1. Asymmetric Information
Chapter 17
Asymmetric Information
© 2006 Thomson Learning/South-Western

2. Asymmetric Information
In a game with uncertainty, asymmetric information refers to the information that one player has but the other does not.

3. Principal-Agent Model
Principal: offers contract in a principal-agent model.
Agent: performs under terms of the contract in the model.
Moral-hazard problem: when agent’s actions benefit the principal but the principal does not directly observe the actions—hidden actions.
Adverse-selection problem: something intrinsic is known to only one party—hidden type or hidden information.

4. Table 17-1: Applications of the Principal-Agent Model
Agent’s private information
Principal
Agent
Hidden action
Hidden type
shareholders
manager
effort, executive decisions
managerial skill
manager
employee
effort
job skill
patient
doctor
effort, unnecessary procedures
medical knowledge, severity of condition
student
tutor
preparation, patience
subject knowledge
monopoly
customers
quality of fabrication
valuation for good
health insurer
Insurance purchaser
risky activity
preexisting condition
parent
child
delinquency
moral fiber

5. Effort Choice Under Full Information
In Figure 17-1, if shareholders could specify the manager’s effort in a contract, they would choose the level e* producing the highest joint surplus.
In upper panel, e* corresponds to the greatest distance between gross profit and manager effort cost.

6. FIGURE 17-1: Effort Choice Under Full Information
Manager
effort cost
Gross profit,
cost
Gross profit
(45-degree line)
Manager
effort
Marginal gross profit,
marginal cost MC MP
Manager
effort e*

7. Incentive Schemes—Moral Hazard
Lines S1, S2, and S3 correspond to various incentive contracts in Figure 17-2.
The slope of the incentive scheme is also called its “power”.
It measures how closely linked the manager’s pay is with firm performance.

8. FIGURE 17-2: Incentive Contracts
Manager
pay
S3 (high power,
45-degree line)
S2 (moderate power)
S1 (constant wage)
Gross
profit

9. Manager Equilibrium Effort Choice
The manager’s effort choice is given by the intersection of marginal pay and marginal effort cost in Figure 17-3.
The marginal pay associated with constant wage scheme S1 leads to no effort.
Effort increases in the power of the incentive scheme.

10. FIGURE 17-3: Manager Equilibrium Effort Choice
Marginal pay,
marginal cost MC S3
Marginal
pay schemes S3 S3
Manager effort e0 e1
e1 = e*

11. Manager Equilibrium Effort Choice
Incentive contract S3 turns out to be equivalent to having the shareholders sell the firm to the manager.
If gross profit depends on random factors in addition to the manager’s effort, then tying the manager’s pay to gross profit will introduce uncertainty into the manager’s pay.
Shareholders must balance the benefits of incentives against the cost of exposing the manager to too much risk.

12. Manager’s Participation Decision
By fixing the slope of the incentive scheme in Figure 17-4, the intercept of the scheme determines the manager’s participation decision.
Shareholders will choose the lowest intercept subject to having the manager participate.

13. FIGURE 17-4: Manager’s Participation Decision
pay S3 S2 S1
Gross
profit

14. Profit-Maximizing Bundle with One Consumer Type—Adverse Selection
In Figure 17-5, a monopolist chooses the bundle q* maximizing the consumer’s and monopolist’s combined surplus.
This can be found in the upper panel as the greatest distance between gross consumer surplus and the total cost curves.
Or, in the lower panel by the intersection of the marginal surplus and marginal cost curves.

15. FIGURE 17-6: Profit-Maximizing Bundle with One Consumer Type
Monopolist’s
total cost
Surplus,
cost
Gross consumer
surplus of representative
consumer GCS
Quantity in bundle/
quality of unit
Marginal
surplus,
marginal
cost A MC B MS
Quantity in bundle/quality of unit q*

16. FIGURE 17-6: Comparing Gross and Ordinary Consumer Surplus
Price
($/shirt) A 15 B E 7 d
Quantity
(shirts) 20

17. Two Consumer Types, Full Information
Facing a high-value and low-value consumer in Figure 17-7, the monopolist chooses bundles given by the intersection between each type’s marginal consumer surplus and marginal cost.
The high type receives a larger bundle qH than the low type, qL

18. FIGURE 17-7: Profit-Maximizing Bundles with Full Information About Two Consumer Types
Marginal
consumer
surplus,
marginal cost C A MC D B
MCSH
MCSL
Quantity in bundle/
quality of unit qL qH

19. Two Consumer Types, Asymmetric Information
The menu of bundles from Figure 17-7 reproduced in Figure 17-8, would not be incentive compatible.
The high-value consumer would gain surplus equal to the area of region C’ by purchasing the qL-unit bundle meant for low-value consumers rather than the qH-unit bundle.

20. FIGURE 17-8: Full Information Solution is Not Incentive Compatible Under Asymmetric Information
Marginal
consumer
surplus,
marginal cost C’ C” A MC D B
MCSH
MCSL
Quantity in bundle/
quality of unit qL qH

21. Example: Insurance Industry
Insurance for car theft with some areas of high probability that a car will be stolen and some other areas thefts are quite rare.
Suppose the insurance company offer the insurance based on the average theft rate.
Only people lives in the high-risk areas will buy the insurance—adverse selection.
Market outcomes are typically less efficient in the presence of the adverse-selection problem.

22. Signaling
The player with private information can take the first action and thereby signal something about his or her type.
The first player makes a move called a signal since it is observed by the second player. Based on the information provided by the signal, the second player updates his or her beliefs about the first player’s type. Then the second player chooses his or her move and the game ends.

23. Spence Education Model
Spence’s education model, named after Michael Spence, who received the Nobel Prize in economics for developing it.
The game tree for the Spence signaling game is shown in Figure Nature moves first, choosing the worker’s skill, low or high, with probability ½ each. The worker observes his or her skill and then makes the decision to get an education or not.

24. Figure 17-10: Spence Signaling Game in Extensive Form.
High talent Probability ½
Low talent Probability ½ . .
Worker
Worker .
None
Education . .
Education
None .
Firm
Firm
Firm
Firm
(Worker payoff = competitive wage – c,
Firm Payoff – zero expected profit)
(Worker payoff = competitive wage,
Firm Payoff – zero expected profit)

25. Equilibrium of Signaling Games
Signaling games often have multiple equilibria, and that is true in this game.
Separation equilibrium
Each type chooses a different action in a signaling game.
Pooling equilibrium
All types choose the same action in a signaling game.