Lecture3- game theory Flashcards
What does game theory analyse?
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
Game theory aka
Interactive decision theory/ multiperson decision theory
Game theory=
Study of strategic decision making
Studies of the dictator game
Mikula 1972
Describe the dictator game
One player is given an amount of money to split between him and another player
Results of dictator game from meta-analysis by Christoph Engel
Most give some to the other, on average 28%. Only 40% keep the money. Result is thought to reflect altruism.
Describe the ultimatum game
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
Studies of the ultimatum game
Guth et al 1982
Ultimatum game results
On average, the first player gives 40%. Offers below 25% on most likely to be rejected. Guth et al 1982
UG compared to DG
Possibility of rejection increases mean givings from 28% to 40%
What happens if a person experienced rejection in the previous round of the ultimatum game?
The amount accepted increases by 7% (Fehr and Fischbacher, 2003)
what is altruistic punishment?
When a person is unfair to somebody else and they get punished too
What does altruistic punishment mean
It means that individuals punish even though it is costly for them, and yields no material gain
Describe a situation of altruistic punishment
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)
What did Fehr and Fischbacher show with altruistic punishment ?
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
Altruistic punishment
The less the dictator gives to the recipient, the more the punishers spend on punishment
What drives altruistic punishment?
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)
Altruistic punishment continued
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.
Camerer and Weigelt (1988)- trust game
Player 1 gives money to experimenter and experimenter gives money to player 2. How much money with player 2 give back to player one
Trust game results
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
Reputation (Novak and Sigmund, 1998)
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.
Reputation cont
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.
Describing interactive games. The payoff matrix
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.
The payoff matrix continued
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.
The payoff matrix continued
Generally, such games are solved using the concept of a Nash equilibrium
The Nash equilibrium
In game theory, a set of strategies is a Nash equilibrium If no player can do better by unilaterally changing his or her strategy.
The Nash equilibrium described
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.
Example of the Nash equilibrium
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
Prisoner’s dilemma (Flood and Dresher, 1950)
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.
Prisoners dilemma cont
If both confess, both get two years each as there is evidence against both. If both deny, they get one year each.
Prisoners dilemma using payoff matrix
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
Why do individuals choose “deny” in the prisoners dilemma?
Because they co-operate to get the best outcome for both. This is not the rational outcome from a self-interested point of view.
Modelling the Cold War (Majesky, 1984) using prisoners dilemma
Payoff matrix of health and defence. Chose defence as best payoff in short term but may change in long term
