Course 6 - Multitask (Multidimensional) & Multiagent moral hazard

Multitask and Multiagent Moral Hazard

Explores how the principal-agent problem becomes more complex

• when agents handle multiple tasks or

• when multiple agents are involved

Multitask Moral Hazard

Situation goes beyond typical trade-off between providing incentives & managing risk-sharing bc:

• Agent must allocate their effort across different tasks

• Effectiveness of incentives for 1 task can impact how much effort agent puts into other tasks

Multitask Moral Hazard - Key insights

1. Neglect of Less-Incentivized Tasks:

   When an agent faces high-powered incentives (significant rewards) for some tasks but not others, they are likely to focus more on the incentivized tasks, potentially neglecting other important responsibilities.

2. Conflicting Tasks Should Be Avoided:

   It’s problematic if an agent = responsible for tasks that conflict with one another

3. Equally Observable Tasks:

   To ensure balanced efforts, agents should work on tasks that = equally observable

Holmström & Milgrom Model (1991)

Standard model by Holmström and Milgrom analyzes situations where an agent performs n ≥ 2 tasks (ai).

Each task ai​ produces an outcome qi​, represented as qi = ai + ϵi​, where:

• ϵi = random parameter following a normal distribution

The randomness (uncertainty) = characterized by a variance-covariance matrix (Σ), capturing variance of each task’s outcome & correlation between them

Cost of Effort: The agent's effort cost function is ∑ciai^2 + δ∏ai​, where δ ≥ 0 indicates the interaction between efforts on different tasks

=> A higher effort in 1 task increases MC of effort in other tasks

Holmström & Milgrom Model (1991) - Main Results

1. Effort Allocation & Incentives:

   Increasing effort on 1 task raises the MC of other tasks, strong incentives for 1 task may draw effort away from other tasks

2. Incentives Design: Incentives for a specific task can be adjusted in 2 ways:

   • Directly rewarding the task

   • Reducing incentives for other tasks, effectively lowering the opportunity cost of focusing on the target task

3. Reduced Observability:

   If the observability of 1 task decreases, the optimal incentives for that task decrease. Consequently, the optimal incentives for other tasks also decrease

Moral Hazard in teams (multiple agents)

When principal deals with multiple agents, each agent's actions may influence the outcomes for others, creating a more complex incentive environment.

Principal must consider both the individual behavior of agents & their interactions

Moral Hazard in teams (multiple agents) - Key Issues

principal must design contracts that consider the strategic behavior of agents. Agents may either:

• Cooperate: When agents work together, they may benefit from each other’s efforts.

• Compete: They may compete for rewards, which could result in actions like sabotage or unhealthy competition.

• Free-Ride: Agents might try to reduce their effort, hoping to benefit from the work of others, especially when outcomes are shared among team members.

Holmström (1982)

Study shows that achieving optimal effort level requires a budget-breaking mechanism

Bc of this "budget breaker" = introduced to ensure each agent receives full marginal benefit of their efforts, overcoming the free-riding problem.

Budget breaker

Compensates agents upfront &

Adjusts payments based on the observed output

→ Agents' efforts can be aligned with optimal level even when their individual contributions ≠ directly observable

Relative Performance Evaluation

principal compares agents' performances, which can help mitigate common risks that affect all agents equally (e.g., market downturns) by evaluating each agent’s relative contribution

→ RPE is best when common shocks are significant and when agents do not need to cooperate closely

Advantages of RPE

• It insures risk-averse agents against external shocks that affect all of them similarly

Disadvantages of RPE

• It can lead to competitive behavior among agents, such as attempts to undermine each other’s performance (sabotage), which can be counterproductive.