Signalling

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

don’t want to fight a strong type.

Signalling in the Lab:Treatment 1

Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $2.00, $1.25 $1.20, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $2.00, $0.75 $1.20, $1.25

• 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

Signalling in the Lab:Treatment 1

Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $2.00, $1.25 $1.20, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $2.00, $0.75 $1.20, $1.25

• 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.

Signalling in the Lab:Treatment 1

Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $2.00, $1.25 $1.20, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $2.00, $0.75 $1.20, $1.25

• So the equilibrium is

• For strong, (Beer, Flee)

• For weak, (Quiche, Fight)

• This is called a separating equilibrium.

• Any incentive to deviate?

Signalling in the Lab:Treatment 1

Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $2.00, $1.25 $1.20, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $2.00, $0.75 $1.20, $1.25

What did you do?

In the last 5 rounds, there were 32 Strong and 13 Weak proposers

13

32

Treatment 2.Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $1.40, $1.25 $0.60, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $1.40, $0.75 $0.60, $1.25

• Can we have a separating equilibrium here?.

• If the proposer is weak, he can choose Beer and get $1.00 instead of $0.60.

Treatment 2.Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $1.40, $1.25 $0.60, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $1.40, $0.75 $0.60, $1.25

•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.

Treatment 2.Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $1.40, $1.25 $0.60, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $1.40, $0.75 $0.60, $1.25

•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?

30 4

8

3

Treatment 2.Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $1.40, $1.25 $0.60, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $1.40, $0.75 $0.60, $1.25

•At Texas A&M, the aggregate numbers were shown.

•In the last 5 periods, 23 proposers were strong and 17 weak.

23

3

14

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).

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.

Types of equilibria

• Separating.– Strong signal– Weak don’t signal.

• Pooling.– Strong and weak both send the signal.– (or Strong and weak both don’t send the

signal.)

Types of equilibria

• Player A is the proposer and B the responder.• The types of player A are s and w.• Let us normalize the value to A when B fights to 0.• The values to A when B flees are Vs and Vw.• The cost to signalling (drinking beer) are Cs and Cw.• We get a separating equilibria if Vs-Cs>0 and Vw-Cw<0.• We get a pooling equilibria if Vs-Cs<0 and Vw-Cw<0 (no

one signals).• We may also get a pooling equilibria if Vs-Cs>0 and Vw-

Cw>0 and there are enough s types.– For this to happen, there must be enough s types such that the

expected payoff of B is higher fleeing than fighting.

Treatment 2: Other pooling?.Payoffs: Proposer, Responder

Flee Fight

Beer (Strong) $1.40, $1.25 $0.60, $0.75

Quiche (Strong) $1.00, $1.25 $0.20, $0.75

Beer (Weak) $1.00, $0.75 $0.20, $1.25

Quiche (Weak) $1.40, $0.75 $0.60, $1.25

•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.

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 tribe’s most valuable possession,

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 haven’t 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.

Valentine’s 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 didn’t buy the

card, your partner would assume that you are not serious and break up with you.

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 doesn’t mean so much, you

wouldn’t 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.

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.

Homework: Simplified Poker.Payoffs: Player A, Player B

Fold Call

Raise (Strong) $1.00, -$1.00 $2.00, -$2.00

Fold (Strong) -$1.00, $1.00 -$1.00, $1.00

Raise (Weak) $1.00, -$1.00 -$2.00, $2.00

Fold (Weak) -$1.00, $1.00 -$1.00, $1.00

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%?