Cheap talk and counter-signalling

Question 1

what are cheap talk games

Answer 1

dynamic games of imperfect information where the informed part plays first (as before) but can send any signal for free

Question 2

what is counter-signalling

Answer 2

dynamic games of imperfect information that may lead to equilibria where the high types send no signal but the medium types do

Question 3

what is the technical difference between a signalling game and a cheap-talk game

Answer 3

they are similar except in a cheap talk game the signal can be produced at no cost

Question 4

in the job market signalling model what would a costless signal convey

Answer 4

in the job-market signalling model, a costless signal would convey no information

Question 5

in a cheap talk game why can there not be a separating equilibrium where low ability workers send el and earn a low wage and high ability workers send eh>el and earn a high wage

Answer 5

the low-ability workers would always deviate from el to eh since doing so costs nothing and allows them to earn the higher wage

Question 6

what is the structure of a cheap-talk game *

Answer 6

at least two player (generally a signal ‘sender’ and a signal ‘receiver’),
nature draws type t for sender,
sender observes type and chooses which signal e to send,
receiver observes signal e (but not type t) and chooses action a,
payoffs are us(t,a) for the sender and ur(t,a) for the receiver

Question 7

what is the difference between the payoffs in the cheap talk game compared with the signalling game

Answer 7

in cheap talk the payoffs do not directly depend on the signal e, instead they depend on the sender’s type and the receiver’s action,
in signalling game, the sender’s payoff does depend on the signal (education)

Question 8

what are the three assumptions necessary to have a separating equilibrium *

Answer 8

different sender types have different preferences over the receiver’s actions,
receiver’s payoffs depend on the sender’s type,
receiver’s preferences over actions are not completely opposed to the sender’s

Question 9

why is the cheap talk assumption ‘different sender types have different preferences over the receiver’s actions’ violated by the job market signalling model

Answer 9

both types of workers prefer the higher wages

Question 10

is the cheap talk assumption ‘receiver’s payoffs depend on the sender’s type’ usually verified

Answer 10

it is usually verified in standard signalling as well as in cheap talk games, if the receiver does not care about the sender’s type, there is no point sending information about it

Question 11

is the cheap talk assumption ‘receiver’s preferences over actions are not completely opposed to the sender’s’ verified

Answer 11

it is necessary to make communication truthful

Question 12

what are the features of a cheap talk game

Answer 12

sender is a worker who can be of high or low ability, t=th or t=tl,
receiver is a firm whose action consists in offering a high or low skilled job to the worker, a=ah or a=al,
worker can reveal his type (signal) truthfully or not, to the firm before being offered a job

Question 13

do the payoffs for cheap talk game depend on e

Answer 13

no, they depend on the sender’s type and the receiver’s action

Question 14

what are the payoffs for the receivers in cheap talk game

Answer 14

firm prefers to offer low skilled job to low ability and high skilled job to high ability so they get 1 if the type matches with the job and 0 if they are not the same (ie masquerading)

Question 15

what happens in the cheap talk game if all workers prefer to work in the high skilled job (w

Answer 15

all workers prefer to work in the high skilled job, the first assumption (different sender types have different preferences over the receiver’s actions) so all workers will claim to have the high ability and the firm will not believe it

Question 16

what happens in the cheap talk game if the low ability workers prefer the high skilled job and the high ability workers prefer the low skilled job (wz)

Answer 16

these preferences are in opposition with the firm’s, so the third assumption is violated (receiver’s preferences over actions are not completely opposed to the sender’s)

Question 17

for the cheap talk game, as long as the assumptions are satisfied (w>x and y

Answer 17

workers truthfully announce their ability to the firm,
if a worker declares he is of the high (resp low) type, the firm’s belief that this worker’s ability is high equals 1 (resp 0),
firm offers high-skilled job to workers who say they are high ability and low skilled job to workers who say they are low ability

Question 18

what is separating equilibria in the job market

Answer 18

the high types ‘sent more signal’ than the low type by choosing more education

Question 19

what is the main feature of counter-signalling

Answer 19

in addition to the signal, there is another source of information about individuals’ types,
the uninformed party has some noisy (that is, imperfect) information about worker’s types, and this information can be made more precise if she receives a signal

Question 20

what does noisy mean

Answer 20

imperfect

Question 21

how many senders do you need for counter-signalling

Answer 21

at least three (say a low, medium and high type)

Question 22

what is a counter-signalling equilibrium

Answer 22

such that the medium signal to separate themselves from the low type, while the high type choose not to signal, in order to separate themselves from the medium type

Question 23

why is it called counter-signalling

Answer 23

because the high type choose not to signal, in order to separate themselves from the medium type

Question 24

how is the counter-signalling game set out *

Answer 24

three types of worker high medium low,
all workers have a letter of recommendation from a previous employer that is freely observable by firms but not observable by workers (this is noisy additional source of info),
letter can be good or bad and is always bad for low types, always good for high and good or bad with equal probabilities for medium types,
in addition to the letter workers can send a signal by obtaining a professional qualification (costs for low but free for medium and high)

Question 25

what is the cost of obtaining the qualification for workers in the counter-signalling model

Answer 25

for low types it costs (300 in example),

it is free for medium and high ability workers (could also make cost slightly larger for medium than the high type)

Question 26

what is the pbe for the counter-signalling model

Answer 26

low ability and high ability do not signal (do not obtain qualification),
medium ability workers signal (obtain qualification),
check by calculating expected payoff

Question 27

how come in counter-signalling model even though neither medium nor high types have to pay for education it is not profitable for medium to masquerade as high and not signal

Answer 27

because if you calculate expected payoff then it will be lower to masquerade as a high because of the 0.5 probability that there is a bad letter of recommendation (back 15)