Dynamic Contracts Research Articles

Research of two‐period insurance contract model with a low compensation period under adverse selection

The phenomenon of adverse selection caused by asymmetric information dominates the insurance market. In this paper, based on principal‐agent theory, we establish a two‐period dynamic insurance contract model with a low compensation period. This model introduces the tools of a low compensation period and the increase and decrease in the bonus to identify the risk types of policyholders. We prove that this model can achieve a strict Pareto improvement relative to the two‐period static insurance contract model with a low compensation period. Moreover, we also graphically analyze the conclusion, which can help insurance companies to design more comprehensive insurance contracts.

Fiscal and Currency Union with Default and Exit

Countries which share a common currency potentially have strong incentives to share macroeconomic risks through a system of transfers to compensate for the loss of national monetary policy. However, the option to leave the currency union and regain national monetary policy can place severe limits on the size and persistence of transfers which are feasible inside the union. In this paper, we derive the optimal transfer policy for a currency union as a dynamic contract subject to enforcement constraints, whereby each country has the option to unpeg from the common currency, with or without default on existing obligations. Our analysis shows that the lack of independent monetary policy, or an equivalent independent policy instrument, limits the extent of risk-sharing within a currency union; nevertheless, in the latter, the optimal state-contingent transfer policy take as given the optimal monetary policy as to implement a constrained efficient allocation that minimises the losses of the monetary union. At the steady state welfare is lower than in a fiscal union with independent monetary policies. Nevertheless, in our simulations, the macroeconomic stabilisation effects and the social values achieved, under the two different union regimes, are quantitatively almost the same.

Long-Term Health Insurance: Theory Meets Evidence

To insure policyholders against contemporaneous health expenditure shocks and future reclassi-fication risk, long-term health insurance constitutes an alternative to community-rated short-term contracts with an individual mandate. Relying on unique claims panel data from a large private insurer in Germany, we study a real-world long-term health insurance application with a life-cycle perspective. We show that German long-term health insurance (GLTHI) achieves substantial wel-fare gains compared to a series of risk-rated short-term contracts. Although, by its simple design, the premium setting of GLTHI contract departs significantly from the optimal dynamic contract, surprisingly we only find modest welfare differences between the two. Finally, we conduct coun-terfactual policy experiments to illustrate the welfare consequences of integrating GLTHI into a system with a “Medicare-like” public insurance that covers people above 65.

Dynamic Contracting with Flexible Monitoring

We study a principal's joint design of optimal monitoring and compensation schemes to incentivize an agent by incorporating information design into a dynamic contracting framework. The principal can flexibly allocate her limited monitoring capacity between seeking evidence that confirms or contradicts the agent's effort, as the basis for reward or punishment. When the agent's continuation value is low, the principal seeks only confirmatory evidence. When it exceeds a threshold, the principal seeks mainly contradictory evidence. Importantly, the agent's effort is perpetuated if and only if he is sufficiently productive and the principal has enough flexibility in allocating monitoring capacity.

Dynamic contract and discretionary termination policy under loss aversion

We explore how the timings of compensation payments and contract terminations are jointly determined in a continuous-time principal–agent model under the discretionary termination policy of investors (the principal) when the manager (agent) has loss–averse preferences. Our theoretical findings provide several new empirical implications for backloaded compensation and forced managerial turnover. Our model also shows that mandatory deferral regulation governing incentive pay induces investors to terminate the contract relation earlier and results in the more frequent replacement of managers.

Aid and terrorism: a dynamic contracts approach with interlinked moral hazard

PurposeIn a global environment where terrorist organisations based in a poor country target a rich nation, this paper aims to study the properties of a dynamically incentive compatible contract designed by the target nation that involves joint counter-terror tasks with costly participation by each country. The counter-terror operations are however subject to ex post moral hazard, so that to incentivise counter-terror, the rich country supplies developmental aid. Development aid also helps avoid unrest arising from counter-terror activities in the target nation. However, aid itself can be diverted to non-developmental projects, generating a novel interlinked moral hazard problem spanning both tasks and rewards.Design/methodology/approachThe authors use a dynamic model where the aid giving countries and aid receiving countries behave strategically. Then they solve for the sub game perfect Nash equilibrium of this game.FindingsThe authors characterise the optimal contract, showing that the dynamic structure of counter-terror resembles the shock-and-awe discussed by military strategists. The authors then prove that it is not necessarily the case that a more hawkish (resp. altruistic) donor is less pro-development (resp. softer on terror). In addition, the authors show that it may be easier to contract for higher counter-terror inputs when the recipient is more sympathetic to terrorists. The authors also discuss other problems faced by developing nations where this model can be readily adopted and the results can endorse appealing policy implications.Originality/valueThe authors characterise the optimal contract, showing that the dynamic structure of counter-terror resembles the shock-and-awe discussed by military strategists. It is proved that it is not necessarily the case that a more hawkish (resp. altruistic) donor is less pro-development (resp. softer on terror). In addition, the authors show that it may be easier to contract for higher counter-terror inputs when the recipient is more sympathetic to terrorists. Other problems faced by developing nations are also discussed where this model can be readily adopted, and the results can endorse appealing policy implications. These results have important policy implications, in particular in today’s world.

Strategic Inventories in a Supply Chain with Downstream Cournot Duopoly

The inventories carried in a supply chain as a strategic tool to influence the competing firms are considered to be strategic inventories (SI). We present a two-period game-theoretic supply chain model, in which a singular manufacturer supplies products to a pair of identical Cournot duopolistic retailers. We show that the SI carried by the retailers under dynamic contract is Pareto-dominating for the manufacturer, retailers, consumers, the channel, and the society as well. We also find that retailer's SI, however, can be eliminated when the manufacturer commits wholesale contract or inventory holding cost is too high. In comparing the cases with and without downstream competition, we also show that the downstream Cournot duopoly undermines the profits for the retailers, but benefits all others.

Towards flexible energy demand – Preferences for dynamic contracts, services and emissions reductions

Households’ preferences for attributes of flexible energy demand are not well understood. This paper evaluates Finnish households’ acceptance of hypothetical contracts and services aimed at increasing demand side flexibility. We conduct a Choice Experiment to analyze households’ willingness to offer flexibility through timing their electricity usage and heating; their interest in dynamic pricing contracts such as real-time pricing, two-rate tariffs, or power-based tariffs; and how emissions reductions affect their choices. The results indicate that households’ sensitivity to restrictions in electricity usage is much stronger than their sensitivity to restrictions in heating. Households also require considerable compensation to choose real-time pricing over fixed fees. Furthermore, other value-creating elements besides monetary compensation could incentivize households to offer demand side flexibility because they value reductions in CO2 emissions at the power system level.

Dynamic contracts with random monitoring

In contractual relationships where the agent executes numerous independent tasks over the lifetime of the contract, it is often infeasible to evaluate his performance on all tasks that he is assigned. Incentives under moral hazard are instead provided by randomly determining whether or not to monitor each of these tasks. We characterize optimal contracts implemented with such random monitoring in a stochastic dynamic environment where the agent’s cost type varies over time. We show that the compensation terms the agent is promised for contingencies where monitoring reveals compliance are as good as those for when no monitoring takes place, and for some cost types are better; these latter types receive a monitoring reward. As time passes and the agent becomes richer, the size of the monitoring reward decreases. Compensation on the equilibrium path exhibits downward rigidity, a feature elicited empirically by earlier literature.

Linear capabilities for fully abstract compilation of separation-logic-verified code

Separation logic is a powerful program logic for the static modular verification of imperative programs. However, dynamic checking of separation logic contracts on the boundaries between verified and untrusted modules is hard, because it requires one to enforce (among other things) that outcalls from a verified to an untrusted module do not access memory resources currently owned by the verified module. This paper proposes an approach to dynamic contract checking by relying on support for capabilities, a well-studied form of unforgeable memory pointers that enables fine-grained, efficient memory access control. More specifically, we rely on a form of capabilities called linear capabilities for which the hardware enforces that they cannot be copied. We formalize our approach as a fully abstract compiler from a statically verified source language to an unverified target language with support for linear capabilities. The key insight behind our compiler is that memory resources described by spatial separation logic predicates can be represented at run time by linear capabilities. The compiler is separation-logic-proof-directed: it uses the separation logic proof of the source program to determine how memory accesses in the source program should be compiled to linear capability accesses in the target program. The full abstraction property of the compiler essentially guarantees that compiled verified modules can interact with untrusted target language modules as if they were compiled from verified code as well.

Dynamic Contracting under Positive Commitment

We consider a firm that sells products that arrive over time to a buyer. We study this problem under a notion we call positive commitment, where the seller is allowed to make binding positive promises to the buyer about items arriving in the future, but is not allowed to commit not to make further offers to the buyer in the future. We model this problem as a dynamic game where the seller chooses a mechanism at each period subject to a sequential rationality constraint, and characterize the perfect Bayesian equilibrium of this dynamic game. We prove the equilibrium is efficient and that the seller’s revenue is a function of the buyer’s ex ante utility under a no commitment model. In particular, all goods are sold in advance to the buyer at what we call the positive commitment price.

A Concept for Set‐based Design of Verification Strategies

AbstractIn current practice, a verification strategy is defined at the beginning of an acquisition program and is agreed upon by customer and contractor at contract signature. Hence, the resources necessary to execute verification activities at various stages of the system development are allocated and committed at the beginning, when a small amount of knowledge about the system is available. However, contractually committing to a fixed verification strategy at the beginning of an acquisition program fundamentally leads to suboptimal acquisition performance. Essentially, the uncertain nature of system development will make verification activities that were not previously planned necessary, and will make some of the planned ones unnecessary. In order to cope with these challenges, this paper presents an approach to apply set‐based design to the design of verification activities to enable the execution of dynamic contracts for verification strategies, ultimately resulting in more valuable verification strategies than current practice.

Dynamic Incentive Mechanism Design for Recycling Construction and Demolition Waste under Dual Information Asymmetry

The generation of construction and demolition waste (CDW) is a problem for societies aspiring to sustainability. In this regard, governments have the responsibility to support the CDW recycling through subsidies. However, the information asymmetry, as well as the “dynamic nature” of the CDW recycling market, results in a number of barriers for the government to promote CDW recycling. In this paper, we establish a mathematical model that includes the government and the recycling enterprise in the presence of dual information asymmetry including the unknown recycling technology level and unobservable recycling efforts in one-stage and two-stage cooperation. Using the incentive theory, the static and dynamic optimal recycling incentive contracts of the government were designed, and the optimal decisions of the recycler were identified. A numerical simulation revealed that by designing reasonable contracts, the government can encourage the recycler to report the true technical level and achieve information screening. Furthermore, the subsidy of the high-tech recycler remained unchanged under different circumstances. However, the subsidy of the low-tech recycler was closely related to the probability of misreporting and the proportion of technology types. This finding suggests that the government and recycler are inclined towards long-term dynamic cooperation.

Task Assignment of the Improved Contract Net Protocol under a Multi-Agent System

Background: The existing contract net protocol has low overall efficiency during the bidding and release period, and a large amount of redundant information is generated during the negotiation process. Methods: On the basis of an ant colony algorithm, the dynamic response threshold model and the flow of pheromone model were established, then the complete task allocation process was designed. Three experimental settings were simulated under different conditions. Results: When the number of agents was 20 and the maximum load value was L max = 3 , the traffic and run-time of task allocation under the improved contract net protocol decreased. When the number of tasks and L max was fixed, the improved contract net protocol had advantages over the dynamic contract net and classical contract net protocols in terms of both traffic and run-time. Setting up the number of agents, tasks and L max to improve the task allocation under the contract net not only minimizes the number of errors, but also the task completion rate reaches 100%. Conclusions: The improved contract net protocol can reduce the traffic and run-time compared with classical contract net and dynamic contract net protocols. Furthermore, the algorithm can achieve better assignment results and can re-forward all erroneous tasks.

Dynamic Relational Contracts for Quality Enforcement in Supply Chains

We model the interaction of a single buyer with a single supplier within a market in a developing country with homogeneous local suppliers and homogeneous buyers from developed nations. The buyer sources a product from a supplier and then inspects and sells it on the market, subject to quality standards such as regulations about chemical content. Suppliers decide how much effort to exert to ensure compliance with quality standards. Buyers are assumed to comply with contracts because they are based in countries with strong legal systems. We assume that legal enforcement of the supplier’s contractual obligations is not possible. We model the interaction between buyer and supplier as a repeated game in which the partnership can be terminated by the buyer if the supplier refuses to pay penalties for quality violations. After termination, the buyer and supplier each search for a new business partner. We model the interaction between buyer and supplier using relational contacts in which penalties for quality failures are set so that the supplier voluntarily pays them. We show that optimal relational contracts have dynamic form in this setting because the value of the outside option available to the parties, if the relationship is terminated, is determined by the contract terms. We characterize the properties of the optimal dynamic equilibria and analyze the use of third-party quality certifications within this framework. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2990 . This paper was accepted by Martin Lariviere, operations management.

Molecular and imaging correlates of exceptional pathologic response to neoadjuvant ADT plus enzalutamide.

61 Background: AR directed therapies are standard of care for metastatic prostate cancer, and their use for high-risk localized disease may improve survival. Previous trials showed that suppression of AR activity resulting in greater pathologic responses improved survival rates. However, the underlying biology and molecular features of exceptionally responding tumors remain unknown. Methods: Men with locally advanced prostate cancer (median Gleason score 8, median PSA 9.58 ng/dl) received mpMRI and MRI/US-fusion targeted biopsies at baseline. Patients received 6 months of ADT plus enzalutamide, then received a second mpMRI, and underwent radical prostatectomy. RP specimens were whole mounted in the same plane as MRI. The location of each tumor on biopsy was mapped to prostatectomy specimens using pathologic and imaging hallmarks. FFPE sections of baseline and post-treatment tumor were stained, laser capture microdissected, and analyzed using whole exome sequencing. Amongst nonresponding patients (residual tumor burden > 0.05 cc) comparison of pre- and post-treatment tumor specimens identified evolutionary phylogenies over space and time representing intrinsic or clonal selection of pre-existing cells. Amongst responding patients, clonal extinction was confirmed by sequencing and immunostaining of surgical specimens. Results: Gleason score at baseline did not differentiate responding and nonresponding patients. Focal ERG staining in biopsies was absent in 100% of responders and present in 60% of responders. Intraductal carcinoma architecture was also absent in all responding tumors. Focal PTEN loss was observed in all nonresponders at baseline. Responding tumor foci were enriched for deletion of chromosome 6q. Comparison of baseline mpMRI sequences indicated a trend towards lower variance on dynamic contract enhanced (DCE) MR and lower local texture heterogeneity metrics in responding lesions. Conclusions: Response to neoadjuvant intense ADT correlates with distinctive pathologic, molecular, and imaging features that can be observed prior to treatment. Selection of patients based on these parameters may improve overall responses to treatment in subsequent clinical trials. Clinical trial information: NCT02430480.

The Welfare Effects of Long-Term Health Insurance Contracts

Reclassification risk is a major concern in health insurance where contracts are typically one year in length but health shocks often persist for much longer. We use rich individual-level medical information from the Utah all-payer claims database to empirically study one possible solution: long-term insurance contracts. We characterize optimal long-term contracts with one-sided commitment theoretically, derive the contracts that are optimal for consumers in Utah, and assess the welfare level that a full implementation of these contracts could achieve relative to several key benchmarks. We find that dynamic contracts perform very well for the majority of the population, for example, eliminating over 94% of the welfare loss from reclassification risk for individuals who arrive on the market at age 25 in good health. However, dynamic contracts instead provide very little benefit to the worst pre-age-25 health risks. Their value is also substantially lower for consumers whose income growth with age is relatively high. With pre-age-25 insurance in place, consumers with flat net income prefer dynamic contracts to an ACA-like environment, but consumers with steeper income profiles prefer the ACA-like environment. Overall, we show that there are scenarios in which dynamic contracts can provide substantial welfare benefits, but that complementary policies are crucial for unlocking these benefits.

Optimal dynamic contracting: The first‐order approach and beyond

We explore the conditions under which the “first‐order approach” (FO approach) can be used to characterize profit maximizing contracts in dynamic principal–agent models. The FO approach works when the resulting FO‐optimal contract satisfies a particularly strong form of monotonicity in types, a condition that is satisfied in most of the solved examples studied in the literature. The main result of our paper is to show that except for nongeneric choices of the stochastic process governing the types' evolution, monotonicity and, more generally, incentive compatibility are necessarily violated by the FO‐optimal contract if the frequency of interactions is sufficiently high (or, equivalently, if the discount factor, time horizon, and persistence in types are sufficiently large). This suggests that the applicability of the FO approach is problematic in environments in which expected continuation values are important relative to per period payoffs. We also present conditions under which a class of incentive compatible contracts that can be easily characterized is approximately optimal.

Dynamic Incentives for Buy-Side Analysts

We develop a dynamic adverse selection model where a career-concerned buy-side analyst advises a fund manager about investment decisions. The analyst's ability is privately known, as is any information she learns over time. The manager wants to elicit information to maximize fund performance while also identifying and retaining high-skill analysts. We characterize the optimal dynamic contract, show that it has several features supported by empirical evidence, and derive novel testable implications. The fund manager's optimal contract both maximizes the value of information and screens out low-skill analysts by incentivizing the analyst to always provide honest advice.

Moral Hazard, Dynamic Incentives, and Ambiguous Perceptions

This paper considers dynamic moral hazard settings, in which the consequences of the agent's actions is not precisely understood. In a new continuous-time principal-agent model with drift ambiguity, the agent's unobservable action translates to drift set for the diffusion processes that describe evolution of output. The agent and the principal has symmetric imprecise information about the technology, and both seek robust performance from a contract in relation to their respective worst-case scenarios. We show that the optimal long-term contract aligns the party's pessimistic expectations and broadly features flattening of the high-powered incentives. Methodologically, we provide a tractable way to formulate and characterize optimal long-run contracts with drift ambiguity. Substantively, our results provide some insights into the formal link between robustness and simplicity of dynamic contracts, in particular that presence of ambiguity flattens high-powered incentives.