UE 8: Moral Hazard in Teams

Question 1

What are the components of Holmström (1982)?

Answer 1

• A team 0f > 2 members
• Members take actions, ai, that cannot be directly observed (strategy set)
• Actions imply private (non-monetary) costs vi, which are differentiable, strictly convex, and increasing
• Combinations of actions produce a joint monetary outcome, x, that must be allocated, which is differentiable, concave, and strictly increasing
• A sharing function determines the share, si, of the output

Question 2

What is the question of Holmström (1982)?

Answer 2

Can joint output 𝑥 be allocated so that there exists a Pareto optimal Nash equilibrium of the non-cooperative game?

Question 3

What would be the implication of a Pareto optimal Nash equilibrium in Holmström (1982)?

Answer 3

That 𝑠′(𝑥(𝑎∗)) = 1

- The derivative of the sharing function of the outcome given an optimal action is 1

Question 4

Can a Nash EQ exist in Holmström (1982)?

Answer 4

No, as 𝑠′(𝑥(𝑎∗)) = 1 is matched with the fact that the addition of all the derivatives of the sharing function must also be 1 via the budget constraint, which is a contradiction.

It’s only possible if the balanced budget constraint is weakened.