We propose a duality approach to solving contracting models with either one-sided or two-sided limited commitment in continuous time. We establish weak and strong duality theorems and provide a dynamic programming characterization of the dual problem. The dual problem gives a linear Hamilton-Jacobi-Bellman equation with a known state space subject to free-boundary conditions, making analysis mu...

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks. Measuring the strength of turbulence is challenging through gas line observations because requirement for high spatial spectral resolution data, an exquisite determination temperature. In this work, taking well-known HD 163296 disk as example, we investigated contrast gaps...

I examine the incentives of firms to communicate entry into an industry where the incumbent writes exclusionary, long-term contracts with consumers. The entrant’s information provision affects the optimal contract proposal by the incumbent and leads to communication incentives that are highly non-linear in the size of the innovation. Entry with small and medium-to-large innovations is announced...

In a multi-agent setting, individuals often compare own performance with that of their peers. These comparisons in‡uence agents’ incentives and lead to a noncooperative game, even if the agents have to complete independent tasks. I show that depending on the interplay of the peer e¤ects, agents’ e¤orts are either strategic complements or strategic substitutes. I solve for the optimal monetary i...

The notion of contracts as reference points provides the basis for a deeper understanding of important phenomena such as the employment contract, vertical integration, firm scope, authority, and delegation. Previous experiments lend support to this notion but they ignore realistic aspects of trading relationships such as informal agreements and ex-post renegotiation or revision. Here we show th...

Reverse share tenancy, i.e., sharecropping between a poor landlord and a rich tenant, is common throughout the developing world. Yet it can only fit the canonical principal-agent model of sharecropping under specific circumstances. This paper develops and tests between three theoretical explanations for reverse share tenancy based respectively on (i) risk-aversion on the part of both the landlo...

Litigation seems to be a Pareto-inefficient outcome of pretrial bargaining; however, this paper shows that litigation can be the outcome of rational behavior by a litigant and her attorney. If the attorney has more information than his client concerning the characteristics of the lawsuit, the client can use litigation as a way of extracting information. I show that, counterintuitively, litigati...

We analyze the bilateral trade of divisible goods in the presence of stochastic transaction costs. Mutual best-response conditions are applied to a model of optimal investment under uncertainty. The first-best solution involves a single transaction, but such behavior is not incentive compatible without courtenforceable contracts. We solve for a second-best policy in which some gains from trade ...

Studies of dynamic economic models often rely on each agent having a smooth value function and a well-defined optimal strategy. For time-homogeneous optimal control problems with a one-dimensional diffusion, we prove that the corresponding value function must be twice continuously differentiable under Lipschitz, growth, and non-vanishing-volatility conditions. Under similar conditions, the valu...

This paper studies the optimal design of delegation rule in a three-tier principalintermediary-agent hierarchy. In this hierarchy, monetary transfer is not feasible, delegation is made sequentially, and all players are strategic. We characterize the optimal delegation mechanism. It is shown that the singleinterval delegation a la Holmstrom is optimal only when the intermediary is moderately bia...