Strategy thinking

Xoxoxoo

09AdverseSelection.pptx

Home >Business & Finance homework help >Economics homework help >Strategy thinking

Adverse Selection

Market Failure, Perfect Bayes’ Equilibrium, Signaling and Screening

Learning Objectives

The Market for Lemons

Perfect Bayes’ Equilibrium

Bayes’ rule to update belief

Pooling and Separating PBE

A lot of examples including Job Market Signaling

©Vidya Atal, Montclair State University

Adverse Selection

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

If an insurance policy costs 5₵ for every $ of coverage, then it attracts all the people who know their risk is higher than 5% (and some additional risk averse people)

Attracting an unfavorable, or adverse, group of people

©Vidya Atal, Montclair State University

Adverse Selection & Market Failure

The Market for “Lemons” (1970)

©Vidya Atal, Montclair State University

George Akerlof

The Market for “Lemons” (1970)

Private used car market for, say, 2010 Honda Element

Could be in truly excellent condition (call peach)

Buyer’s valuation - $16000; Seller’s valuation - $12000

Could be in bad condition that cannot be checked in usual regular inspection (call lemon) – seller’s private information

Buyer’s valuation - $6000; Seller’s valuation - $3000

Buyers value more than sellers, so it is efficient to be traded

Assuming limited amount of sellers and a lot of buyers

Hence with symmetric information (i.e., buyers can find out the car’s condition), PP = $16000 and PL = $6000, and all cars will be sold

©Vidya Atal, Montclair State University

Market for Lemons and Asymmetric Information

Note that p ≥ 12000

Lemon seller won’t sell if p < 3000

Peach seller won’t sell if p < 12000

Also, expected payoff of buyer ≥ 0

f∙(6000 – p) + (1 – f)∙(16000 – p) ≥ 0

16000 – 10000f ≥ p

Combining, we get f ≤ 0.4

©Vidya Atal, Montclair State University

If more than 40% of the used cars are lemon, then peach market fails and bad cars drive good cars out of the market

Nash Equilibrium Concepts

		Timing of the game
		Simultaneous Move	Sequential Move
Information type	Complete
	Incomplete

©Vidya Atal, Montclair State University

Pure and Mixed Strategy Nash Equilibrium

Subgame Perfect Nash Equilibrium (SPE)

Bayesian Nash Equilibrium (BNE)

Perfect Bayes Equilibrium (PBE)

Perfect Bayes Equilibrium

Bayes’ Rule - Pooling and Separating Equilibrium

©Vidya Atal, Montclair State University

Bayes’ Rule and Updated Belief

Initial belief (p)

Updated (conditional) belief (q)

Conditional upon receiving a gift from player 1, player 2’s updated belief that 1 is a friend

where and are the probabilities that the friend and enemy types of player 1 choose to give a gift

©Vidya Atal, Montclair State University

Perfect Bayes Equilibrium

Separating PBE

Different types of the player select different action

Pooling PBE

Different types of the player select the same action

©Vidya Atal, Montclair State University

A Perfect Bayes Equilibrium in a game is

a list of strategies, one for each player,

and a list of beliefs, one for each information set of the less-informed player,

such that the strategies are sequentially rational given the beliefs about the types of players

and less-informed players update their beliefs using Bayes’ Rule whenever possible

Example 1: Perfect Bayes Equilibrium

Separating with NFGE:

q = 0

2’s best response is R

But if 2 plays R, then 1’s best response is NFNE

Hence not a PBE

Separating with GFNE:

q = 1

2’s best response is A

But if 2 plays A, then 1’s best response is GFGE

Hence not a PBE

©Vidya Atal, Montclair State University

Example 1: Perfect Bayes Equilibrium (continued)

Pooling with GFGE:

q = p

iff p ≥ 0.5

2’s best response is A if and only if p ≥ 0.5 and R when p ≤ 0.5

But if 2 plays R, then 1’s best response is NFNE, hence not a PBE

If 2 plays A, then 1’s best response is GFGE

Hence when p ≥ 0.5, there is a PBE in which q = p and (GFGE, A) is played

©Vidya Atal, Montclair State University

Example 1: Perfect Bayes Equilibrium (continued)

Pooling with NFNE:

Bayes’ rule cannot be applied

Start with any value of

1’s best response is NFNE only when 2 plays R

2’s best response is R if and only if q ≤ 0.5

Hence there is a PBE in which q ≤ 0.5 and (NFNE, R) is played

©Vidya Atal, Montclair State University

Algorithm to find Perfect Bayes Equilibrium

Start with a pooling or separating strategy for player 1

Separating when the types of the player behave differently, pooling when the types behave the same

If possible, calculate updated beliefs using Bayes’ Rule

If Bayes’ rule cannot be used (when denominator is zero), then arbitrarily select an updated belief checking different potential values using steps 3 and 4

Given the updated beliefs, calculate player 2’s optimal strategy

Check whether player 1’s strategy is a best response to player 2’s strategy. If so, you have a Perfect Bayes Equilibrium

Example 2

Is there a separating equilibrium?

Yes: (LH, OI) with q = 1

Is there a pooling equilibrium?

(1 – q)

Exercise 1

Is there a separating equilibrium?

Is there a pooling equilibrium?

Yes: (LL, OI) with q = 0.4

(1 – q)

Exercise 2

Is there a separating equilibrium?

Is there a pooling equilibrium?

Job Market Signaling (1973)

Education adds value

Prospective employers pay a premium for hiring a well-trained, intelligent labor

Education has another important role in the marketplace

An academic degree is a sign of quality to the extent that highly productive people may be more likely than less productive people to attain higher degrees (gross generalization)

Degrees may serve as signaling mechanisms

Michael Spence

Example: Job Market Signaling

Education is costly

Cost for H is 4 and for L is 7

Is there a pooling equilibrium?

Yes: (NN’, CC’) with p = 1/3 and q ≤ 0.4

Example: Job Market Signaling continued…

Is there a separating equilibrium?

Yes: (EN’, MC’) with p = 0 and q = 1

The only way for the high type to get the managerial job is to signal her type by getting education

Exercise: Beer or Quiche Game

Is there a separating equilibrium?

Does there exist a pooling equilibrium where the wimp drinks beer as well?

Yes: (BB, NF) with m = 0.1 and n ≥ 0.5

(1 – m)

(1 – n)