Chris Starmer

TSU Short course in Experimental and Behavioural economics, 5-9 November 2012

Day 4 - Experimental Games

Route Map

Part 1:– Modelling social/strategic interaction as ‘games’

• Some basic ideas in game theory

– From theory to empirics• What people do and how to do well

Part 2:– Identifying Social Preferences– The impact of Social Preferneces

Preferences

Game theoryOne of the main tools of modern econ analysis

Models strategic interaction through stylised ‘games’

e.g. prisoner’s dilemma……..

The Background Story

• Two people arrested on suspicion of a crime– Police not enough evidence to convict

• Idea – place in separate cells (no communication)- Each has two options (confess or silent)- Consequences…………

Consequences for each depend on actions of both

• If both confess:– Each get Moderate/High sentence (6 years)

• If neither confess:– Each get Moderate/Light sentence (3 Years)

• If one confesses while other remains silent– Confessor – gets very light sentence (1 year)– Silent gets very harsh sentence (10 Year)

In game theory, analysis just requires the RANKING of payoffs

That is, we translate from the absolute material payoffs to ordinal rankings

Consequences for each depend on actions of both

• If both confess:

– Each get Moderate/High sentence (6 years) [2]• If both remain silent:

– Each get Moderate/Light sentence (3 Years) [3]• If one confesses while other remains silent

– Confessor – gets very light sentence (1 year) [4]

– Silent gets very harsh sentence (10 Year) [1]

Interpreting Payoffs

• These red numbers are called ‘utilities’

• They represent each player’s own ranking of the possible outcomes of the ‘game’

• For the game to be correctly specified, these ranking should include consideration of everything that the players care about– E.g. if there is ‘honour among thieves’ so they hate to

confess, this should be reflected in ranking (and might change the rankings on previous slide)

Normal Form

• Now represent the game in ‘Normal Form’– Matrix– One player selects rows– Other selects columns

Prisoner’s dilemma

3,3

2,24,1

1,4Player 1- Rati

Player 2 - Marina

confess

Silent

ConfessSilent

(utility) payoffs in each cell with Row (Rati) written first in each pair

What will be the outcome of this game?

• What does game theory predict rational players would do?

• What do ordinary people do in situations like this?

• Will look at both of these questions but first………..

What would you do?

3,3

2,24,1

1,4

Player 2 - the other prisoner

STAY SEATEDSilent

STAND UPConfess

ConfessSilent

To help you – I’ve highlighted your (row) payoffs in RED

Now the game theory prediction

Very simple for this game

Game Theoretic Prediction

3,3

2,24,1

1,4Player 1- Rati

Player 2 - Marina

confess

silent

silent Confess

Dominant Strategy

Dominant Strategy

(utility) payoffs in each cell with Row (Rati) written first in each pair

NOTICE

3,3

2,24,1

1,4Player 1- Rati

Player 2 - Marina

Silent

Confess

ConfessSilent

The predicted outcome is (Pareto) SUBOPTIMAL - at the predicted outcomes, both players are worse off than they could have been

3 cheers for rational choice theory

• This simple game demonstrates the power of rational choice analysis…..

• It captures a fundamental insight of social science.– It is a mistake to assume that individual pursuit of self-

interest fosters the good of all– Pursuit of rational self interest can lead to outcomes which

are worse for all than others available

• Maybe models many important social problems (e.g. pollution control, arms races etc.)

Real play

When real people play experimental games with payoffs structured so that they would be prisoner’s dilemma’s IF all they cared about was money payoffs they often manage to reach the pareto-superior outcome…….

In games with Money payoffs, people often reach the better joint payoff

3,3

2,24,1

1,4Player 1- Rati

Player 2 - Marina

Silent

Confess

ConfessSilent

How do they escape the dilemma?

• Happy ignorance?– They don’t understand the game

• Enlightened reasoning?– E.g. Schelling reasoning

• They have “social preferences”?– They don’t care just about the money– They care about each other’s outcomes

• Players think of the game as part of an ongoing social game

Next

Part 2

2. Repeated Games

• Would things be different if people play a PD game repeatedly?– Reputation building

• GT tells us: – If PD games is one shot no opportunity for

rational players to develop cooperative reputations

• Repeated Game: can be Much More Complex and support cooperative strategies

Robert Axelrod’s (book)The Evolution of Cooperation

• Cooperation emerges spontaneously in the world in surprising places– e.g. trench warfare

• Axelrod’s question– What’s the best strategy for playing the

repeated prisoner’s dilemma?

en.wikipedia.org/wiki/Evolution_of_cooperation

Axelrod’s Tournament

• Invited game theorists to participate in tournament– Repeated prisoner’s dilemma

• Each participant submitted a strategy– Strategy, specifies ‘Coop’ or ‘Not’ for each

round– can use history of moves to determine choice in

any round

Round Robin

• 14 entries submitted, all by ‘professionals’

• Strategies coded as computer programmes

• Every strategy played repeated PD against:– every other strategy– itself– random (plays coop/not with p=0.5)

• Each pairing played– 200 rounds– repeated 5 times (average performance)

The winner

• Anatol Rapoport (Univ. Toronto)

• Tit-for-Tat– first round: coop– subsequent rounds: copies opponents play in

previous round

Why was TFT successful?

• A single characteristic distinguished high from low-scoring strategies….

• Being ‘NICE’?

• NICE means;– don’t be the first to defect– cooperating in first round

• Large gap between average scores of nice and not-nice strategies

Why did nice rules do well?

• Because of the environment

• Nice rules score highly when they meet– (they cooperate all the way through)

• And,– there were enough nice rules around for them to

raise each other’s scores

Which Nice Rules Did Best?

• Most successful nice rules tended to be ‘FORGIVING’

• Forgivingness – is willingness to resume cooperation after the

other player has failed to cooperate.

• Notice: TFT is forgives rapidly– TFT resumes cooperation as soon as it observes

the other player doing so

Why is it good to be forgiving?

• Compare with another nice but non-forgiving strategy….

• TRIGGER– Cooperates until it observes non-cooperation– then will never cooperate again

• This strategy does: – well with other nice rules– But with non-nice rules, once a non-cooperative move

happens, there is never any future cooperation

Axelrod’s advice for playing repeated PDs

• Don’t be envious– don’t try to beat the other player– can only do this by actions which will undermine

cooperation and joint payoff max

• Don’ t be first to ‘cheat’• Reciprocate cooperation and cheating• Don’t be too clever!

– Cooperation is helped by people understanding your behaviour

Concluding Observations

• GT predicts the behaviour of real people (worryingly) well in some settings– e.g. one shot, high payoff.

• Cooperation may be more viable when there is repetition

– what it is optimal to do depends on the environment

Session 4 – Part 2

Social Preferences

People care about each others outcomes

“participants in experiments frequently choose actions that do not maximise their own monetary payoffs when those actions affect others’ payoffs. They sacrifice money in simple bargaining environments to punish those who mistreat them and share money with other parties who have no say in allocations” (Charness and Rabin, QJE 2002, p817)

Evidence

• Some of the early and most famous experimental evidence supporting this claim comes from studies using:

–The Ultimatum game

Ultimatum Game

• Two players have to divide a fixed pie p

• Player 1 (the proposer) proposes a division• (x, p-x) x = proposer’s share

• Player 2 (the responder) observes the offer and either accepts or rejects.

• If she accepts the agreed upon division is implemented

• If she rejects both players get nothing

Game theoretic prediction

Standard assumptions:

•Both players are rational, i.e. everyone maximizes only his/her monetary income

Standard analysis (‘Backward induction’)

•Player 2 will accept any positive offer

•So, Player 1 will offer the smallest possible positive amount to player 2

Stylised Facts from UG Expmts

• Play deviates (systematically) from GT predictions:

– close-to-even splits are often proposed

– ‘low’ offers often rejected

Specific StudyGüth, Schmidtberger, Schwarze (1982, JEBO)

• Pie size varied from 4 to 10 DM• Subjects were in one room, but no subject knew the

person with whom he/she was paired• Real monetary stakes

Two treatments• “Naive” (inexperienced) subjects• Experienced subjects: Same experiment one week

later with same subjects

Ultimatum game experiments Güth, Schmidtberger, Schwarze (1982, JEBO)

Results• “Naive” subjects

Modal offer: 50% of the pie (7 of 21)Mean offer: 37% of the pie

• Experienced subjectsMean offer: 32% of the pie2/21 offer 50%

Systematic deviation from game theoretic prediction

GSS conclude: Game theory is “of little help in explaining ultimatum game behaviour”

What happens when stakes rise?

Cameron (1999, Econ Inquiry) Experiments in Indonesia

pie = from Rupiah 5000 (≈ $ 2.5) to R200 000 (≈ $ 100)

R 200 000 ≈ 3 x average monthly expenditure

• Results:

• Offers approach 50/50 with increasing stakes

• Responders more willing to accept a given percentage in higher stakes games

What accounts for this behaviour?

Two possible explanations:

• Fairness, Altruism

• Strategic concerns, fear of rejections

• This has been investigated using ‘Dictator Games’………

Dictator versus Ultimatum Games

Forsythe, Horowitz, Savin and Sefton (Games and Economic Behavior, 1994)

Dictator Game:

Proposer decides on division (x, p-x), responder has no choice but to accept.

• If concerns with fairness fully explain behaviour, the distribution of offers should be the same in both games

Dictator versus Ultimatum Game Results:Source Fig 4.4. Forsythe, et al. 1994.

Results suggest UG behaviour reflects a mix of altruistic and strategic concerns

An application of Social Preferences

Voluntary Contributions to Public Goods

Public Goods

• (Pure) Public good– Once provided everybody benefits– Can’t exclude people from the benefit

• Examples:Street lights, National defense

• Standard economic analysis– PGs may not be provided by market because, self-

interested individuals will not pay– (free ride)

Public Goods Experiments

• Voluntary Contribution Mechanism– N Individuals; each allocated T tokens

– divide between ‘private’ vs ‘public’ account

• Public contributions raised by factor m• Each individual (i) receives payoff:

πi = T – ci + (m/N).(∑contributions)• with 1 < m < N

– full contribution (social optimum)

– zero contribution (individual optimum)

Public Goods Experiments findings

• Marwell & Ames (J. Pub Econ, 1981)– On average 40-60% contribution

– except economists • Most people are willing to contribute

than theory (as usually interpreted) predicts

Subsequent work on Public Goods

Lots of experimental research on PGs using VCM.

Two significant dimensions include experiments exploring:

– Repetition

– Role of social sanctions• Opportunity to punish ‘free riders’

Repeated Play in VCM

• When groups play the PG game repeatedly

• Contributions go down toward the game theory prediction (based on private money maximisation)

The role of social sanctions

Fehr and Gächter, (AER 2000)– a very influential experimental finding.

Used a repeated VCM but;– modified to allow group members to

sanction (i.e. punish) ‘free riders’.

50

51

Design (Fehr and Gächter, AER 2000)

2-stage game: 1st stage: standard Public good game

2nd stage: punishment stageEach member learns contribution of othersCan then assign punishment points

A punishment point costs the punisher 1 point and reduces the punished member’s payoff by 3 points.

• (Perfect stranger design)• Punishment is second order public good

• GT Prediction: no punishment, no contributions

52

Results: people do punish (even though it’s a costly public good)

53

Cooperation and punishment(Fehr and Gächter, AER 2000)

Punishment opportunities INCREASE contributions towardsthe socially optimal level

Significance

• Pattern replicated in MANY studies

• Many regard this finding (sanctions promote cooperation) as identifying an important mechanism that supports human cooperation.– May reflect psychological propensity to punish– That propensity supports the common good

• It has been influential in many disciplines:– Including sociology, politicital science, anthropology

and biology

Conclusions• Large literature exploring social preferences

• These studies point to the need for economic models to take account of ‘other regarding’ motives– May be more important than economists have

traditionally thought

• Experimental research in social preferences may be revealing insights into fundamental mechanisms that support human cooperation