of involvement in the development—directly or through royalties—should decrease. Only a risk-averse licensor should include both up-front and milestone payments. Moral hazard alone is not detrimental to the licensor's value, but may create an additional value loss when combined with adverse selection. Our results inform managerial practice about the advantages and disadvantages of the different terms included in licensing contracts and recommend the optimal composition of the contract.

Contingency management under asymmetric information

We model a monopolist supplier whose supply to multiple buyers is disrupted. The supplier can take costly, speed-dependent actions, to restore supply. Buyers experience private backorder costs that are unknown to the supplier. We analyze the supplier's optimal contract structure and explore the impact of an alternate supplier.

Optimal Incentive Contracts Under Inequity Aversion

We analyze the Moral Hazard problem, assuming that agents are inequity averse. Our results differ from conventional contract theory and are more in line with empirical findings than standard results. We find: First, inequity aversion alters the structure of optimal contracts. Second, there is a strong tendency towards linear sharing rules. Third, it delivers a simple rationale for team based incentives in many environments. Fourth, the Sufficient Statistics Result is violated. Dependent on the environment, optimal contracts may be either overdetermined or incomplete.

Vertical Foreclosure in Experimental Markets

We report the results of experiments designed to test recent theories of vertical foreclosure. Consistent with the theory, the upstream firm has more difficulty commiting to supply the monopoly quantity in treatments with non-integration and secret contracts than in either treatments with integration or treatments with public contracts. Integration allows the upstream firm to extract a larger share of surplus than public contracts, a bargaining effect which has been underemphasized in the recent foreclosure literature. Motivated by a number of observations that are difficult to reconcile with existing theory, we extend received theory by allowing downstream subjects to have heterogeneous out-of-equilibrium beliefs (a mixture of passive and symmetric beliefs). The resulting model generates a number of surprising results about the structure of optimal contracts. We conclude with a comparison of our results to those of previous experiments on bargaining.

Optimal Contracts when Enforcement is a Decision Variable

This paper analyzes choice-theoretic costly enforcement in an intertemporal contracting model with a differentially informed investor and entrepreneur. An intertemporal contract is modeled as a mechanism in which there is limited commitment to payment and enforcement decisions. The goal of the analysis is to characterize the effect of choice-theoretic costly enforcement on the structure of optimal contracts. The paper shows that simple debt is the optimal contract when commitment is limited and costly enforcement is a decision variable (Theorem 1). In contrast, stochastic contracts are optimal when agents can commit to the ex-ante optimal decisions (Theorem 2). The paper also shows that the costly state verification model can be viewed as a reduced form of an enforcement model in which agents choose payments and strategies as part of a perfect Bayesian Nash equilibrium.