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Chris Starmer. Day 4 - Experimental Games. TSU Short course in Experimental and Behavioural economics, 5-9 November 2012. 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:

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Chris starmer

Chris Starmer

Day 4 - Experimental Games

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


Route map
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
Preferences

Game theory

One of the main tools of modern econ analysis

Models strategic interaction through stylised ‘games’

e.g. prisoner’s dilemma……..


The background story
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
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

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 both1
Consequences for each depend on actions of both payoffs

  • 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
Interpreting Payoffs 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
Normal Form payoffs

  • Now represent the game in ‘Normal Form’

    • Matrix

    • One player selects rows

    • Other selects columns


Prisoner s dilemma
Prisoner’s dilemma payoffs

Player 2 - Marina

Silent

Confess

1,4

3,3

Silent

Player 1

- Rati

4,1

2,2

confess

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


What will be the outcome of this game
What will be the outcome of this game? payoffs

  • 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
What would you do? payoffs

Player 2 - the other prisoner

Silent

Confess

STAY SEATED

Silent

1,4

3,3

4,1

STAND UP

Confess

2,2

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


Now the game theory prediction

Now the game theory prediction payoffs

Very simple for this game


Game theoretic prediction
Game Theoretic Prediction payoffs

Player 2 - Marina

Dominant

Strategy

Confess

silent

1,4

3,3

silent

Player 1

- Rati

4,1

2,2

confess

Dominant

Strategy

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


Notice
NOTICE payoffs

Player 2 - Marina

Silent

Confess

1,4

Silent

3,3

Player 1

- Rati

4,1

2,2

Confess

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


3 cheers for rational choice theory
3 cheers for rational choice theory payoffs

  • 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
Real play payoffs

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

Player 2 - Marina

Silent

Confess

1,4

Silent

3,3

Player 1

- Rati

4,1

2,2

Confess


How do they escape the dilemma
How do they escape the dilemma? joint payoff

  • 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

Part 2

Next


2 repeated games
2. Repeated Games joint payoff

  • 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
Robert Axelrod’s (book) joint payoffThe 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
Axelrod’s Tournament joint payoff

  • 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
Round Robin joint payoff

  • 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
The winner joint payoff

  • Anatol Rapoport (Univ. Toronto)

  • Tit-for-Tat

    • first round: coop

    • subsequent rounds: copies opponents play in previous round


Why was tft successful
Why was TFT successful? joint payoff

  • 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
Why did nice rules do well? joint payoff

  • 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
Which Nice Rules Did Best? joint payoff

  • 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
Why is it good to be forgiving? joint payoff

  • 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
Axelrod’s advice for playing repeated PDs joint payoff

  • 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
Concluding Observations joint payoff

  • 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

Session 4 – Part 2 joint payoff

Social Preferences


People care about each others outcomes
People care about each others outcomes joint payoff

“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
Evidence joint payoff

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

    • The Ultimatum game


Ultimatum game
Ultimatum Game joint payoff

  • 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 prediction1
    Game theoretic prediction joint payoff

    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
    Stylised Facts from UG Expmts joint payoff

    • Play deviates (systematically) from GT predictions:

      • close-to-even splits are often proposed

      • ‘low’ offers often rejected


    Specific study g th schmidtberger schwarze 1982 jebo
    Specific Study joint payoffGüth, 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 g th schmidtberger schwarze 1982 jebo
    Ultimatum game experiments joint payoffGüth, Schmidtberger, Schwarze (1982, JEBO)

    • Results

    • “Naive” subjects

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

    • Mean offer: 37% of the pie

    • Experienced subjects

    • Mean offer: 32% of the pie

    • 2/21 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
    What happens when stakes rise? joint payoff

    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
    What accounts for this behaviour? joint payoff

    Two possible explanations:

    • Fairness, Altruism

    • Strategic concerns, fear of rejections

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


    Dictator versus ultimatum games
    Dictator versus Ultimatum Games joint payoff

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

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


    An application of social preferences

    An application of Social Preferences joint payoff

    Voluntary Contributions to Public Goods


    Public goods
    Public Goods joint payoff

    • (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
    Public Goods Experiments joint payoff

    • 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
    Public Goods Experiments findings joint payoff

    • 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
    Subsequent work on Public Goods joint payoff

    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
    Repeated Play in VCM joint payoff

    • 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
    The role of social sanctions joint payoff

    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’.


    Design fehr and g chter aer 2000
    Design joint payoff(Fehr and Gächter, AER 2000)

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

    2nd stage: punishment stage

    Each member learns contribution of others

    Can 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



    Cooperation and punishment fehr and g chter aer 2000
    Cooperation and punishment public good)(Fehr and Gächter, AER 2000)

    Punishment opportunities INCREASE contributions towards

    the socially optimal level


    Significance
    Significance public good)

    • 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
    Conclusions public good)

    • 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


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