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Moral Hazard & Mechanism Design

Learning Objectives

Risk taking ability

Moral hazard versus adverse selection

Mechanism design

The Principal-Agent problem

©Vidya Atal, Montclair State University

Risk Taking Ability

©Vidya Atal, Montclair State University

Risk versus Uncertainty

Taking risk is under your control, but uncertainty is not

One can take risk to manage uncertainty

Risk-taking ability differs individually

Risk-averse

Risk-neutral

Risk-loving

©Vidya Atal, Montclair State University

Risk Aversion

Payoff is value of money

More money better is increasing

Examples:

Risk aversion means

First two examples don’t satisfy this

Concave utility functions capture risk aversion

©Vidya Atal, Montclair State University

Levels of Risk Aversion

Consider

risk neutral

As gets closer to 0, risk aversion increases

©Vidya Atal, Montclair State University

Mechanism Design

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Example 1: Airline’s Price Discrimination Adverse Selection & Mechanism Design

Suppose 100 customers, 70 are tourists and 30 are business executives

If airline knows the type of each individual, then PE = 140 and PF = 300

Hence profit = (140 – 100)x70 + (300 – 150)x30 = 7300

©Vidya Atal, Montclair State University

Airline’s Price Discrimination continued…

But airlines don’t know the type of individual; they cannot force a business executive to buy a first class ticket

Device price structure so that business executives buy first class tickets and tourists buy economy class tickets

If PE = 140 and PF = 300, consumer’s surplus to a business executive from first class = 300 – 300 = 0, whereas from economy = 225 – 140 = 85

No one buys first class; airline’s profit = (140 – 100)x100 = 4000

©Vidya Atal, Montclair State University

Airline’s Price Discrimination continued…

Instead, design PF = 300 – 85 = 215 so that consumer’s surplus to a business executive from first class = 300 – 215 = 85, hence buys first class

Hence profit = (140 – 100)x70 + (215 – 150)x30 = 4750

First class ticket price can be raised only if economy class ticket price raised, say PE = 170 and PF = 245. But tourists would not buy; hence PE = 140

©Vidya Atal, Montclair State University

(Incentive Compatibility Constraint)

(Participation Constraint)

The Principal-Agent Problem

Moral Hazard & Mechanism Design

©Vidya Atal, Montclair State University

Adverse Selection vs. Moral Hazard

In adverse selection, the asymmetric information is regarding the player’s type (screening needed)

In moral hazard, the asymmetric information is regarding the player’s action (monitoring needed)

Mechanisms are designed by the principal (when possible) to enforce the desired action by the agent

©Vidya Atal, Montclair State University

less informed party

more informed party

©Vidya Atal, Montclair State University

Principal

Agent

Hires

Performs

Asymmetric Information

Adverse Selection

Asymmetric Information

Moral Hazard

Self

interest

Self

interest

The Principal-Agent Problem

Principal (CEO) is hiring Agent (software engineer)

Agent can put High effort or Low effort. If L, project is unsuccessful for sure and revenue to P is R=2. If H, project is successful with probability ½ and revenue to P is R=6

Payoffs for monetary wages :

A is risk averse: if high effort, and if low effort

P is risk neutral:

In the ideal world of full information, P knows whether A puts H or L

Hence offers contract “w=1 if H and w=0 if L,” which would be accepted by A because his outside option is 0

©Vidya Atal, Montclair State University

Principal-Agent Problem with Asymmetric Info

P is less informed about A’s effort exertion, so designs a bonus mechanism to ensure A exerts high effort

©Vidya Atal, Montclair State University

Expected Payoff & Profit Maximization

No bonus case:

Agent will always shirk, hence P will choose w to maximize (2-w) so that

This gives us and Principal’s payoff = 2

Incentive or Bonus Mechanism

P’s objective:

such that:

(Incentive Compatibility:– high type payoff more than low type payoff)

(Participation Constraint:– high type payoff more than outside option)

At optimality, the constraints hold with equality because P’s payoff is decreasing in w and b

Solving, we get the following contract: “ and if project successful”

Check that the contract will be accepted by A

Make sure that P wants to offer this contract, i.e., P’s payoff with bonus is more than without bonus:

Example 2: Highway Construction

Highway to be built by state’s contractor and government decides how many lanes (n)

Social value: , Contractor’s fee = F (includes per lane cost of $3B or $5B, depending upon soil condition)

Government’s objective:

If full information, government knows soil condition and chooses n to maximize if cost $3B/lane, or if cost $5B/lane

Hence

Highway Construction continued…

Asymmetric information: Contractor knows actual cost but government knows cost is low with probability 2/3

Government’s objective:

such that:

Participation constraints:

Incentive compatibility constraints:

(actually low cost type does not mimic high cost type)

(actually high cost type does not mimic low cost type)

Solving Highway Construction Problem

Combining 2(a) and 1(b), we get:

Hence 1(a) is automatically satisfied, so ignore it

Let’s ignore 2(b) for the time being and solve, then we can check if it is satisfied as well

Re-writing the remaining two constraints:

Government wants to pay the least fees so that the two constraints are satisfied, hence (Note that low cost contractor gets a premium for being honest)

Solving Highway Construction Problem

Re-writing government’s objective:

This gives

Check that constraint 2(b) is satisfied indeed and (V – F) > 0

	nL	FL	nH	FH
Complete Information	12	36	10	50
Asymmetric Information	12	48	6	30