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Problem definition: We investigate the optimal salesforce compensation scheme in the context of private information and unobservable actions, considering common operational factors encountered in practice, including inventory costs, contractible versus censored demand information, and controlled versus delegated ordering. Methodology/results: Based on an agency model with general demand and cost functions, we derive optimality conditions for implementable contracts that can achieve the second-best outcome in all scenarios. The contracts are in the forms of a menu with linear compensation for demand or sales, incorporating inventory costs. Moreover, the contracts feature adjustments in compensation corresponding to the ordering level if it is delegated. Managerial implications: Our study reveals that, under reasonably mild conditions, optimal salesforce contracts can still maintain relatively simple forms, even when confronted with common operational factors and generalized demand and cost functions. However, the contracts must be tailored to suit the operational settings. Intriguingly, neither the loss of demand information nor the delegation of inventory decisions would compromise system efficiency at optimum. Funding: H. Song is partially supported by the Key International Cooperation and Exchange Projects of the NSFC [Grant W2411062] and the Foundation for Innovative Research Groups of the NSFC [Grant 71821002]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0400. [ABSTRACT FROM AUTHOR]

We study how a principal with an outside option optimally delegates information acquisition to an agent in a parsimonious environment in which the principal can observe neither the agent's effort nor signal realizations. When the principal chooses an outside option, the true state is not revealed and thus not contractible. We precisely characterize an optimal contract for the principal, illustrating how to construct an optimal contract. [ABSTRACT FROM AUTHOR]

We analyze a principal-agent model with moral hazard where the principal is risk neutral while the agent is risk averse or risk neutral. The agent is free to choose any probability distribution over outcomes, where some distributions require more effort than others. The agent's effort-cost function is of "Legendre type" and satisfies an axiom of invariance under mergers of outcomes that are equally paid by the principal. We analyze a family of such effort-cost functions. For a canonical subclass of these, and arbitrary outcome spaces, the principal's contract problem allows for closed-form solutions. Optimal contracts then combine debt with a monotonic sharing rule for the surplus above a threshold chosen by the principal. When the agent is risk neutral, the contract boils down to a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares. [ABSTRACT FROM AUTHOR]

We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean field equilibrium, and it is shown to be the limit of associated n-player games. Conversely, the mean field strategy induces n-player ε-Nash equilibria for any continuous reward function—but not for discontinuous ones. In a second part, we study the problem of a principal who can choose how to distribute a reward budget over the ranks and aims to maximize the performance of the median player. The optimal reward design (contract) is found in closed form, complementing the merely partial results available in the n-player case. We then analyze the quality of the mean field design when used as a proxy for the optimizer in the n-player game. Surprisingly, the quality deteriorates dramatically as n grows. We explain this with an asymptotic singularity in the induced n-player equilibrium distributions. Funding: M. Nutz is supported by an Alfred P. Sloan Fellowship and the Division of Mathematical Sciences of the National Science Foundation [Grants DMS-1812661 and DMS-2106056]. Y. Zhang is supported in part by the Natural Sciences and Engineering Research Council of Canada [NSERC Discovery Grant RGPIN-2020-06290]. [ABSTRACT FROM AUTHOR]

We, first with discrete outcomes and continuous effort, characterize the optimal contracts when a spiteful principal interacts with an other-regarding agent. We show that the optimal wage is weakly decreasing in principal's spitefulness. When the principal and the agent have exactly opposite other-regarding preferences, under certain situations, we get back the self-regarding benchmark optimal contract. Next with continuous outcomes and general functional forms, we characterize the optimal wage schedule and get back the sufficient statistics result when the principal and the agent have exactly opposite other-regarding preferences. • We characterize the optimal contract when a spiteful principal interacts with single agent. • The analysis is conducted both in closed form and in a general structure. • The optimal wage falls (weakly) with a ceteris paribus increase in principal's spite. • Self-regarding benchmark is achieved with exactly opposite other-regarding preferences. • We get back sufficient statistics result with exactly opposite other-regarding preferences. [ABSTRACT FROM AUTHOR]

We consider a novel principal–agent model that captures some salient features of an agile software development project. Specifically, the project is technically complex, can be modularized via a set of independent stories which are developed in sprints, and has requirements that can change over time due to exogenous changes in business needs, technologies, or market conditions. In addition, given the iterative nature of agile development, our model also captures and analyzes the interaction between two types of learning effects, namely, viability learning and cost learning, which until our paper have been examined only individually in the literature. Our paper makes the following contributions to the literature: (i) We characterize an optimal contract for the principal in closed‐form and generate managerial insights on how the agent's incentive to work changes, and consequently how the optimal contracting terms offered by the principal change, depending upon the business environment. We show that the interaction between the two learning effects and need‐risk plays an important and yet unexplored role in influencing the dynamics in the optimal contract. (ii) Using the optimal contract as the benchmark, we examine the performance of time‐and‐material contracts that are popularly used in agile projects. (iii) We obtain an optimal contract for precedence‐dependent stories in which one story must be completed before starting another story. Overall, our results provide both prescriptive and qualitative guidance to firms outsourcing agile software development projects. [ABSTRACT FROM AUTHOR]

We examine a continuous-time principal-agent problem under mean-volatility joint ambiguity uncertainties. Both the principal and the agent exhibit Gilboa–Schmeidler's extreme ambiguity aversion with exponential utilities. We distinguish between expost realized and exante perceived volatilities, and argue that the second-best contract necessarily consists of two sharing rules: one for realized outcome and the other for realized volatility. The outcome-sharing rule is for uncertainty sharing and work incentives, as usual, and the volatility-sharing rule is to align the agent's worst prior with that of the principal. At optimum, their worst priors are symmetrized, and realized compensation is positively related to realized volatility. This theoretical positive relation can be consistent with popular managerial compensation practices such as restricted stock plus stock option grants. A closed-form solution to a linear-quadratic example is provided. [ABSTRACT FROM AUTHOR]

We study a finite horizon optimal contracting problem with limited commitment. A risk-neutral principal enters into an insurance contract with a risk-averse agent who receives a stochastic income stream and cannot commit to keeping the contract. We consider a general concave utility function and a general process. We use the dual approach and the Lagrangian method to solve our optimization problem by transforming the dual problem into an infinite series of optimal stopping problems. We derive the optimal contract by representing the optimal intermediate and terminal payments from the principal to the agent in a closed-form. We show that the contract begins with a low level of payment to the agent and ratchets up the payment if the stochastic income of the agent rises above a pre-specified threshold level. In particular, if the agent's income follows a geometric Brownian motion, the threshold level is a deterministic decreasing function of time. We also show that the final payment depends on the history of the agent's income and the sale value of the production facility at the final time. [ABSTRACT FROM AUTHOR]

Problem definition: To improve the poor performance of supply chains caused by misaligned incentives under the wholesale price contract, theory proposes coordinating contracts. However, a common finding of experimental studies testing such contracts is that they tend to yield only a marginal, if any, performance improvement over wholesale pricing. These studies identify several behavioral factors that are at play but none accounted for by the theory proposing coordinating contracts. Among them, identified as the single most detrimental for the supply chain performance, is incomplete information about preferences for fairness causing contract rejections. Can the supply chain performance be improved with a contract designed allowing for this type of information asymmetry? What does this contract (mechanism) look like? Academic/practical relevance: The extant research characterized the optimal contracting mechanisms for such important practical cases as the suppliers' private information about production cost or the retailers' private information about the end customer demand. The present study addresses the gap in another important practical case: when the source of information asymmetry is the private information about preferences for fairness. Methodology: The underlying research method is mechanism design. Results: We prove that the optimal mechanism consists of a single contract positioned on the Pareto frontier and characterize the optimal profit split between the supplier and the retailer. We show that, under a wide range of preferences for fairness, the efficiency loss because of private information is strictly positive, but exceptions are possible. We also show that the optimal mechanism can be implemented with a variety of commonly used in practice and widely studied in academic literature contracts, including the minimum order quantity and the two-part tariff ones. Managerial implications: We establish a direct link between a large volume of theoretical and empirical literature on social preferences with the research on supply chain contracts. Because rejections that are because of incomplete information are an important cause of contract inefficiency observed in the laboratory, managers should avoid take it or leave it offers when they negotiate contracts. Instead, the bargaining process should be geared toward discovering the extent of the fairness preferences of the contracting parties. [ABSTRACT FROM AUTHOR]

The theory of optimal contracts refers to the market state, in which the bidders, the participants in the execution of transactions, have a certain number of certain information higher or lower. Normally, anyone who concludes a contract, regardless of its nature and we refer to the business environment, seeks to place himself on an optimal solution, i.e. one that according to the Latin principle “aurea mediocritas” gives him a chance to average, but protects him the realization of a contract subject to many risks. Normally, the conclusion of any contract is based on an interest, which starting from the principle of the free market, based on the ratio between supply and demand, may end up in the situation of concluding one or another of the contracts. In the literature the problem of optimal contracts is not so new, only that there is less information and materials published by specialists on this topic. In principle, in the capital market, those operating in the capital market must consider the possibility of concluding a contract on optimal terms. Nowadays, when we are in the Big Data era, in which databases are enormous, it is essential that companies or agencies that mediate business know very clearly the information that underlies the transaction to be concluded. As always, there is a clear enough difference between the level of information held by one or another of the customers. In this article we started the theoretical problem in very synthetic terms, because it is known and we tried to substantiate a model that could be the basis for renting optimal contracts. It should be noted that it started from the utility function, in the sense of von Neumann-Morgenstern, as well as the Lagrange function and last but not least from the Kuhn-Tucker multiplier, often used in microeconomic analyzes based on consistent models. In this article we started from the estimation of the multiplier between two equations to obtain an optimal result. The optimal contract for an agent, best placed, is a solution given by a system of two equations that lead to Pareto optimality, or if you will to Pareto efficiency. On the other hand, the optimal contract in the situation of asymmetric information for the interested agent is the optimal Pareto or Pareto-optimal. In this situation, in this article we took a numerical case, from whose analysis it is clear how the study should be based in the perspective of substantiating the decisions to conclude an optimal contract. Finally, the mathematical model is concretely formulated, imposing some participation restrictions or compatibility restrictions that must always be taken into account by the one who enters the market and wants to conclude an optimal contract. It follows that the model can be simplified, in order to remove some restrictions or to establish that some of them can be satisfied by using the Kuhn-Tucker multiplier. Thus, if a second agent or another market participant signs the contract, he assumes some risks. There are a lot of solutions in the market study, however, and then it must be borne in mind that these contracts are satisfactory if we take into account the conditions of the mathematical model we talked about. In this article we started from the theoretical elements, analyzing them in the mathematicaleconomic sense, in order to reach the relationship that the conditions for concluding an optimal contract imply.

We analyze a principal-supervisor-two-agent hierarchy with inefficient supervision. The supervisor may collect an incorrect signal on the agents' effort levels. When reporting to the principal, the supervisor may collude with one or both agents to manipulate the signal in exchange for a bribe. In the hierarchy, we identify a new trade-off between inefficient supervision and supervisor-agent collusion: Due to the incorrect supervisory signal, truthfully reporting the supervisory signal under collusion proofness may mistakenly punish the agents. As a result, allowing a certain type of collusion helps correct the incorrect signal and provides a higher incentive for the agents to work. We characterize the optimal no-supervision, collusion-proof, and collusive-supervision contracts, and show that the collusive-supervision contract dominates the others when supervisory efficiency is at an intermediate level. [ABSTRACT FROM AUTHOR]

This paper investigates optimal contracts between risk-neutral parties when both exert efforts and the agent faces limited liability. We identify a sufficient and necessary condition for any contract to implement the second-best outcome, i.e., the best possible outcome in double moral hazard even when the agent faces unlimited liability. It is shown that a simple share-or-nothing with bonus contract (SonBo for short) is optimal and implements the second-best outcome when the condition holds. SonBo contracts have one degree of freedom, which is very useful in dealing with heterogeneous circumstances while still maintaining consistency in contracting. SonBo admits as special cases the option-like and step bonus contracts, which are widely used in dealing with limited liability. Nevertheless, we demonstrate that a step bonus contract is more powerful because an option-like contract can be problematic in some situations. The paper also discusses the performance of SonBo when the principal also faces liability constraint and investigates the optimal contract when the second-best outcome is not achievable. [ABSTRACT FROM AUTHOR]

This paper aims to determine the optimal contract for the principal and the agent in imperfect market, when murabahah and ijarah are used. The financial contracting enforceability approach is employed to determine the contract that maximizes the value of the firm subject to agents’ constraints when the shock is low and high, and regarding market frictions. Furthermore, this approach allows us to assess the level of market frictions that agents may bear in case of low shock and high shocks. Findings reveal that the simulated values of the market frictions’ parameters for both contracts increase when moving from the low shock to the high shock. Such evidence implies that the agent is more likely to cheat and hide significant information about the project when the shock is high. As a response to this higher risk, the simulated values of the profit margin parameters for the principal rise also when the shock is high in order to compensate for the increase of market frictions and mitigate conflicts of interest. By comparing both contracts based on the simulated optimal values of the firm, it is noticeable that the gap between both contracts is very tight, which can be attributed to their common debt-based financial arrangements. However, the results show that ijarah allows the principal and the agent to generate the highest value in case of low shock and high shock, comparing to murabahah. Therefore, ijarah seems to be more attractive for the principal and the agent than murabahah.

In order to ensure profitability for shareholders, optimal contracting recommends the alignment between executive compensation and company performance. Large organizations have therefore adopted executives remuneration systems in order to induce positive market reaction and motivate executives. Complex compensation schemes are designed by Boards of Directors using strong pay-performance incentives that explain high levels of executive pay along with company size, demand for management skills and executive influence. However, the literature remains inconclusive on the pay-performance relationship owing to the various empirical methods used by researchers. Additionally, there has been little effort in the literature to compare methodologies on the pay-performance relationship. Using the dominant agency theory framework, the purpose of this study is to establish and examine the relationship between firm performance and executive pay. In addition, it intends to assess the characteristic of model specifications commonly adopted. To this aim, a quantitative analysis consisting of three complementary methods was performed on panel data from South African listed companies. The results of the main unrestricted first difference model indicate a strong non-linear relationship where the impact of current and previous firm performance on executive pay can be observed over 2 to 4-year period providing support to the optimal contracting theoretical perspective in the South African business context. In addition, CEO pay is more sensitive to firm performance as compared to Director pay. Lastly, although it affects executive pay levels, company size is not found to improve the pay-performance relationship.

Contract farming is among the institutional arrangements essential for agricultural products. In most cases, these contracts lead to increased incomes and welfare of farmers. However, this type of business has not been taken seriously in Iran. This study aimed to analyze the effect of contract farming on the income and risk of the farmer’s income. To this end, pistachio and saffron farmers in the Yazd Province, in central Iran, were considered in the harvest year of 2017-2018. We divided the farmers into three homogeneous groups, each with different input consumption levels and production per hectare. We calibrated the cost functions of representative farmers in each group. These functions were employed to develop an ideal formal contract model and relational contract model. According to the results, formal contracts and relational contracts increased income and relational contracts reduced the risk to farmers when they were compatible with the incentive constraints of the farmer. Policymakers should provide favorable conditions for the development of contract farming. For instance, they can present contract farming to farmers and encourage agricultural enterprises to participate in contracts by facilitating access to credit and other investment incentives.

Contract farming is among the institutional arrangements essential for agricultural products. In most cases, these contracts lead to increased incomes and welfare of farmers. However, this type of business has not been taken seriously in Iran. This study aimed to analyze the effect of contract farming on the income and risk of the farmer's income. To this end, pistachio and saffron farmers in the Yazd Province, in central Iran, were considered in the harvest year of 2017-2018. We divided the farmers into three homogeneous groups, each with different input consumption levels and production per hectare. We calibrated the cost functions of representative farmers in each group. These functions were employed to develop an ideal formal contract model and relational contract model. According to the results, formal contracts and relational contracts increased income and relational contracts reduced the risk to farmers when they were compatible with the incentive constraints of the farmer. Policymakers should provide favorable conditions for the development of contract farming. For instance, they can present contract farming to farmers and encourage agricultural enterprises to participate in contracts by facilitating access to credit and other investment incentives. [ABSTRACT FROM AUTHOR]

This paper emphasizes on the conflicts of interest between agents in order to assess whether venture capital can be a potential model of musharakah in imperfect markets. To achieve this purpose, this study opts for the financial contracting enforceability approach and Monte-Carlo simulation to identify the contract that maximizes the value of the firm subject to the enforcement constraint for the agent and the participation constraint for the principal, taking into account market frictions, and the two levels of the industrial shocks. Findings reveal that musharakah is the optimal contract for agents, subject to their constraints when the shock is low and high. In addition, the simulation results indicate that the increase in market frictions engenders higher profit-sharing ratio for the financier when venture capital and musharakah financings are used. The increase in the value of the firm in case of high shock is attributed to the increase in the profit-sharing ratios for both contracts to mitigate the selfish behavior of the agent. Therefore, the financier tends to require a higher profit-sharing ratio as a compensation for the severer information asymmetry. [ABSTRACT FROM AUTHOR]

It is standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. Yet it may be useful to consider social forces in mechanism design and contract theory. We devise an experiment to explore optimal contracts in a hidden information context. A principal offers one of three possible contract menus to a team of two agents of unknown types. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable menus is proposed and agents accept a contract, selecting actions according to their types. The consensus menu differs across treatments that vary the payoffs resulting from a rejection. We find that an agent is more likely to reject a contract menu if her teammate rejected a contract menu in the previous period, suggesting that agents may be learning social norms; in addition, low-ability agents have a particularly adverse reaction to reduced wage offers.

It is standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. Yet it may be useful to consider social preferences in mechanism design and contract theory. We devise an experiment to explore optimal contracts in an adverse-selection context. A principal offers one of three possible contract menus to a team of two agents of unknown types. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable menus (which one depends on the reservation payoffs) is proposed and agents accept a contract, selecting actions according to their types. We estimate the Fehr and Schmidt (1999) and Charness and Rabin (2002) models of social preferences with our data, and calculate ex post optimal social-preference contracts. In both cases, the principal could substantially enhance his profitability if he could offer the derived optimal contract menu. We also find evidence that an agent is substantially more likely to reject a contract menu if her teammate rejected a contract menu in the previous period, suggesting that agents may be learning social norms.

In this article, the authors propose to conduct a pertinent analysis of the use of mathematical models in relation to optimal effort taxation. The effort taxation must be a balance between allocative efficiency and distribution. It is a question of determining the optimal tax level for three conditions. The theory is that the shift to a fixed amount, a single share, is not feasible for wage compensation, being important to note that this condition is one that must be considered. The mathematical model proposed by the authors regarding optimal taxation of multi-condition effort is relevant and suggestive for the analysis. It is well known that, in order to increase tax revenue, they must inevitably be based on the unobservable variant, which is the potential gain or, most importantly, on the individual productivity of labor. Solving a problem of this sensibility, such as the optimal taxation of multi-state effort, needs to be analyzed and conditioned by the establishment of a mathematical-econometric model that highlights both the aspects of a minimum expectation threshold or a situation that depends on the economic outcome. The authors consider the existing variants and establish variants based on a mathematical model that is analyzed to best answer the problem of the adverse selection ie the balance between allocation efficiency and distribution. We analyze the optimization problem from Lagrange’s function and associated multiplier, highlighting the mathematical functions that can be used. Further, the authors consider the case of adverse selection based on asymmetric information. For the objective function and budget constraint, the authors consider that they need to add incentive restrictions, especially when they are taxed on income. By analyzing this hypothesis in depth, the authors propose and demonstrate a mathematical function that best suits these adjustment needs and solve the adverse selection. The way in which the authors suggest and demonstrate the implementation condition that is equivalent to the assertion that the plurality of admissible solutions is unclear gives a solution perspective applicable in most cases. The authors propose, by synthesizing, conditions (sentences) that demonstrate that the model used is one that must be considered and can be successfully used in optimal taxation of the multi-state effort. In the explanatory approach, it is also appreciated that the combination of the Kuhn-Tucker multipliers of the two constructions can determine the Lagrange function. This feature built by all Kuhn-Tucker multipliers is strictly positive and the level of effort is optimal given by a series of equalities that imply a final aspect of its use.

We examine the optimality of budget policies imposed by a funding authority on a bureaucrat who operates under a fixed budget. In particular, we study a "use‐it‐or‐lose‐it" (UILI) policy under which the bureaucrat has to return any unspent budget without being able to "roll over" any part to the next period. Instead of returning the unspent budget, the bureaucrat can go on a spending spree and engage in policy drift, which is inversely related to his motivation. The bureaucrat's motivation represents how well matched he is with the bureaucracy's mission. We show that a UILI policy is complementary to motivation as it has stronger ex ante positive incentive effects on more motivated bureaucrats. Such ex ante positive effects can overcome the ex post inefficiency of the policy and make a UILI policy optimal when the bureaucrat is well matched with the bureaucracy's mission or when its budget is large. [ABSTRACT FROM AUTHOR]

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and are paid a reward based on their relative rank. First, we propose a tractable Poissonian model in which we can describe the optimal effort for a given reward scheme. Second, we study the principal–agent problem of designing an optimal reward scheme. A surprising, explicit design is found to minimize the time until a given fraction of the population has reached the goal. [ABSTRACT FROM AUTHOR]

Using a Nash bargaining approach, we analyze the financing contract between the entrepreneur and the venture capitalist with double-sided moral hazard in a start-up enterprise. Our results show that there exists an optimal contract set between the entrepreneur and the venture capitalist, in which all contracts achieve an identical second-best social state. Within the optimal contract set, there exists continuum of joint debt-equity financing. The pure equity financing contract exists in the optimal contract set when the ratio of total social surplus to the amount of investment is greater than a threshold. [ABSTRACT FROM AUTHOR]

This paper describes how plaintiff should compensate lawyers, who choose unobservable effort, when litigation may proceed from the trial to the appeals court. We find that, when it is very likely that the defendant will appeal, transfers made to the lawyer only after an appeals court's ruling are key instruments in incentivizing both trial and appeal court effort. Indeed, the lawyer may not receive any transfer after the trial court's ruling. In contrast, when reaching the appeals stage is unlikely, a favorable trial court ruling triggers a positive transfer to the lawyer and first-best appeals effort. In our setup, the lawyer may receive a lower transfer after winning in both the trial and the appeals court as compared to the scenario in which the first-instance court ruled against the plaintiff and the appeals court reversed that ruling. [ABSTRACT FROM AUTHOR]

Highlights • Integrate real option theory and principal-agent model with incomplete information. • Consider both demand uncertainty and information asymmetry. • Characterize optimal contracts for infrastructure provision under various regimes. • Compare regulation and deregulation regimes in terms of social welfare. Abstract This study contributes to the body of knowledge by characterizing the optimal contracts for infrastructure provision that involve the choices of investment timing, price, quality, subsidy/tax, and franchise fee in regulation and deregulation regimes; and comparing the two regimes in terms of social welfare under demand uncertainty and information asymmetry. The results suggest that regulation under information symmetry dominates regulation under information asymmetry and deregulation. Whether deregulation dominates regulation under information asymmetry depends on the interplay of shadow cost of public funds, the demand volatility, the government's imperfect information on the firm's cost structure, and the franchise fee. [ABSTRACT FROM AUTHOR]