11 Jun Review at least 4 articles on TEAM DYNAMICS and write power point presentation 12 slides
130 © 2018 Annals of Pediatric Cardiology | Published by Wolters Kluwer – Medknow
Address for correspondence: Mr. Sivaram Subaya Emani, 300 Longwood Ave., Boston, MA 02115, USA. E-mail: semani@college.harvard.edu
INTRODUCTION
Optimal patient outcomes during Intensive Care Unit (ICU) resuscitation depend heavily on effective team dynamics among caregivers, especially in cardiac ICU (CICU) settings, where crisis events occur commonly.[1] Nearly half of adverse events in the ICU can be attributed to deficiencies in teamwork and communication.[2,3] Suboptimal team dynamics may lead to adverse patient
outcomes in low-resource health-care settings as well.[4] Efforts to improve outcomes in these settings require interventions that promote an environment of effective communication and structured role clarity.
Crisis resource management (CRM) training applies a deliberative practice model to simulated crisis scenarios
Simulation training improves team dynamics and performance in a low‑resource cardiac intensive care unit Sivaram Subaya Emani1, Catherine K Allan1,2,3, Tess Forster1, Anna C Fisk4, Christine Lagrasta4, Bistra Zheleva5, Peter Weinstock1,3, Ravi R Thiagarajan2,3 1Simulator Program, and Departments of 2Cardiology, 4Nursing, Boston Children’s Hospital, 3Anesthesiology, Perioperative and Pain Medicine, Division of Critical Care Medicine, Boston Children’s Hospital, Boston, MA, 5Children’s HeartLink, Minneapolis, MN, USA
ORIGINAL ARTICLE
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Website: www.annalspc.com
DOI: 10.4103/apc.APC_117_17
This is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial- ShareAlike 4.0 License, which allows others to remix, tweak, and build upon the work non-commercially, as long as appropriate credit is given and the new creations are licensed under the identical terms.
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How to cite this article: Emani SS, Allan CK, Forster T, Fisk AC, Lagrasta C, Zheleva B, et al. Simulation training improves team dynamics and performance in a low-resource cardiac intensive care unit. Ann Pediatr Card 2018;11:130-6.
ABSTRACT
Introduction : Although simulation training has been utilized quite extensively in high‑income medical environments, its feasibility and effect on team performance in low‑resource pediatric Cardiac Intensive Care Unit (CICU) environments has not been demonstrated. We hypothesized that low‑fidelity simulation‑based crisis resource management training would lead to improvements in team performance in such settings.
Methods : In this prospective observational study, the effect of simulation on team dynamics and performance was assessed in 23 health‑care providers in a pediatric CICU in Southeast Asia. A 5‑day training program was utilized consisting of various didactic sessions and simulation training exercises. Improvements in team dynamics were assessed using participant questionnaires, expert evaluations, and video analysis of time to intervention and frequency of closed‑loop communication.
Results : In subjective questionnaires, participants noted significant (P < 0.05) improvement in team dynamics and performance over the training period. Video analysis revealed a decrease in time to intervention and significant (P < 0.05) increase in frequency of closed‑loop communication because of simulation training.
Conclusions : This study demonstrates the feasibility and effectiveness of simulation‑based training in improving team dynamics and performance in low‑resource pediatric CICU environments, indicating its potential role in eliminating communication barriers in these settings.
Keywords : Crisis resource management, intensive care, nursing empowerment, simulation training
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open expression of urgent clinical information to other team members and acknowledgment of receipt of that information. Idea acceptance was defined as the thoughtful consideration of suggestions made by other team members in clinical decision-making during a crisis. To demonstrate the importance of optimal team dynamics, each group of participants was asked to participate in a “tennis ball” exercise, which has been previously utilized.[9] During the introductory session, participants were also introduced to the concept of simulation training and were shown a video demonstrating a well-executed simulation exercise. Management algorithms for low cardiac output, arrhythmias, airway distress, and cardiac arrest were also reviewed. Figure 1 depicts the overall course design.
Presimulation questionnaire
Before participation in the simulation training course, participants completed a questionnaire in which they rated their baseline utilization of role clarity, closed-loop communication techniques, and idea acceptance in clinical practice. Participants rated their clinical environment in each of these parameters on a scale from 1 to 5, with 1 (“strongly agree”) representing high competency and 5 (“strongly disagree”) representing deficiency.
Simulation scenarios
The simulation sessions were designed to replicate the native work environment and were conducted in a bed space within the CICU using clinically available equipment (medication carts, monitors, ventilation, and surgical instruments). Participants were instructed to speak in language of their own preference. The scenarios presented in the training course included patients experiencing low cardiac output, supraventricular tachycardia (SVT), cardiac tamponade, and respiratory distress.
The simulation exercises were performed on a newborn patient simulation mannequin (Newborn HAL S3010 Tetherless Newborn Simulator, Guamard Scientific, Miami, FL), which was connected to a bedside monitor displaying vital signs and physiological data. This high- fidelity mannequin simulates full body assessment incorporating both auditory and visual cues including cyanosis, chest wall movement, pulses, heart sounds, breath sounds, and movement of extremities. Participants utilized physiological data and symptoms provided by the simulation mannequin to diagnose, perform interventions, and assess the response to interventions. Interventions could include (1) administration of intravenous fluids and medication, (2) ventilation by endotracheal intubation or bag-valve-mask, (3) ventilation by endotracheal intubation or bag-valve- mask, (3) Electric defibrillation, and (4) cardiopulmonary resuscitation. Figure 2 shows the simulator setup.
to improve communication and teamwork.[5-7] The use of simulation training for extracorporeal membrane oxygenation resuscitation education, for example, has been shown to improve team dynamics and participant comfort level.[8-10] Although simulation training has been shown to improve outcomes in many developed countries, it has not been widely adopted in developing countries due to lack of data indicating its efficacy and utility. Before the adoption of this methodology for team training in low-resource settings, further data regarding its efficacy are necessary. Given the positive impact of simulation-based team training in high-resource systems, we designed a simulation-based training curriculum that would engender cross-disciplinary teamwork in low-resource pediatric CICU and hypothesized that it would lead to measurable improvements in team dynamics and performance. We analyzed the application of such a simulation-based CRM training program in a low-resource pediatric CICU.
METHODS
Study design
The study is a prospective observational study of 23 health-care providers in a low-resource pediatric CICU in Southeast Asia who underwent a simulation-based team training program designed by Boston Children’s Hospital. Participants were informed of the nature of the study and provided informed consent. Approval for the study was obtained from the institutional review board at Boston Children’s Hospital and the local institution. The impact of the simulation training program on team dynamics and time to intervention was assessed by participant questionnaires and independent observers.
Overall course design
The CRM training program utilized in this study consisted of four 1-h multimedia and interactive discussion sessions that introduced principles of effective teamwork and four 1-h scenario simulation sessions delivered over a 5-day period. The duration of the simulation program was established according to previous protocols.[11] Participants were divided into two training groups, each consisting of at least 1 surgeon, 1 anesthesiologist, 1 attending intensivist, and 3–4 nursing staff.
The program was initiated with a 1-h interactive lecture, in which simulation participants were introduced to the importance of effective team dynamics in hospital care. The interactive lecture emphasized three major aspects of effective team dynamics: Role clarity, closed-loop communication, and idea acceptance. Role clarity was defined as the assigning of specific clinical roles (i.e., bedside nurse, airway manager, recorder, etc.) and the delegation of specific clinical tasks during a crisis. Closed-loop communication was defined as the clear and
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For each simulation session, a primary bedside nurse was assigned, and all other participants were asked to leave the vicinity of the bed space. Course facilitators presented background information regarding the patient diagnosis, past medical history, and recent surgical procedure to the primary nurse. The nurse was instructed to conduct routine activities of patient care and recruit additional help as needed. Other than providing background clinical information to the primary nurse, course facilitators did not interact with participants during the exercise. Following a period of stability, perturbations in vital signs were generated remotely by course facilitators. Within a single simulation exercise, multiple hemodynamic or respiratory perturbations were provided, and each perturbation was treated as a separate event during subsequent analysis. Participants’ responses to changes in vital signs were recorded by video and by the observing simulation staff. Following the simulation, a debriefing was conducted during which participants were asked to reflect on challenges and possible solutions related to role clarity, closed-loop communication, and idea acceptance.
Daily evaluation of simulation performance
After each session, participants completed a questionnaire assessing the team’s utilization of role clarity, closed-loop communication, and idea acceptance. Respondents rated themselves and their team members with respect to the above criteria on a scale from 1 to 5, with a score of 1 (“strongly agree”) representing optimal and 5 (“strongly disagree”) representing deficient performance in each component of team dynamics.
A blinded observer reviewed a video recording of the simulation exercise and measured parameters relating to team dynamics as well as time to therapeutic intervention during simulation. To derive the frequency of role clarity, the total number of instances in which a team member designated a role or delegated a task was divided by the total time of the exercise. Similarly, the frequency of closed-loop communication was calculated from the number of instances, in which team members utilized closed-loop communication. Video analysis was also used to determine the time duration between hemodynamic or respiratory perturbation (change in vital signs or critical laboratory value) and appropriate therapeutic intervention by the team. Appropriate intervention was defined as adenosine administration or cardioversion for SVT, defibrillation for ventricular tachycardia, bag-mask ventilation or intubation for respiratory distress, and fluid administration or inotropic support for low cardiac output/ hypotension. The time duration between perturbation and team response for each group was plotted over time.
Program evaluation/assessment
At the conclusion of the simulation training program and at 1 month after its completion, participants completed
a questionnaire in which they assessed the improvement in their team dynamics as a result of simulation training. Questionnaires were specifically designed to determine integration of closed-loop communication, role clarity, and idea acceptance into their clinical practice as a result of simulation exercises [Table 1]. In addition to these questions, participants were asked to rate their overall improvement in team dynamics, the improvement in patient care attributable to improved team dynamics, and how often they thought simulation should be repeated.
Statistical analysis
Results of questionnaires completed by participants were collected, and the median score for each question was displayed. A Friedman test was utilized used to detect differences in participant scores across multiple test attempts. P < 0.05 was considered to be statistically significant. Participants who did not participate on day 1 but joined for later simulation exercises were excluded from this analysis. Nonparametric comparisons of responses from different groups of respondents (nurses, physicians in training, and doctors) were performed using a Mann–Whitney U-test. Spearman rank correlation test was used to detect the association between training day and communication or role clarity score, with a significant P value indicating a relationship between the variables.
RESULTS
Demographics
A total of 23 participants participated in eight simulation sessions over a 5-day period. Nurses (n = 8), anesthesiologists (n = 8), surgeons (n = 6), and cardiologists (n = 1) were divided into two groups and participated in four simulation sessions each.
Presimulation questionnaire
The median responses to the questions given in the presimulation questionnaire are displayed in Table 2. The median score for each of the six questions was 1 – “strongly agree/excellent” or 2 – “agree/good,” indicating a perception of overall proficiency in team dynamics before simulation.
Daily participant questionnaires
Table 3 depicts the median participant response given to the six questions asked on the daily participant evaluation administered after each simulation session over the 4-day training program. A significant improvement in each component of team dynamics (role clarity, effective communication, and idea acceptance) was detected over the study period by a Friedman test (P < 0.05).
Observer analysis
Time to intervention following a perturbation in hemodynamic or respiratory status decreased
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over the course of the training program [Figure 3]. The total frequency of communication increased significantly (P < 0.01) from 2.2 to 4.9 communications per minute for Group 1, whereas the change in communications per minute for Group 2 was not statistically significant (2.3–3.8, P = 0.07). The frequency of role clarity also increased over the training period for both groups, rising from 1.3–2.1 to 0.5–1.4 role clarifications per minute for groups 1 and 2, respectively. There was no statistically significant difference in the aggregate performance of Group 1 compared to Group 2.
Postsimulation questionnaire
Figure 4 depicts the participant responses to the postsimulation questionnaire. A median response of 1 or 2 to each of the six questions indicates a perception of significant improvement due to simulation training. Scores provided by nurses on this questionnaire
differed significantly from scores provided by physician staff (median score 1 [1–1] vs. 2 [2–2], respectively, P < 0.01).
Follow‑up questionnaire
Table 4 displays the median scores provided by participants to the questions asked in the 1-month follow-up questionnaire. A median response score of 1 (interquartile range [IQR] 1–2) was observed for questions regarding continued improvements in team dynamics. A median score of 2 (IQR 1–2) was observed for questions related to ongoing closed-loop communication in their clinical practice. Regarding optimal frequency of simulation training, 6 out of 14 respondents expressed “every month,” 2 out of 14 expressed “once every 3 months,” and 6 out of 14 respondents expressed “once per year.”
Discussion and analysis
The purpose of this study was to investigate the effectiveness of simulation training in promoting better team dynamics among pediatric CICU caregivers in a low-resource health-care setting. The major findings were that a short simulation training session can improve participant and observer perception of team dynamics as well as time to therapeutic intervention in such healthcare environments.
Its feasibility, low cost, and high impact make simulation, a technique that is ideally suited for low-resource health-care settings in developing countries. Although this study utilized the Newborn HAL device, previous studies have shown that the type of simulator does not appreciably impact results.[12,13] The technology necessary to perform low-fidelity simulation by creating a realistic crisis environment – mannequin, monitor, and laptop with software to control monitor output – can be accessible to low-resource hospitals. Equipment necessary to conduct simulation training exercises described in this study ranges in cost from United States Dollar (USD)
Table 1: Questions asked in participant questionnaires by component of team dynamics Role clarity Effective communication Idea acceptance
Presimulation questionnaire
Q1: Roles are defined clearly Q2: Comfortable seeking help from peers Q5: Ideas are valued Q3: Problems are presented clearly Q4: Understand the thresholds for communication
Daily participant evaluation
Q1: You understood your role Q3: Problems were presented clearly Q6: Ideas were valued Q2: Others understood roles Q4: Understood the thresholds for communication
Q5: Overall communication during exercise Postsimulation questionnaire
Q1: Roles are more clearly defined Q3: More comfortable seeking help from peers Q8: Ideas are valued more Q2: More likely to define roles Q4: More comfortable expressing ideas to supervisor
Q5: More comfortable speaking up in a crisis Q6: More likely to use closed‑loop communication Q7: Higher understanding of thresholds for communication
1‑month follow‑up Q1: Roles are clearer Q3: More comfortable seeking help from peers Q2: How often are roles defined Q4: More comfortable expressing ideas to supervisor
Q5: How often is closed‑loop communication used
Table 2: Presimulation questionnaire data Question asked Median score (IQR) Roles are clearly defined 2 (1‑2) Comfortable seeking help from peers 1 (1‑1) Problems are presented effectively 2 (2‑2) Understand thresholds for communication 1 (1‑2) Ideas are valued 2 (1‑2) Knowledge base 2 (2‑3)
1: Strongly agree/excellent, 2: Agree/good, 3: Neutral/fair, 4: Disagree/ poor, 5: Strongly disagree/very poor. IQR: Interquartile range
Table 3: Daily participant questionnaire data Component assessed Median score (IQR) P*
Day 1 (n=15)
Day 2 (n=7)
Day 3 (n=7)
You understood your role 1 (1‑2) 1 (1‑1) 1 (1‑1) 0.043 Others understood roles 2 (2‑3) 1.5 (1‑2) 1 (1‑2) 0.026 Problem presentation 2 (1‑2) 1 (1‑1) 1 (1‑1) 0.004 Communication thresholds 1 (1‑2) 1 (1‑1) 1 (1‑1) 0.020 Overall communication 2 (1‑3) 1 (1‑2) 1 (1‑1) 0.018 Ideas valued 2 (1‑2) 2 (1‑2) 1 (1‑1) 0.033
*Kruskal–Wallis statistical analysis. 1: Strongly agree/excellent, 2: Agree/ good, 3: Neutral/fair, 4: Disagree/poor, 5: Strongly disagree/very poor. IQR: Interquartile range
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500 to USD 2500, with negligible costs for reusable supplies and equipment maintenance. The mannequin is reusable and generally lasts for 3–5 years with regular use. Thus, the low cost, practical structure, and limited personnel time commitment make simulation a feasible tool for improving team dynamics in low-resource CICU environments.
The significant improvement in perceived team dynamics before and after simulation despite high baseline ratings suggests unrecognized potential for improvement of team dynamics. Participants may not have noticed the deficiencies in their team dynamics until they participated in simulation exercises. Thus, simulation training reveals deficiencies in team dynamics and motivates self-improvement. Importantly, participants reported that improvements in role clarity, closed-loop communication, and idea acceptance persisted beyond the immediate training period.
Analysis of simulation videos by the blinded reviewer revealed significant improvement in objective metrics of team dynamics and time to therapeutic intervention as simulation training progressed. As these data are less susceptible to subjective assessment and observer bias,
they provide important evidence to support the value of simulation training. Furthermore, since the interventions performed in simulation scenarios required complex interactions among team members, the improved time to response cannot simply be attributed to improvement in technical proficiency of individual participants.
Not only did simulation training have an immediate impact on team dynamics within the simulation environment, but participants reported sustained effect up to 1 month following training exercises. The sustained effect of simulation training has been reported in several studies, but the duration of effect is not known. The durability is dependent on multiple factors including staff turnover rate, experience level, and case mix complexity.
Although this study was not designed to determine the optimal frequency and duration of training programs, most participants indicated that training every 3–6 months would be optimal in the 1-month follow-up questionnaire. The current recommendation for frequency of training in centers that regularly perform simulation training is every 6 months.
The personnel required to conduct simulation training includes at least two nursing staff members, an intensivist or anesthesiologist, a surgeon, and an educator who provides simulation scenario and conducts feedback sessions. The necessary personnel can be located within the institution with appropriate training of the educator. An effective educator is critical to the success of the simulation training program. This individual should be a medical caregiver by training, either nurse or physician. Educator skills of facilitation, debriefing, and root cause analysis can be developed by attending several “train the trainer” courses that are available worldwide.
Table 4: 1‑month follow‑up questionnaire data Question Median response (IQR) Role clarity has improved because of simulation
1.5 (1‑2)
How often do you define roles in a crisis
2 (“often”) (2‑3)
You are more comfortable asking for help because of simulation
1 (1‑2)
You are more comfortable speaking up because of simulation
2 (1‑2)
How often do you use closed‑loop communication in a crisis
2 (“often”) (2‑3)
Simulation has improved communication overall
2 (1‑2)
Simulation has improved patient care overall
2 (1‑2)
How often do you think simulation should be repeated
3 (“once every 3 months”) (2‑4)
1: Strongly agree/excellent, 2: Agree/good, 3: Neutral/fair, 4: Disagree/ poor, 5: Strongly disagree/very poor. IQR: Interquartile range
Figure 1: Timeline of overall simulation course and daily simulation sessions including questionnaires and didactics
Figure 2: Schematic depicting simulator and monitor setup
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Figure 3: Time to response following perturbations in clinical status during simulated scenario and the frequency of closed‑loop communication and role clarity are plotted as a function of simulation trial number. Group 1 data are shown in closed circles and Group 2 data are shown in open circles. Group 1 demonstrated a significant increase in the frequency of closed‑loop communication (P < 0.05)
Figure 4: Participant responses to questions in the postsimulation questionnaire are given in bar graphs
Nursing empowerment is a key feature of improvement in team dynamics, especially in developing countries where steep hierarchy provides barriers to communication between nurses and physicians.[14,15] In this study, there was a trend toward nurses perceiving greatest improvement in components of team dynamics, suggesting a large potential for improvement among nurse participants. In environments where baseline
levels of nursing empowerment and engagement are low, simulation training may demonstrate the value of nursing engagement and autonomy. By demonstrating the value of nursing engagement and establishing an expectation of nursing empowerment, simulation may also serve to improve professional practice models in developing countries.
There are several important limitations to this study. First, this is an observational study without comparison to a control group. Second, the sample size for this study was relatively small, thus limiting the power of the study. Finally, since this is a single-center study, results may not be generalizable. A multicenter controlled study is necessary to confirm the utility of simulation training in such health-care settings.
CONCLUSIONS
Simulation training implemented in low-resource environments can result in significant improvements in communication among caregivers as well as decreases in response times to key resuscitation interventions. Furthermore, simulation fosters a culture of open communication and idea acceptance which are traditionally problematic in low-resource settings. Its feasibility and affordability make it a practical tool for improving team dynamics in low-resource medical environments, and its widespread application warrants further investigation.
Financial support and sponsorship
Funding for this study was provided internally by Children’s HeartLink and Boston Children’s Hospital.
Conflicts of interest
There are no conflicts of interest.
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5. Eppich WJ, Adler MD, McGaghie WC. Emergency and critical care pediatrics: Use of medical simulation for training in acute pediatric emergencies. Curr Opin Pediatr 2006;18:266-71.
6. Weinstock PH, Kappus LJ, Kleinman ME, Grenier B, Hickey P, Burns JP, et al. Toward a new paradigm in hospital-based pediatric education: The development of an onsite simulator program. Pediatr Crit Care Med 2005;6:635-41.
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8. Allan CK, Pigula F, Bacha EA, Emani S, Fynn-Thompson F, Thiagarajan RR, et al. An extracorporeal membrane oxygenation cannulation curriculum featuring a novel
integrated skills trainer leads to improved performance among pediatric cardiac surgery trainees. Simul Healthc 2013;8:221-8.
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Review of Economic Studies (2015) 82, 187–218 doi:10.1093/restud/rdu031 © The Author 2014. Published by Oxford University Press on behalf of The Review of Economic Studies Limited. Advance access publication 18 September 2014
Projects and Team Dynamics GEORGE GEORGIADIS
Boston University and California Institute of Technology
First version received November 2011; final version accepted June 2014 (Eds.)
I study a dynamic problem in which a group of agents collaborate over time to complete a project. The project progresses at a rate that depends on the agents’ efforts, and it generates a pay-off upon completion. I show that agents work harder the closer the project is to completion, and members of a larger team work harder than members of a smaller team—both individually and on aggregate—if and only if the project is sufficiently far from completion. I apply these results to determine the optimal size of a self-organized partnership, and to study the manager’s problem who recruits agents to carry out a project, and must determine the team size and its members’ incentive contracts. The main results are: (i) that the optimal symmetric contract compensates the agents only upon completing the project; and (ii) the optimal team size decreases in the expected length of the project.
Key words: Projects, Moral hazard in teams, Team formation, Partnerships, Differential games
JEL Codes: D7, H4, L22, M5
1. INTRODUCTION
Teamwork and projects are central in the organization of firms and partnerships. Most large corporations engage a substantial proportion of their workforce in teamwork (Lawler et al., 2001), and organizing workers into teams has been shown to increase productivity in both manufacturing and service firms (Ichniowski and Shaw, 2003). Moreover, the use of teams is especially common in situations in which the task at hand will result in a defined deliverable, and it will not be ongoing, but will terminate (Harvard Business School Press, 2004). Motivated by these observations, I analyse a dynamic problem in which a group of agents collaborate over time to complete a project, and I address a number of questions that naturally arise in this environment. In particular, what is the effect of the group size to the agents’ incentives? How should a manager determine the team size and the agents’ incentive contracts? For example, should they be rewarded for reaching intermediate milestones, and should rewards be equal across the agents?
I propose a continuous-time model, in which at every moment, each of n agents exerts costly effort to bring the project closer to completion. The project progresses stochastically at a rate that is equal to the sum of the agents’effort levels (i.e. efforts are substitutes), and it is completed when its state hits a pre-specified threshold, at which point each agent receives a lump sum pay-off and the game ends.
This model can be applied both within firms, for instance, to research teams in new product development or consulting projects, and across firms, for instance, to R&D joint ventures. More broadly, the model is applicable to settings in which a group of agents collaborate to complete a project, which progresses gradually, its expected duration is sufficiently large such that the agents discounting time matters, and it generates a pay-off upon completion. A natural example is the Myerlin Repair Foundation (MRF): a collaborative effort among a group of leading scientists in quest of a treatment for multiple sclerosis (Lakhani and Carlile, 2012). This is a long-term venture,
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progress is gradual, each principal investigator incurs an opportunity cost by allocating resources to MRF activities (which gives rise to incentives to free-ride), and it will pay off predominantly when an acceptable treatment is discovered.
In Section 3, I characterize the Markov perfect equilibrium (MPE) of this game, wherein at every moment, each agent observes the state of the project (i.e. how close it is to completion), and chooses his effort level to maximize his expected discounted pay-off, while anticipating the strategies of the other agents. A key result is that each agent increases his effort as the project progresses. Intuitively, because he discounts time and is compensated upon completion, his incentives are stronger the closer the project is to completion. An implication of this result is that efforts are strategic complements across time, in that a higher effort level by one agent at time t brings the project (on expectation) closer to completion, which in turn incentivizes himself, as well as the other agents to raise their future efforts.
In Section 4, I examine the effect of the team size to the agents’ incentives. I show that members of a larger team work harder than members of a smaller team—both individually and on aggregate—if and only if the project is sufficiently far from completion.1 Intuitively, by increasing the size of the team, two forces influence the agents’ incentives. First, they obtain stronger incentives to free-ride. However, because the total progress that needs to be carried out is fixed, the agents benefit from the ability to complete the project quicker, which increases the present discounted value of their reward, and consequently strengthens their incentives. I refer to these forces as the free-riding and the encouragement effect, respectively. Because the marginal cost of effort is increasing and agents work harder the closer the project is to completion, the free-riding effect becomes stronger as the project progresses. On the other hand, the benefit of being able to complete the project faster in a bigger team is smaller the less progress remains, and hence the encouragement effect becomes weaker with progress. As a result, the encouragement effect dominates the free-riding effect, and consequently members of a larger team work harder than those of a smaller team if and only if the project is sufficiently far from completion.
I first apply this result to the problem faced by a group of agents organizing into a partnership. If the project is a public good so that each agent’s reward is independent of the team size, then each agent is better off expanding the partnership ad infinitum. However, if the project generates a fixed pay-off upon completion that is shared among the team members, then the optimal partnership size increases in the length of the project.2
Motivated by the fact that projects are often run by corporations (rather than self-organized partnerships), in Section 5, I introduce a manager who is the residual claimant of the project, and he/she recruits a group of agents to undertake it on his/her behalf. His/Her objective is to determine the size of the team and each agent’s incentive contract to maximize his/her expected discounted profit.
First, I show that the optimal symmetric contract compensates the agents only upon completion of the project. The intuition is that by backloading payments (compared to rewarding the agents for reaching intermediate milestones), the manager can provide the same incentives at the early stages of the project (via continuation utility), while providing stronger incentives when the project is close to completion. This result simplifies the manager’s problem to determining the team size and his/her budget for compensating the agents. Given a fixed team size, I show that the manager’s optimal budget increases in the length of the project. This is intuitive: to incentivize
1. This result holds both if the project is a public good so that each agent’s reward is independent of the team size, and if the project generates a fixed pay-off that is shared among the team members so that doubling the team size halves each agent’s reward.
2. The length of the project refers to the expected amount of progress necessary to complete it (given a fixed pay-off).
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the agents, the manager should compensate them more, the longer the project. Moreover, the optimal team size increases in the length of the project. Recall that a larger team works harder than a smaller one if the project is sufficiently far from completion. Therefore, the benefit from a larger team working harder while the project is far from completion outweighs the loss from working less when it is close to completion only if the project is sufficiently long. Lastly, I show that the manager can benefit from dynamically decreasing the size of the team as the project nears completion. The intuition is that he/she prefers a larger team while the project is far from completion since it works harder than a smaller one, while a smaller team becomes preferable near completion.
The restriction to symmetric contracts in not without loss of generality. In particular, the scheme wherein the size of the team decreases dynamically as the project progresses can be implemented with an asymmetric contract that rewards the agents upon reaching different milestones. Finally, with two (identical) agents, I show that the manager is better off compensating them asymmetrically if the project is sufficiently short. Intuitively, the agent who receives the larger reward will carry out the larger share of the work in equilibrium, and hence she/he cannot free-ride on the other agent as much.
First and foremost, this article is related to the moral hazard in teams literature (Holmström, 1982; Ma et al., 1988; Bagnoli and Lipman, 1989; Legros and Matthews, 1993; Strausz, 1999, and others). These papers focus on the free-rider problem that arises when each agent must share the output of his/her effort with the other members of the team, and they explore ways to restore efficiency. My article ties in with this literature in that it analyzes a dynamic game of moral hazard in teams with stochastic output.
Closely related to this article is the literature on dynamic contribution games, and in particular, the papers that study threshold or discrete public good games. Formalizing the intuition of Schelling (1960),Admati and Perry (1991), and Marx and Matthews (2000) show that contributing little by little over multiple periods, each conditional on the previous contributions of the other agents, mitigates the free-rider problem. Lockwood and Thomas (2002) and Compte and Jehiel (2004) show how gradualism can arise in dynamic contribution games, while Battaglini, Nunnari and Palfrey (2013) compare the set of equilibrium outcomes when contributions are reversible to the case in which they are not. Whereas these papers focus on characterizing the equilibria of dynamic contribution games, my primary focus is on the organizational questions that arise in the context of such games.
Yildirim (2006) studies a game in which the project comprises of multiple discrete stages, and in every period, the current stage is completed if at least one agent exerts effort. Effort is binary, and each agent’s effort cost is private information, and re-drawn from a common distribution in each period. In contrast, in my model, following Kessing (2007), the project progresses at a rate that depends smoothly on the team’s aggregate effort. Yildirim (2006) and Kessing (2007) show that if the project generates a pay-off only upon completion, then contributions are strategic complements across time even if there are no complementarities in the agents’ production function. This is in contrast to models in which the agents receive flow pay-offs while the project is in progress (Fershtman and Nitzan, 1991), and models in which the project can be completed instantaneously (Bonatti and Hörner, 2011), where contributions are strategic substitutes. Yildirim also examines how the team size influences the agents’ incentives in a dynamic environment, and he shows that members of a larger team work harder than those of a smaller team at the early stages of the project, while the opposite is true at its later stages.3
This result is similar to Theorem 2(i) in this article. However, leveraging the tractability of my
3. It is worth pointing out, however, that in Yildirim’s model, this result hinges on the assumption that in every period, each agent’s effort cost is re-drawn from a non-degenerate distribution. In contrast, if effort costs are deterministic,
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model, I also characterize the relationship between aggregate effort and the team size, which is the crucial metric for determining the manager’s optimal team size.
In summary, my contributions to this literature are 2-fold. First, I propose a natural framework to analyse the dynamic problem faced by a group of agents who collaborate over time to complete a project. The model provides several testable implications, and the framework proposed in this article can be useful for studying other dynamic moral hazard problems with multiple agents; for example, the joint extraction of an exhaustible common resource, or a tug of war between two teams (in the spirit of Cao, 2014), or a game of oligopolistic competition with demand that is correlated across time (as in Section IV of Sannikov and Skrzypacz, 2007). Moreover, in an earlier version of this article, I also analyse the cases in which the agents are asymmetric and the project size is endogenous (Georgiadis, 2011). Secondly, I derive insights for the organization of partnerships, and for team design where a manager must determine the size of his/her team and the agents’ incentive contracts. To the best of my knowledge, this is one of the first papers to study this problem; one notable exception being Rahmani et al. (2013), who study the contractual relationship between the members of a two-person team.
This paper is also related to the literature on free-riding in groups. To explain why teamwork often leads to increased productivity in organizations in spite of the theoretical predictions that effort and group size should be inversely related (Olson, 1965; Andreoni, 1988), scholars have argued that teams benefit from mutual monitoring (Alchian and Demsetz, 1972), peer pressure to achieve a group norm (Kandel and Lazear, 1992), complementary skills (Lazear, 1998), warm- glow (Andreoni, 1990), and non-pecuniary benefits such as more engaging work and social interaction. While these forces are helpful for explaining the benefits of teamwork, this paper shows that they are actually not necessary in settings in which the team’s efforts are geared towards completing a project.
Lastly, the existence proofs of Theorems 1 and 3 are based on Hartman (1960), while the proof techniques for the comparative statics draw from Cao (2014), who studies a continuous-time version of the patent race of Harris and Vickers (1985).
The remainder of this paper is organized as follows. Section 2 introduces the model. Section 3 characterizes the MPE of the game, and establishes some basic results. Section 4 examines how the size of the team influences the agents’ incentives, and characterizes the optimal partnership size. Section 5 studies the manager’s problem, and Section 6 concludes. Appendix A contains a discussion of non-Markovian strategies and four extensions of the base model. The major proofs are provided in Appendix B, while the omitted proofs are available in the online Appendix.
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