(1.3) Bystander effect

Question 1

1

Define the individual bystander effect

Answer 1

the conjecture that the bigger the audience witnessing a crime, the less individuals in the audience are motivated to act against the crime (provide a public good)

Question 2

1

What model do we use for the bystander effect?

Answer 2

Kitty Genovese model

Question 3

1

What economic issue does the bystander effect relate to?

Answer 3

Free-riding off public goods

Question 4

Is it possible in bystander effect for individual prob of helping to fall, but collective prob to increase?

Answer 4

yes

Question 5

4

Give an example where individual probability of helping decreases with crowd size, but collective probability increases

Answer 5

• 1 person alone: 0.4 chance of helping
• 10 people: 0.1 each
• Probability no-one helps: 0.9^10 = 0.35 (2dp)
• Probability someone helps in 10 person game = 0.65

Question 6

3

What are major assumptions we make under the Kitty Genovese case?

Answer 6

• the crime itself is not affected by the size of the crowd that witnessed it
• Rationality
• Assumptions around primitives

Question 7

3

Take these primitives for a Kitty Genovese problem
* Players: 38
* Actions: call or not call
* Payoffs:
* cost of calling = 1
* benefit if someone calls: x > 1

What is the best outcome, second best, worst?

Answer 7

• Best: someone else calls: X
• Second best: you call: X - 1
• No-one called: 0

Question 8

2

What does rationality mean for players?

Answer 8

• people respond optimally to their beliefs
• to maximise payoffs

Question 9

2

What does a Nash Equillibrium require?

Answer 9

• (1) players are rational
• (2) Correct beliefs

Question 10

2

What do correct beliefs mean for players?

Answer 10

• beliefs about players match their actual behaviour
• So can successfuly form probability of possible action

Question 11

4

Take these primitives for a Kitty Genovese problem
* Players: n
* Actions: call or not call
* Payoffs:
* cost of calling = 1
* benefit if someone calls: x > 1

Find the payoff from calling

Answer 11

• Conjecture probability p that each neighbour calls the police
• You definitely call police with p = 1
• Regardless of what other players do, will get payoff X-1
• Payoff = 1(X-1) + 0(X-1) = X -1

Question 12

5

Take these primitives for a Kitty Genovese problem
* Players: n
* Actions: call or not call
* Payoffs:
* cost of calling = 1
* benefit if someone calls: x > 1

Find the payoff from not calling

Answer 12

• Conjecture probability p that each neighbour calls the police
• P(someone else calls) = 1 - P(no-one else calls)
• P (no-one else calls) = (1-p)^n-1
• P(someone else calls) = 1 - (1-p)^n-1
• Payoff from not calling = X x (1-(1-p)^n-1) + (0)(1-p) = X x (1-(1-p)^n-1)

Someone else =/= someone

Question 13

3

Find the NE solution be for the kitty genovese problem (hint: mixed NE)?

Need to do maths

Answer 13

• NE solution where player indifferent between calling and not calling
• X - 1 = (1-(1-p)^n-1) x X
• p = 1 - (1/x)^(1/n-1)

Question 14

1

What is the probability that someone calls (not ‘someone else’)?

Answer 14

1-(1-p)^n

Question 15

2

What are the policy implications of the bystander effect?

Answer 15

• Reduce costs - 911 system
• Change social values - increase X parameter

Question 16

2

In the Kitty Genovese model, what are the endogenous variables?

Answer 16

• Each bystander’s strategy
• Probability someone helps (aggregate behaviour)

Question 17

4

In the Kitty Genovese model, what are the exogenous variables?

Answer 17

• Benefit of calling
• Cost of calling
• Number of bystanders
• Social value of X