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In a homogeneous good industry composed of a dominant firm and a fringe of followers that can choose non-linear pricing contracts to sell the good, we demonstrate that only the dominant firm uses them. Compared with the standard dominant firm model in which only linear pricing contracts are feasible, the dominant firm supplies an inefficiently low number of customers as a way to extract more surplus, since the alternative for customers is a fringe cluttered by excess demand. Thus, allowing market-power firms to deploy non-linear pricing contracts leads to market segmentation, and customers end up worse off than under linear pricing contracts. Fringe firms, in contrast, are better off since they end up charging a higher price for the good. Finally, aggregate welfare under non-linear pricing increases (decreases) as compared to linear pricing if the dominant firm’s share of production capacity is (is not) large enough.

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa-Kalai-Smorodinsky (K-S) solution, which is the intersection point of the feasible region's boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties' financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash's bargaining solution.

We show that demanding team incentives to be robust to nonquantifiable uncertainty about the game played by the agents leads to contracts that align the agents’ interests. Such contracts have a natural interpretation as team-based compensation. Under budget balance they reduce to linear contracts, thus identifying profit-sharing, or equity, as an optimal contract absent a sink or a source of funds. A linear contract also gives the best profit guarantee to an outside residual claimant. These contracts still suffer from the free-rider problem, but a positive guarantee obtains if and only if the technology known to the contract designer is sufficiently productive.

This paper presents a supply chain game with a manufacturer and its supplier, where each firm seeks to allocate its own resources between improving design quality and reducing the production cost of a finished product over finite contract duration. The firms agree on a linear contract where the supplier either periodically updates the transfer price, i.e., cost-plus contract (CPC), or sets a definitive transfer price at the beginning of the contract, i.e., wholesale price contract (WPC). Assuming a committed manufacturer, we account for the possibility that the supplier is either committed or non-committed, and derive homogeneous and heterogeneous Nash equilibrium strategies under a CPC and a WPC. We then compare the impact of the supplier's strategy on the tradeoff between quality and efficiency and the firms' payoffs, and shed light on the relative merits of a CPC and a WPC. We notably show that a CPC is more robust to the supplier's strategy type than a WPC in terms of efficiency, quality, and profits. Contrary to the literature, we conclude that a variable transfer price is preferable to a constant transfer price.

We study a class of models of moral hazard in which a principal contracts with a counterparty, which may have its own internal organizational structure. The principal has non-Bayesian uncertainty as to what actions might be taken in response to the contract, and wishes to maximize her worst-case payoff. We identify conditions on the counterparty’s possible responses to any given contract that imply that a linear contract solves this maxmin problem. In conjunction with a Richness property motivated by much previous literature, we identify a Responsiveness property that is sufficient—and, in an appropriate sense, also necessary—to ensure that linear contracts are optimal. We illustrate by contrasting several possible models of contracting in hierarchies. The analysis demonstrates how one can distill key features of contracting models that allow their findings to be carried beyond the bilateral setting.

We study contracting when both principal and agent have to exert noncontractible effort for production to take place. An analyst is uncertain about what actions are available and evaluates a contract by the expected payoffs it guarantees to each party in spite of the surrounding uncertainty. Both parties are risk-neutral; there is no limited liability. Linear contracts, which leave the agent with a constant share of output in exchange for a fixed fee, are optimal. This result holds both in a preliminary version of the model, where the principal only chooses to supply or not supply an input, and in several variants of a more general version, where the principal may have multiple choices of input. The model thus generates nontrivial linear sharing rules without relying on either limited liability or risk aversion.

We study dominant strategy incentive compatibility in a mechanism design setting with contingent contracts where the payoff of each agent is observed by the principal and can be contracted upon. Our main focus is on the class of linear contracts (one of the most commonly used contingent contracts) which consist of a transfer and a flat rate of profit sharing. We characterize outcomes implementable by linear contracts and provide a foundation for them by showing that, in finite type spaces, every social choice function that can be implemented using a more general nonlinear contingent contract can also be implemented using a linear contract. We then qualitatively describe the set of implementable outcomes. We show that a general class of social welfare criteria can be implemented. This class contains social choice functions (such as the Rawlsian) which cannot be implemented using (uncontingent) transfers. Under additional conditions, we show that only social choice functions in this class are implementable.

We study the bilateral trading problem under private information. We characterize the range of possible mechanisms which satisfy ex-post efficiency, incentive compatibility, individual rationality, and budget balance. In particular, we show that the famous Myerson–Satterthwaite impossibility result no longer holds when contingent contracts are allowed.

This paper studies optimal sales force compensation plans in a multiperiod moral-hazard model when the firm wants to implement high effort in every period but only obtains aggregate information on sales. The sales agent chooses effort each period after observing previous sales, and his incentive responsiveness might change over time. The paper derives conditions under which a linear incentive scheme—a pure commission—dominates a bonus plan and vice versa. A commission is optimal if the agent is most difficult to motivate in the last period. Otherwise, combining the commission with a bonus plan can lower the firm’s cost of providing incentives in earlier periods. The results are robust to different types of cost externalities and demand externalities across periods. However, if the firm obtains intermediate sales information, bonus plans dominate commissions. This paper was accepted by J. Miguel Villas-Boas, marketing .

This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others' effort levels and draft enforceable side-contracts on effort levels and realized returns. Standard constraints, resulting in incentive contracts, fail to ensure implementability, and we examine centralized collusion-proof contracts and decentralized team contracts, as well. We prove that the principal may restrict attention to team contracts whenever returns from the project satisfy a mild monotonicity condition.