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Strategic interaction and prosocial behaviour (Games of social interaction…
Strategic interaction and prosocial behaviour
Pro-social behaviour
A host of different and disparate concepts and motives
Cooperation, coordination, altruism, fairness, positive reciprocity, negative reciprocity, trust, trustworthiness…
Many ramifications in: economics, psychology, neuroscience, biology, business, marketing management, sociology, political science, philosophy, ethics, international studies, military studies…
We study pro-social economics through games. This is a specific approach to studying behavioural economics
these sets of specific games model specific aspects of pro-social behaviour. These are all ways of formally modelling different aspects of pro-social behaviour
These games are tapping into different perspectives and nuances of pro-social behaviour. The games are designed to assess different behaviours
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Games of social interaction
Trust Game
(Berg et al. 1995)
player 1: trust
player 2: trustworthiness, positive reciprocity
•Player 1 (Sender):Has an endowment of £10 and chooses how much to invest
•Investment is multiplied by 3
•Player 2 (Receiver):Decides how much of multiplied investment to give back to player 1, keeping the rest
Only Nash equilibrium (moving backward): Player 2 keeps everything, Player 1 invests 0
•Positive reciprocity
•On average Senders invest 50% (5 invest all)
•Average amount repaid is 95% of what invested
•But wide dispersion: half repaid nothing
Public Good Game
(Fehr and Gachter, 2000) Cooperation
The basic game
•4 players, each endowed with 20 tokens
•Choose an x to keep from[0, 20], giving the rest to a group project (public good)
•Payoffs: x + (project*1.6)/4
•Only Nash equilibrium: Everyone gives 0
Ultimatum Game
player 1: fairness, anticipation of negative reciprocity
player 2: anticipation of negative reciprocity
When one player moves first and its a sequential movement, this is an ultimatum game. The outcome of these games need to be considered differently.
Player 1 has £30, and can go 2 things. Can propose to split the £30 (equally) or can keep 25 and give 5. Player 2 then can either accept or reject the offer. If he accepts then he walks away with either 5 or 15. If player 2 rejects the offer, both players walk away with nothing. Accepting any offer should be the best solution. £15 each is best outcome for player 2. However, if player 1 chooses to split the money 25, 5, they will recieve less. But whatever happens, they will recieve more than 0 if they accept.
If player 1 accepts the rational point of view from player 2, then the most rational thing for player1 to do would be an unequal split, as this would most benefit player 1.
Further..
Player 1 (Proposer):Choose an allocation, splitting 30 between him and other (continuous strategy space)
Player 2 (Responder):“Accept” allocation, or “reject” and both get 0 (2 actions)
from the perspective of player 2, 1p is better than 0, and so should accept the offer. So should player one do this offer???
Player 1 keeps 29.99, player 2 accept
Do subjects play NE???
But what actually happens, when people are asked to play the ultimatum game (1p v 29.99£), player 2 would reject this offer..
If the game is unfair, people would rather walk away with nothing than keep a smaller proportion than the other person...Guth et al. (1982), Roth et al. (1991)
Dozens of replications for UG. Typically:
•Proposers offer $4-5 out of $10 on average.
•Responders reject offers of $2 or less half of the time.
Costly punishment of unfair behaviour: negative reciprocity
•Responders reciprocate unfair behaviour
•By harming the person who treated them unfairly
•At a substantial cost to themselves
•Provided that unfair Proposer is harmed more
Prisoners Dilemma
Coordination
The outcome that is effecting the prisoner is dependent on the decision of the other player. In many other situations, when you make a decision the outcome of the decision only depends on what youre doing, but here it is entirely dependent on the other person. This is arguably relevant in all the pro-social behaviour situations.
there are 2 strategies B is to stay quiet A is to confess
If they both confess, the police can convict both prisoners and they get 5 years. Not v desirable outcome
Prisoner 1 confesses and 2 stays silent. The police know the crime was done so put 2 in prison for 10 years and reward 1 with freedom immediately (and vice versa)
If they both stay quiet, they walk away with a mild punishment (1 year)
Strategy A is always the dominant strategy because it can give lower chances of going to prison for longer.
So if both play the dominant strategy (A and A), 5 years in prison each
Apply NE...
Dictator Game
Altruism
Player one is asked to split £30.
Player 2 decides nothing.
Player 1, rationally, should offer zero.
There is a proportion of people offering a positive amount- giving something. The behaviour of player 1 in the dictator game has been described as altruist.
(Kahneman, et al, 1986); Forsythe et al. 1994); Hoffman et al. 1996)
Theories..
Game theory
Based on RATIONAL decision making --> what is optimal for the player to do?
•A theory of ‘strategic’ decision-making
•Outcomes depend on what others do as well
•Games played by rational players
•Analysis of optimal strategies
•Equilibrium is a central concept
History..
First modern game theory papers: Emile Borel, John von Neumann, 1920s
Foundational game theory book: “The theory of games and economic behavior”, von Neumann and Morgenstern (1944)
In 1951 John Nash proves the existence of at least one Nash equilibrium in any finite game
In 1994, Nobel Prize in Economics to Nash, Harsanyiand Selten
In 2007 Hurwicz, Maskin, Myerson, in 2012 Lloyd-Shapley, Roth
Basic elements of a game
Players
Rules: everyone knows strategies and payoffs
Outcomes: combination of strategies
Payoffs: utility over consequences
STRATEGY
Behavioural game theory
• How people ‘do’ play versus ‘should’ play
• Also, allows to test too bold, too vague, or too many predictions of GT
• Using experiments!
game theory on its own is completely agnostic on the way that real players would play that game. Game theory gives the optimal solution. Behavioural game theory is concerned with HOW do people ACTUALLY play these games.
Types of games
•Cooperative vs. non-cooperative
•Simultaneous vs. sequential(or dynamic)
•Finite vs. infinite
•Discrete vs. continuous
•With complete information vs. incomplete information
•With perfect information vs. imperfect information
•Zero-sum vs. non-zero-sum
When one player moves first and its a sequential movement, this is an ultimatum game. The outcome of these games need to be considered differently.
Pure strategies:
deterministic Mixed strategies: probabilistic
we focus on PURE: The player can only choose between one strategy or the other in a deterministic way. We are specifically looking at pure strategies games. You either confess or stay quiet, these are the only 2 options.
How to solve a game..
Is there a dominant strategy?
You consider a game and first of all you look at the number and see if theres a strategy that is always a dominant strategy. This would be a rational way of playing the game. If you dont see a dominant strategy, you look at strategies that can be eliminated
Can a dominant strategy be elimiated? if not need to work out best response..
Apply Nash equilibrium
mutual best responses
•Given what the other does, I cannot do better…
•No-one has incentive to move away
•Both players best-react to each other
The stag hunt game
Stag is the dominant response for both player 1 and 2. But if player 2 plays rabbit, then it is best to respond rabbit aswell.