Signalling

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Signalling
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Experiment game

• We ran an experiment on what is called the
  Beer-Quiche Game (Cho Kreps, 1987).
• Proposer has 2/3 chance of being strong.
• He can eat Beer or Quiche.
• Strong types like Beer. Weak types like Quiche.
• Responder can fight or flee. Responders dont
  want to fight a strong type.

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Signalling in the LabTreatment 1

• For a strong proposer, (Beer, flee)(Beer,
  fight)(Quiche, flee)(Quiche, fight).
• For a weak proposer, (Quiche, flee)(Quiche,
  fight)(Beer, flee)(Beer, fight).
• Strong chooses Beer and Weak chooses Quiche

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Signalling in the LabTreatment 1

• Responder now knows that Beer is the choice of
  the strong type and Quiche is the choice of the
  weak type.
• For Beer he flees, for Quiche he fights.

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Signalling in the LabTreatment 1

• So the equilibrium is
• For strong, (Beer, Flee)
• For weak, (Quiche, Fight)
• This is called a separating equilibrium.
• Any incentive to deviate?

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Signalling in the LabTreatment 1
32
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What did you do? In the last 5 rounds, there were
32 Strong and 13 Weak proposers
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Treatment 2.

• Can we have a separating equilibrium here?.
• If the proposer is weak, he can choose Beer and
  get 1.00 instead of 0.60.

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Treatment 2.

• Can choosing Beer independent of being strong or
  weak be an equilibrium?
• Yes! The responder knows there is a 2/3 chance of
  being strong, thus flees.
• This is called a pooling equilibrium.

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Treatment 2.
4
30
3
8

• Did we have a pooling equilibrium?
• In the last 5 rounds there were 34 strong
  proposers and 11 weak proposers.
• Do you think there is somewhat to help the
  pooling equilibrium to form?

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Treatment 2.
23
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3

• At Texas AM, the aggregate numbers were shown.
• In the last 5 periods, 23 proposers were strong
  and 17 weak.

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Signalling game

• Spence got the Nobel prize in 2001 for this.
• There are two players A and B. Player A is
  either strong or weak.
• Player B will chose one action (flee) if he knows
  player A is strong
• and another action (fight) if he knows player A
  is weak.
• Player A can send a costly signal to Player B (in
  this case it was to drink beer).

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Signal

• For signalling to have meaning,
• we must have either cost of the signal higher for
  the weak type.
• Or the gain from the action higher for the strong
  type.

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Types of equilibria

• Separating.
• Strong signal
• Weak dont signal.
• Pooling.
• Strong and weak both send the signal.

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Types of equilibria

• The types of player A are s and w.
• Let us normalize the value to fleeing as 0.
• The values are Vs and Vw.
• The cost to signalling (drinking beer) are Cs and
  Cw.
• We get a separating equilibria if Vs-Cs0 and
  Vw-Cw
• We get a pooling equilibria if Vs-CsVw-Cw
• We may also get a pooling equilibria if Vs-Cs0
  and Vw-Cw0 and there are enough s types.

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Treatment 2 Other pooling?.

• How about both proposers eat quiche and the
  responder flees? Is this an equilibrium?
• If responders think anyone who drinks Beer must
  be weak.
• Cho-Kreps introduce an intuitive criteria that
  says this does not make sense.
• Any proposer drinking Beer must be strong,
  because the weak type can only lose from doing so.

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Gift giving

• Gift giving can be wasteful. (Why not give ?)
• Basically, you get someone a gift to signal your
  intent.
• American Indian tribes, a ceremony to initiate
  relations with another tribe included the burning
  of the tribes most valuable possession,

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Courtship gifts.

• Dating Advice.
• Advice 1 never take such advice from an
  economist.
• Advice 2.
• Say that there is someone that is a perfect match
  for you. You know this, they just havent figured
  it out yet.
• Offer to take them to a really expensive place.
• It would only make sense for you to do this, if
  you knew that you would get a relationship out of
  it.
• That person should then agree to go.

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Valentines Day

• Who bought a card, chocolate, etc?
• We are forced to spend in order to signal that we
  really care.
• Say that you are either serious or not serious
  about your relationship.
• If your partner knew you were not serious, he or
  she would break up with you.
• A card is pretty inexpensive, so both types buy
  it to keep the relationship going.
• Your partner keeps the relationship since there
  is a real chance you are serious.
• No real information is gained, but if you didnt
  buy the card, your partner would assume that you
  are not serious and break up with you.

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Higher value and/or Lower Cost

• Higher value
• You buy someone a gift to signal that you care.
• Sending a costly signal means that they mean a
  lot to you.
• For someone that doesnt mean so much, you
  wouldnt buy them such a gift.
• Lower cost
• The person knows you well.
• Shopping for you costs them less.
• They signal that they know you well.

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Other types of signalling in the world

• University Education.
• Showing up to class.
• Praying. Mobile phone for Orthodox Jews
• Poker Raising stakes (partial).
• Peacock tails.
• Limit pricing.

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Homework Simplified Poker.
Assume the odds of a strong hand is 80. Find any
equilibrium. Is it signalling or pooling? Extra
hard what happens if it is 60?