Signalling

1
Signalling
Often a player wants to convey his private
information to other players. It might be
information about his own payoffs (My costs are
low, so I can profitably undercut your price) or
about another players (If you hire me, your
payoffs will be high because I am so
hard-working) A SIGNAL is an action that a
player takes to credibly convey to other
players some information that he has but they do
not. For the signal to work, it must be more
costly if the player is a liar than if he is
telling the truth. Also, it must not be too
costly for the truthful player, or he will
prefer to keep his information private.

2
Definitions

• Suppose there are two types of sellers, good
  (high quality) and bad (low quality). A
  particular seller shows up in front of a buyer.
• ADVERSE SELECTION.
• The good type of seller leaves the
  market to sell somewhere else where his quality
  can get a higher price. The bad type remains in
  this market.
• SIGNALLING.
• The good type of seller demonstrates his
  type by doing something (the signal) too costly
  for the bad type to want to imitate.
• SCREENING.
• The buyer offers to pay the seller more
  if the seller does something (the signal) too
  costly for the bad type to want to do.

3
Game Trees

4
Education As Signalling

• Nature chooses 60 percent of workers to have High
  ability, with marginal products of 200, and 40
  percent to have low ability, with marginal
  products of 100.
  
• Each worker chooses whether or not to get a
  diploma. The diploma costs 120 for the
  low-ability type, and 60 for the high- ability
  type.
• Employers compete with each other to hire
  workers. They cannot observe ability directly.
  They chooses wages of N for workers without a
  diploma and D for workers with a diploma.
  
• This is an example from John Macmillan's book,
  Games, Strategies, and Managers.

5
A Separating Equilibrium

• Low-ability workers choose not to get diplomas.
  
• High-ability workers choose to get diplomas.
  
• Employers offer N 100 and D200.
  
• Payoff(High, Diploma) 200 -60 140.
• Payoff(High, No Diploma) 100 -0 100.
  
• Payoff(Low, Diploma) 200 -120 80.
• Payoff(Low, No Diploma) 100 -0 100.
• Employers all earn zero profits. (If one employer
  could get more productivity from workers, then
  that firm would hire all the workers at the
  equilibrium wages and make positive profits.)
• This is an example from John Macmillan's book,
  Games, Strategies, and Managers.

6
A Pooling Equilibrium

• Low-ability workers choose not to get diplomas.
• High-ability workers choose not to get diplomas.
  
• Employers offer N 160 and D160.
• Payoff(High, Diploma) 160 -60 100.
• Payoff(High, No Diploma) 160 -0 160.
• Payoff(Low, Diploma) 160 -120 40.
• Payoff(Low, No Diploma) 160 -0 160.
• Employers all earn zero profits. (If one employer
  could get more productivity from workers, then
  that firm would hire all the workers at the
  equilibrium wages and make positive profits.)
• (Note that D200 would still maintain the
  equilibrium)
• There is no high-signal pooling equilibrium in
  this game.
• This is an example from John Macmillan's book,
  Games, Strategies, and Managers.

7
SCREENING

• Suppose we keep everything the same, except we
  say that the cost of the diploma is 30 for the
  high-ability workers and 120 for the low-ability.
• There is still a pooling equilibrium in which
  neither type of worker acquires a diploma, and
  the wages are ND160 and a separating
  equilibrium in which HIGHs get diplomas, LOWs do
  not, and N200, D100.
• Suppose we start in the pooling equilibrium of
  the signalling game, but one employer is allowed
  to move first, offering an (N,D) pair. If that
  employer offers N100 and D195, he will attract
  all the HIGH workers, who will get diplomas, and
  none of the LOW workers.
• In this SCREENING game, in which one or more
  employers move before the workers decide whether
  to acquire diplomas, the separating equilibrium
  is the only equilibrium.

8
Education Story Lessons

• Not being able to distinguish different types of
  workers results in adverse selection.
  
• Signalling can result in a separating equilibrium
  in which high ability workers are paid more, but
  must pay for a costly signal.
  
• It is essential that the signal be costlier for
  the low-ability worker than for the high-ability
  worker. Otherwise, signalling will fail.
  
• If nobody expects signalling to work, it won't.
  No worker will acquire education, and that will
  be self-confirming, because no employer will want
  to pay workers with diplomas a higher wage. All
  workers will be pooled'' with the same low
  wage.
• If an employer can move first, before workers
  make their education decisions, then he may be
  able to break out of pooling by offering higher
  wages for educated workers. This is called
  screening''.

9
Strikes as Signals

• Suppose all unions like money and job security,
  and hate strikes, but some hate strikes more than
  others, because there are two types of unions
  
• Type 1 Likes Money Best. Risk Loving. High wages
  are most important, strikes are not so bad.
  
• Type 2 Likes Security Best. Risk -Averse. High
  wages are not so important, but strikes are very
  bad.