1 economics 776 experimental economics first semester 2007 topic 4: public goods assoc. prof....

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Economics 776Experimental Economics

First Semester 2007Topic 4: Public Goods

Assoc. Prof. Ananish ChaudhuriDepartment of Economics

University of Auckland

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Public Goods

• Public goods (social or collective goods) are goods that are non-rival in consumption and/or their benefits are non-excludable.

• Public goods have characteristics that make it difficult for the private sector to produce them profitably (market failure).

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The Characteristics of Public Goods

• A good is non-rival in consumption when A’s consumption of it does not interfere with B’s consumption of it. The benefits of the good are collective—they accrue to everyone.

• A good is non-excludable if, once produced, no one can be excluded from enjoying its benefits. The good cannot be withheld from those that don’t pay for it.

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Examples of Public Goods

• Fire Service

• Police

• National Defense

• Highways

• Public Parks

• Environment

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Problems of Cooperation

• Cooperative hunting and warfare (important during human evolution)

• Exploitation of common pool resources

• Clean environment

• Teamwork in organizations

• Collective action (demonstrations, fighting a dictatorship)

• Voting

6

Problems of Cooperation

• Basic economic problem– Cooperative behavior has a positive

externality.– Hence, social marginal benefit is larger than

private marginal benefit – Results in under-provision of the public good

relative to the efficient level.

7

A Generic Voluntary Contributions Mechanism / Public Goods Game

• Group of 4 players• Each of them have $5• Can contribute to either a private account or a

public account• Money put in the private account remains

unchanged• Money contributed to the public account

doubled and redistributed equally among group members

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• Analogous to a n-person Prisoner’s Dilemma

• Social optimum is for each player to invest all $5 into the public account

• A total of $20 which gets doubled to $40 • Redistributed equally gets $10 for each

player• 100% return on investment

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• Dominant strategy is to free-ride• Suppose I contribute $1 into the public

account, but no one else does• $1 gets doubled to $2• Redistributed equally gets $0.50 for each

group member• I lose $0.50 while other players (who have

not contributed anything) gain $0.50

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• Individual rationality suggests that no player has an incentive to contribute

• Thus an individual participant has no incentive to contribute

• This game has been used extensively to look at issues involving voluntary contributions to a public good

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A Basic Design

• Group of n subjects.

• yi is endowment of player i.

• 2 investment possibilities– Private account– Public Account (proxy for the public goods)

• ci = contribution to the public good.

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A Basic Design

• Per period payoff to player i

– with 0 < < 1

• Simultaneous contribution decision.• One-shot game or finitely repeated game.• Average contribution in the group or contribution

vector as feedback.

n

jjiii ccy

1

)(

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Prediction

• If α < 1: ci = 0 is a dominant strategy• If nα > 1 surplus maximization requires ci = yi

• Typical example• n = 4• yi = 10• α = 0.5

– Either groups randomly re-matched for 10 periods (“stranger” design)

– Or stable group composition for 10 periods (“partner” design)

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Typical pattern of contributions in finitely repeated public goods game

Pattern of Contributions

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10

Rounds

Pe

rce

nt

co

ntri

bu

ted

Contribution

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Determinants of Voluntary CooperationIsaac and Walker (1988)

• Aim: Isolate effects of group size and the MPCR α.

• α measures the private marginal benefit, • nα the social marginal benefit.• Income from private account was private

information.• Income from group account (αΣci) was public

information.• 10 periods, public information• Information feedback at the end of each period:

sum of contributions and private income.

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Determinants of Voluntary CooperationIsaac, Walker, Thomas (1984)

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Results

•Table shows average contributions in percent

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Results

• Cooperation increases with MPCR for both n.• Cooperation increases with n if MPCR is low

(not when it is high).• Cooperation decreases with n if group benefit nα

constant.• Cooperation decreases over time, in particular in

treatments with low MPCR.• MPCR-effect is present in all periods.• Group size effect at low MPCR vanishes over

time.

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Communication & Voluntary Cooperation(Isaac & Walker 1988)

• n = 4, α = 0.3, two sequences with 10 periods each, partner design.

• Communication opportunities (C): Players can discuss what they want to do in the experiment.

• Treatments:– 1. C – NC, players have the same endowment.– 2. NC – C, players have the same endowment– 3. C – NC, asymmetric endowments.

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Results

• Start with C: High cooperation rates; also in the second NC-phase.

• Start with NC: Unraveling of cooperation in NC but after C rapid increase in cooperation.

• Asymmetric endowments partly undermine positive communication effects.

Interpretation:• If selfishness and rationality is common knowledge

communication should play no role.• Suggests that subjects have motives beyond self-interest• Keeping promises, sympathy, social approval• Conditional cooperation

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Why do people cooperate?

• Mistakes, initially they don’t understand that zero cooperation is a dominant strategy.

• Strategic cooperation (Kreps et al., JET 1982)• There are strategic (rational) and tit-for-tat players.• Strategic players cooperate (except in the final period) if

they believe they are matched with tit-for-tat players.• Strategic players mimic tit-for-tat players (i.e. they

cooperate) to induce other strategic players to cooperate.

• Social preferences– Altruism, “warm glow”, “efficiency”-seeking motives– Conditional cooperation, Reciprocity

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Why does cooperation decline over time?

• Mistakes – It takes time to learn to play the dominant strategy.

• Strategic cooperation if group composition is constant. (Reputation building)

• Social preferences– Subjects are conditionally cooperative and learn that

there are free-riders in the group.– As a response they punish other group members by

choosing lower cooperation levels.

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Discriminating between competingexplanations

• One-shot-game rules out strategic cooperation but it also rules out learning to play the dominant strategy.

• Partner-Stranger-Comparison (Andreoni 1988)– Partner: same group composition in all periods.– Stranger: random re-matching of subjects in every

period.– If partners cooperate more: support for strategic

cooperation hypothesis• Surprise restart: if subjects cooperate again after

a surprise restart the decline in cooperation cannot be explained with “learning to play the dominant strategy”.

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Miller and Andreoni (1991)

• Evolutionary interpretation of free riding in public goods game

• Payoff to player i

– I is the endowment– ci is player i’s contribution– m is the known MPCR– g is the group size– c (bar) is the average contribution– “g” times the average contribution gives total contribution

cmgcI ii

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• Suppose there are N types of strategies interacting in a population of fixed size

• Each strategy of type i always contributes ci dollars to the public good

• Let xit be the proportion of type i strategies in the

population at time t. • Then the expected payoff to an agent using

strategy type i ist

ijt

N

jjii cmgcIxcmgcI

1

where ct (bar) is the average contribution at time t

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• Replicator dynamics provide a natural algorithm for allowing the weights, xi

t to evolve over time

• The dynamics are given by

tt

tit

iN

j

tjj

iti

ti

cmgcI

cmgcIx

x

xx

1

1(1)

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Deriving the previous result

– Since cjxj is the weighted average of all contributions

cmgcI jj

jjjjjj xcmgxcIxx

cmgcIxcmgxcxIx jjjjjj

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• Proposition 1:• From Equation (1),

• The weights on those strategies that contribute less than the average increase and the average declines

1),(1

ti

ti

x

x

ast

i cc ),(

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• The average contribution will fall over time as – The weights on contributions below the

average increase– The weights on contributions above the

average decrease

• The system will converge asymptotically to the strategy that does the most free riding

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• As mg increases– the rate of adjustment slows– the decline in contribution slows

• Figures 1 and 2 are based on an initial population of 20 strategies distributed between giving 0% and 100%.– Figure 1 is based on a uniform distribution– Figure 2 illustrates a population that is concentrated

around 50%

• MPCR = 0.3

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Direct Evidence for Conditional Cooperation

(Fischbacher, Gächter & Fehr Econ Lett 2001)

• n = 4, MPCR = 0.4• One-shot game• Subjects choose

– An unconditional contribution– A conditional contribution, i.e., for every

given average contribution of the other members they decide how much to contribute.

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Direct Evidence for Conditional Cooperation

(Fischbacher, Gächter & Fehr Econ Lett 2001)

• At the end one player is randomly chosen. For her the contribution schedule is payoff relevant, for the other three members the unconditional contributions are payoff relevant.– A selfish player is predicted to always choose

a conditional contribution of zero.– Note that a selfish player may have an

incentive to choose a positive unconditional contribution if she believes that others are conditionally cooperative.

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Evidence of Conditional Cooperation (n = 88)

Source: Chaudhuri and Paichayontvijit (2005)

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Average Contr ibution of Other Group Members

Free Riders(16.2%)

WeakCooperators(7.4%)

ConditionalCooperators(61.8%)

Hump ShapedContribution(5.9%)

Overall Mean

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Results

• Unconditional cooperation is virtually absent.

• Heterogeneity:– Roughly half of the subjects are conditional

cooperators.– Roughly one third is selfish.– A minority has a “hump-shaped” contribution

schedule

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Results

• Question: Can the observed pattern of conditional cooperation explain the unraveling of cooperation?– Assume adaptive expectations. Subjects believe that

the other group members behave in the same way as in the previous period.

– This implies that over time the conditional cooperators contribute little although they are not selfish.

– This result holds qualitatively for any kind of adaptive expectations.

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Cooperation, Punishments and Social Norms

• A social norm is – a behavioral regularity that rests on a

common belief of how one should behave – and might be enforced by informal sanctions.

• Remark: In the case that there is no conflict between privately optimal behavior and the behavior prescribed by the norm there is nothing to enforce.

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A cooperation and punishment experiment (Fehr and Gächter, 2000)

• Stage 1: typical linear public goods design: – n = 4, α = 0.4.

• Stage 2: Punishment opportunity– Subjects are informed about each member’s

contribution.– Subjects can punish other group members at

a cost to themselves.– A punished subject could not lose more than

the first-stage income.

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A cooperation and punishment experiment

Two “partner” sessions:(1) no punishment – punishment (2) punishment – no punishmentEach part of the sequence lasted 10 periods.Subjects in the first part of the sequence did not know that there is a second part.

Three “Stranger” sessions: two times punishment – no punishment. Once no punishment – punishment.

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Predictions

• It is common knowledge that each subject is a money maximizer and rational:– No punishment– No contribution regardless of whether there is a punishment

opportunity.

• If common knowledge is absent, subjects in the partner treatment are able to build up a group reputation (“There are punishers in the group, hence it is better to cooperate”)– Partner: Cooperate and punish in early periods but stop

cooperating and punishing at least in the final period.– Stranger: no punishment and no cooperation.

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Alternative Views

• Part of the subjects have a preference for reciprocity. They reward nice and punish hostile behavior.

• The relevant reference point for the definition of kindness is “conditional cooperation”. Two variants:– If I cooperate the other members should cooperate as well.– The other group members’ average cooperation as a reference

point.• Conditional cooperation is perceived as nice. Free-riding

relative to the reference point is perceived as hostile and is, hence, punished.

• Punishment stabilizes cooperation in the group.

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Chaudhuri, Graziano and Maitra (2005) - The Inter-generational paradigm

• A group of 5 subjects are recruited in the lab and play the public goods game for 10 periods.

• After her participation, each agent is replaced by another, who plays the game for 10 periods again.

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The Inter-generational paradigm

• Advice from generation “t” subject given to “t+1” successor via free-form messages

• Payoffs span generations in the sense that payoff to a generation t player is equal to the sum of her payoff plus 50% of her successor’s payoff

• Incentives exist, therefore, to pass on intelligent advice

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Three Different Advice Treatments

• In the private advice treatment advice from generation “t” player is given only to her successor in generation “t+1”

• In the public advice almost common knowledge treatment advice from all players in generation “t” is given to all the players in generation “t+1”

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Three Different Advice Treatments

• In the public advice common knowledge treatment advice from all players in generation “t” is given to all the players in generation “t+1”and is also read aloud by the experimenter

• The advice treatments are compared to behavior in a control group – where we simply replicate a standard public goods game a number of times without generations or advice

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The Inter-generational Paradigm

• The contention is that previous experiments looking at a variety of social dilemmas may not be descriptive of what we see in the real world.

• In actual practice, games like the public goods game are played differently than the format depicted in previous experiments.

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• When someone goes to play these games, they have access to the wisdom of the past in the sense that predecessors, or at least immediate predecessors, of this person are available to give her advice.

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• Conventions passed from one generation of decision makers to the next may not be efficient solutions to the problem

• But they at least avoid the need to have these problems solved repeatedly each time a new agent or set of agents arrive.

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• Playing the public goods game with advice may lead to the evolution of norms of cooperation – so-called “memes” (Dawkins, 1976)

• The evolutionarily stable strategy concept does not adequately capture the way in which social evolution, as opposed to biological evolution, might function.

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• We view social conventions as artefacts that can be established in an early generation and passed on in the history of a human society.

• The inter-generational framework tries to capture the evolution of such social norms.

59


• Conjecture:

– Playing a public goods game using such an inter-generational design will lead to the evolution of norms of cooperation

– later generations • will achieve higher levels of contribution • Manage to mitigate problems of free-riding.

60

Set of Five Experiments

• Experiment 1 was carried out at Wellesley College during October 2002 – Wellesley I

• Experiment 2 was carried out at the Indian Statistical Institute-Calcutta during February 2004

• Experiment 3 was carried out at the University of Auckland (Auckland – I) during March/April 2004

• Experiment 4 was carried out at Wellesley College during May 2004 – Wellesley II

• Experiment 5 was carried out at the University of Auckland during May 2004 – Auckland II

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Set of Five Experiments

Progenitor No Advice Private Advice

Almost Common

Common

Wellesley – I 1 5 5 -- 6

Wellesley – II 1 -- 4 4 4

ISI 1 -- 4 -- 4

Auckland – I 1 3 3 3 3

Auckland – II -- -- -- 4 4

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Experiment 3 (Auckland)

ALMOST COM. KNOWLEDGE

Generation #1

Generation #2

Generation #3

PRIVATE ADVICE

Generation #1

Generation #2

Generation #3

COMMONKNOWLEDGE

Generation #1

Generation #2

Generation #3

REPLICATOR NO ADVICE

Group #1

Group #2

Group #3

Generation #2

PROGENITOR

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Pattern of Contributions

02

46

8A

vera

ge C

ontr

ibut

ion

0 2 4 6 8 10Period

No Advice Private Advice

Common Knowledge Almost Common Knowledge

Pooled Data

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Contributions Across Rounds – Experiments 1 - 4

Overall Round 1

Round 10

Rds.

1 - 5

Rds.

6 - 10Common Knowledge

64.4 75 46.1 72.4 56.4

No Advice 50.4 63.3 35.5 56.8 44

Private Advice

47.8 67.8 24.1 60.3 35.4

Almost Common

37.5 64.5 9.1 52.8 22.3

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Results from Regression of Contributions – Experiments 1 - 4

Variables Random Effects Tobit

Private Advice 0.0045

Comm Know 1.5884***

Almost Comm -0.6728

Inverse of time 4.9684***

Lag Contribution 0.8091***

Lag Difference from Group Average

0.6301***

Constant -0.4625

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Evolution of Contributions Across Generations – Private Advice

0 1 2 3 4 5 6 7 8 9 10

Private Knowledge Generation 10

2

4

6

8

10

12

14

16

18

Percentage

Tokens

Private Know ledge Generation 1

67


0 1 2 3 4 5 6 7 8 9 10



0

5

10

15

20

25

Percentage

Tokens

68


0 1 2 3 4 5 6 7 8 9 10




0

5

10

15

20

25

Percentage

Tokens

69

Contributions Across Generations – Almost Common Knowledge

0 1 2 3 4 5 6 7 8 9 10

Almost Common Knowledge Generation10

5

10

15

20

25

30

Percentage

Tokens

Almost Common Know ledge Generation 1

70


0 1 2 3 4 5 6 7 8 9 10



0

5

10

15

20

25

30

Percentage

Tokens

71


0 1 2 3 4 5 6 7 8 9 10




0

10

20

30

40

50

60

70

Percentage

Tokens

72

Contributions Across Generations – Common Knowledge

0 1 2 3 4 5 6 7 8 9 10

Common Knowledge Generation 10

2

4

6

8

10

12

14

16

18

Percentage

Tokens

Common Know ledge Generation 1

73


0 1 2 3 4 5 6 7 8 9 10



05

101520253035404550

Percentage

Tokens

74


0 1 2 3 4 5 6 7 8 9 10




05

101520253035404550

Percentage

Tokens

75

Role of Advice• Subjects were asked to indicate a specific

contribution in addition to providing free-form advice

• Often, advice specified a dynamic rule:– “I would pick a high number for the first round like 9. But when

you see the average start to drop, pick a small number so you don’t lose money.”

• In the later generations of common knowledge public advice, subjects advised unconditional contribution:– “Keep faith! No one should mess it up for the others. All 10 for

all 10 rounds!”– “For goodness’ sake don’t be that morally vacant girl who

prioritizes her own profit & takes advantage of everyone else!”

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Coding of Advice

• Besides free form advice, we also asked each subject to indicate a particular token number as round 1 contribution to her successor (the successor is told this number)

• We use that number to code the advice

• If subjects left a range such as 5 - 6 or 7 – 9 then we use the average such as 5.5 or 8 respectively

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02

04

06

0

Pe

rce

nta

ge

0 1 2 3 4 5 6 7 8 9 10Advice Left

Private Advice

02

04

06

0

Pe

rce

nta

ge

0 1 2 3 4 5 6 7 8 9 10Advice Left

Almost Common Knowledge

02

04

06

0

Pe

rce

nta

ge

0 1 2 3 4 5 6 7 8 9 10Advice Left

Common Knowledge

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Evolution of Advice

• Advice evolves very differently across treatments

Gen. #1 Gen. # 2 Gen. # 3

Private 6.8 7.9 6.3

Almost Common

7.0 3.0 3.4

Common 8.4 8.8 9.3

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Chaudhuri & Paichayontvijit (2005)

• Replicate Fischbacher, Gächter and Fehr’s results about the presence of conditional cooperators

• Does asking people about their actions based on others’ actions affect the contribution level?

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• Does additional information change contribution levels? If so, to what extent?

• Given the existence of conditional cooperators, there are two possible arguments, one of which argues in favour and the other against such information enhancing efficiency.

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• In the presence of conditional cooperators and knowledge of such, – non-cooperators have more of an incentive to

imitate the cooperators initially and free–ride later in the game. This might induce more free-riding

– it is possible that the game that is effectively played has multiple equilibria where full defection is one equilibrium and full cooperation another with other equilibria in between. (Rabin, 1993)

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Treatments

4 different treatments

• Treatment 1 is the control treatment (standard public goods game)

• Treatments 2, 3 and 4 then progressively build on that by providing more information to the subjects

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Treatment 2

• Same as T1 + Conditional Cooperation

• Example of the questionnaire

If the average of tokens contributed by other people of my group is

between

Then I will contribute

$0 – $0.99 $ x

$1 - $1.99 $ y

$2 - $2.99 $ z

Etc etc

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Treatment 3

• Same as T2 + Common Information

• Example of the common information

If the average of tokens contributed by other people of

my group is between

Average contribution

0 - 0.99 0

1 - 1.99 0.5

2 – 2.99 1.3

etc etc

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Treatment 4

• Same as T3 + Announcement

• “You should invest all 10 tokens in each period.

As you can see, a majority of people in your group have indicated that they will invest more if others in the group invest more. If each participant in your group invests 10 tokens in every period, then the average choice of others will be 10 tokens and each participant will earn 20 tokens in every period”

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Experiment 1

• 88 subjects

• Participants are undergraduate and postgraduate students

• 20 subjects in T1 (Control treatment)• 24 subjects in T2• 24 subjects in T3• 20 subjects in T4

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Mechanics of the experiment

• Experiments are carried out in a computer lab using an online programme developed by Charles Holt at the University of Virginiahttp://veconlab.econ.virginia.edu/admin.htm

• Instructions of the game read aloud.

• Subjects can also read these instructions privately on their computer screen

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• Subjects complete questionnaires

• Randomly pick one person

• Participants are given 10-15 minutes to read through online instructions and ask any questions that they might have

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• The game consists of 10 rounds

• Subjects are put into groups of 4

• Subjects are randomly re-matched every round.

• At the end of the session subjects collect their payoffs privately:

• Session lasts about an hour

90

Conditional Cooperation

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10Average C ontribution of Other Group Members

Ow

n C

ontr

ibut

ion

Free Riders(16.2%)

WeakCooperators (7.4%)ConditionalCooperators (61.8%)HumpShaped(5.9%)OverallMean

91

Contributions Over Time

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10Rounds

Ave

rag

e C

on

trib

uti

on

T1

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Rounds

Ave

rag

e C

on

trib

uti

on

T1 T2

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Rounds

Ave

rag

e C

on

trib

uti

on

T1 T2 T3

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Rounds

Ave

rag

e C

on

trib

uti

on

(to

ken

s)

Control CC

CC+Info CC+Info+Ann

92

Average Contribution (percentages)

Treatment 1

Treatment 2

Treatment 3

Treatment 4

Overall 19.2 27.7 31.5 31.1

Round 1 28.5 46 37.7 62

Round 10 4.5 9.4 12.1 13.6

Rounds

1- 5

25.4 37.3 39.6 37.7

Rounds

6 – 10

12.9 18.1 23.4 24.4

93

• A non-parametric Kruskal-Wallis test for equality of populations finds a significant difference between treatments 1 – 4

• chi-squared = 17.194 (with 3 d.f.)

• probability = 0.0006

94

Pair-wise Wilcoxon ranksum test of significance

• Each cell provides the value of the test-statistic and the corresponding p-value

T1 T2 T3 T4

T1 -- -4.07

(0.00)

-3.82

(0.00)

-1.39

(0.16)

T2 -- -- -0.17

(0.87)

1.51

(0.13)

T3 -- -- -- 1.61

(0.11)

95

Conditional Cooperation

• Given that a majority of our subjects are conditional cooperators, we next focus in depth on what they did

96

Pattern of Contribution of Conditional Cooperators

024

68

10

1 2 3 4 5 6 7 8 9 10

Rounds

CC CC+InfoCC+Info+Ann

97

Average Contributions of Conditional Cooperators

Treatment 2

Treatment 3

Treatment 4

Average 33.1 37.2 52.9

Round 1 53.3 39.1 84.4

Round 10 14.1 15.9 30.2

98

Comparing Behavior of Conditional Cooperators across Treatments

• Each cell presents the value of the test-statistic (Wilcoxon ranksum test) and the corresponding p-value

Treatment 2

Treatment 3

Treatment 4

Treatment 2

-- -0.229

(0.82)

-3.7

(0.00)

Tretment 3 -- -- -3.00

(0.00)

1 economics 776 experimental economics first semester 2007 topic 4: public goods assoc. prof....

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public goods ci

public accountmoney

collective goods

player i

endowment of player

average contribution

contribution vector

group memberi