Week 4- Social Preferences

Question 1

In game theory, what is an “equilibrium”

Answer 1

The set of “best” strategies players pick in trying to maximise their individual payoffs.

Question 2

What is Nash equilibrium?

Answer 2

An equilibrium in which each player’s action or strategy is optimal given the action of strategies of the other players ie no player can benefit by changing their strategy whilst the other players keep theirs unchanged.

Question 3

In a cheat/cooperate prisoners dilemma, what is the dominant strategy and the Nash equilibrium?

Answer 3

To cheat, making the Nash equilibrium (Cheat,Cheat).

Question 4

Is the (Cheat,Cheat” Nash Equilibrium Pareto efficient? Why/why not?

Answer 4

No, as it is Pareto dominated by (Cooperate, Cooperate)

Question 5

If we play Prisoners Dilemma 20 times, what is the Nash Equilibrium, and how can we see this?

Answer 5

It would still be (Cheat, Cheat) due to backwards induction.

Question 6

Which strategy won Axelrod’s 1980 tournament?

Answer 6

Not the Nash Equilirbium, but the “tit for tat” strategy.

Question 7

What was the “tit for tat” strategy?

Answer 7

Cooperate in Round 1, and then in later rounds mimick what the opponent had done in the previous round, rewarding co-operation and punishing cheating.

Question 8

What does Axelrod’s “reciprocal altruism” mean?

Answer 8

Basically means “I’ll be nice to you if you’re nice to me”, hence why tit for tat ends up being the Nash equilibrium, as 2 players co operating beat 2 players cheating.

Question 9

What did Andreoni and Miller (1993) observe in their study of repeated Prisoners Dilemma?

Answer 9

They observed widespread cooperation in initial rounds but this cooperation collapsed towards the final round.

Question 10

Why could Andreoni and Miller have observed this co operation at the start but not at the end?

Answer 10

Perhaps players were trying to build an altruistic reputation, which they would then cash in at the end, in what is called “rational irrationality”. Or players wanted to get a “warm glow” from co operating, and avoid a “cold prickle” from cheating.

Question 11

What are the three models of altruism and their equations?

Answer 11

• Pure Altruism- Ui=pi+αpj
• Duty- Ui=pi+α (α>0 if i cooperates)
• Reciprocal Altruism- Ui=pi+α (α>0 if i and j cooperate)

Question 12

Which 3 tests did Andreoni and Miller (1993) use to try and weed out the “rational irrational” people?

Answer 12

•”Strangers”- subjects are randomly paired each round so cannot build a reputation.
•”Partners”- where subjects play 10 rounds with a partner when they can build a reputation, but then are randomly reallocated
“Computer 50s”- subjecs have 50% chance of either playing 10 rounds with a computer which plays “tit for tat” or with a fellow subject.

Question 13

In the tests, what behaviour would be expect pure altruists to display in games “stranger” and “partner”?

Answer 13

We would expect a pure altruist to co operate equal amounts in both games.

Question 14

In the tests, what behaviour would be expect reputation builders to display in games “stranger” , “partner” and “computer 50”?

Answer 14

We would expect a reputation builder to co operate most in computer 50, the next most in partner, and least in stranger

Question 15

In the Ultimatum Game, what is the Nash Equilibrium offer?

Answer 15

£0.01

Question 16

In the ultimatum game, what happens to low offers and why is this strange?

Answer 16

They often get rejected, which is strange as it shows a preference for nothing over something- this is effectively reciprocal punishment instead of reciprocal altruism.

Question 17

How can we find out if proposers in the Ultimatum Game are altruistic or “rationally irrational”?

Answer 17

By removing the right for the responder to respond- creating the Dictator Game, where the Nash equilibrium is x=£0.

Question 18

What’s the Nash Equilibrium in the Public Good Game?

Answer 18

To keep all tokens private and to “free ride” off those who put their goods in the public pot, however this privately optimal strategy is socially inefficient.

Question 19

Why is there a decaying of cooperation in the Public Good Game?

Answer 19

• Perhaps players learn as they play that free riding is the individual optimal strategy.
• It may just be rational co operation at the start
• Perhaps people just get frustrated at other’s selfishness so act selfish themselves (frustrated kindness).

Question 20

What did Isaac and Walker (1988) find out?

Answer 20

In their 2 consecutive Public Good Games, people ended their first game generally more selfishly than they started game 2, suggestive of rational co-operation or a frustrated kindness.

Question 21

What is Andreoni’s regular condition?

Answer 21

This is just the standard Public Good Game

Question 22

What is the crucial factor of Andreoni’s rank condition?

Answer 22

The fact that the amount of money being paid out is fixed means that there is no incentive to be altruistic. the only way to increase your payoff is to get a higher payoff than other people.

Question 23

According to Andreoni’s experiment, about what percentage of all cooperative moves can be classified as kindness? What does this signify?

Answer 23

50% So therefore there are strong social and cultural propensities for kindness and generosity.

Question 24

What do the results imply about the effects of learning as the game goes on?

Answer 24

The results imply that learning didn’t have much of an effect, and was dominated by frustrated attempts at kindness.

Question 25

How did Fehr and Gachter (2000) try and prevent this decay?

Answer 25

By removing anonymity, and allowing players (at a cost to themselves) to place penalties on other players.

Question 26

Why does the idea of punishing something go against standard game theory?

Answer 26

As it is costly to punish another player- so there should be no incentive to do so.

Question 27

What was the effect of adding punishment?

Answer 27

•Cooperation increased throughout the game!
•Free riders got punished, so many stopped free riding
However there was also some retaliatory punishments!