Lecture3- game theory

Question 0

What does game theory analyse?

Answer 0

Decision-making processes when there is more than one decisionmaker where each agent’s pay off possibly depends on the actions taken by other agents

Question 1

Game theory aka

Answer 1

Interactive decision theory/ multiperson decision theory

Question 2

Game theory=

Answer 2

Study of strategic decision making

Question 3

Studies of the dictator game

Answer 3

Mikula 1972

Question 4

Describe the dictator game

Answer 4

One player is given an amount of money to split between him and another player

Question 5

Results of dictator game from meta-analysis by Christoph Engel

Answer 5

Most give some to the other, on average 28%. Only 40% keep the money. Result is thought to reflect altruism.

Question 6

Describe the ultimatum game

Answer 6

One player is given an amount of money to splits between him and another player. So if the other accepts they both get the money, otherwise nobody gets anything

Question 7

Studies of the ultimatum game

Answer 7

Guth et al 1982

Question 8

Ultimatum game results

Answer 8

On average, the first player gives 40%. Offers below 25% on most likely to be rejected. Guth et al 1982

Question 9

UG compared to DG

Answer 9

Possibility of rejection increases mean givings from 28% to 40%

Question 10

What happens if a person experienced rejection in the previous round of the ultimatum game?

Answer 10

The amount accepted increases by 7% (Fehr and Fischbacher, 2003)

Question 11

what is altruistic punishment?

Answer 11

When a person is unfair to somebody else and they get punished too

Question 12

What does altruistic punishment mean

Answer 12

It means that individuals punish even though it is costly for them, and yields no material gain

Question 13

Describe a situation of altruistic punishment

Answer 13

A and B participate in a dictator game. Third-party C observes how much A gives to B; C can spend a proportion of his endowment on punishing A. (Fehr and Fischbacher 2004)

Question 14

What did Fehr and Fischbacher show with altruistic punishment ?

Answer 14

50 to 60% of the third parties punish selfish deviations from the equal split. Suggest that giving more than 50% in the dictator game violates a fairness norm

Question 15

Altruistic punishment

Answer 15

The less the dictator gives to the recipient, the more the punishers spend on punishment

Question 16

What drives altruistic punishment?

Answer 16

Emotions - and a group game, when one player invested much less than the other players these other players became angry with the free rider (Fehr and Gartner, 2002)

Question 17

Altruistic punishment continued

Answer 17

The more unfair a free rider was the more angry the others became. People not participating in this game show the same emotions. Thus, emotions may help us to behave in a cooperative manner towards others, including people to whom we are not genetically related. This can explain human cooperation.

Question 18

Camerer and Weigelt (1988)- trust game

Answer 18

Player 1 gives money to experimenter and experimenter gives money to player 2. How much money with player 2 give back to player one

Question 19

Trust game results

Answer 19

Despite the incentive to cheat, more than 50% of player 2s transfer money back. Transfers are higher the more player 1 transferred initially. Shows altruistic rewarding

Question 20

Reputation (Novak and Sigmund, 1998)

Answer 20

In this game, one subject plays a donor and the other a recipient. The donor can help the recipient. The recipient’s reputation is established by his decisions in a previous public goods game, in which the donor does not participate.

Question 21

Reputation cont

Answer 21

The recipients’ reputation in the public goods game are an important determinant for the donors’ decision. Donors punish the recipients by being less likely to help when the recipients defected in the public goods game. Recipients behave better in the public goods game when they knew that the donor was informed of their behaviour.

Question 22

Describing interactive games. The payoff matrix

Answer 22

A simple interactive game. Two players can raise either they’re left or right hand. If they raise the same hand, they get one coin. If they raise different hands, they get nothing. A simple way to describe the games and losses in this game is the payoff matrix.

Question 23

The payoff matrix continued

Answer 23

This matrix representation is called the normal form in game theory. For two players, one player is the row player, and the other, the column player. Each row or column represents a strategy and each box represents the payoffs to each player for every combination of strategies.

Question 24

The payoff matrix continued

Answer 24

Generally, such games are solved using the concept of a Nash equilibrium

Question 25

The Nash equilibrium

Answer 25

In game theory, a set of strategies is a Nash equilibrium If no player can do better by unilaterally changing his or her strategy.

Question 26

The Nash equilibrium described

Answer 26

Amy and John are in Nash equilibrium if Amy is making the best decision she can, taking into account John’s decision, and John is making the best decision he can, taking into account Amy’s decision.

Question 27

Example of the Nash equilibrium

Answer 27

Coordination game. John and Amy want to go out together, but prefer different things. John likes football, Amy likes a movie. Nash equilibrium. Both go to the movie or both go to football. Osborne and Rubinstein 1994

Question 28

Prisoner’s dilemma (Flood and Dresher, 1950)

Answer 28

Two criminals arrested. Each prisoner is given two options. Either to confess his crime or to deny it. If Bill confesses but Al denies, then Bill serves as testimony against Al and Bill goes free, while I’ll gets full term of three years. Same vice versa.

Question 29

Prisoners dilemma cont

Answer 29

If both confess, both get two years each as there is evidence against both. If both deny, they get one year each.

Question 30

Prisoners dilemma using payoff matrix

Answer 30

Best if both confess. If bill confesses, confessing Al gets 2 years and denying Al= 3 years. If Bill denies confessing Al gets 0 years, denying Al gets 1 year

Question 31

Why do individuals choose “deny” in the prisoners dilemma?

Answer 31

Because they co-operate to get the best outcome for both. This is not the rational outcome from a self-interested point of view.

Question 32

Modelling the Cold War (Majesky, 1984) using prisoners dilemma

Answer 32

Payoff matrix of health and defence. Chose defence as best payoff in short term but may change in long term