Theory of Games and Common Pool Resources Pedro Ribeiro de Andrade DSSA/CCST/INPE São José dos...

Theory of Games and Common Pool Resources

Pedro Ribeiro de AndradeDSSA/CCST/INPESão José dos Campos, 2010

What Drives Tropical Deforestation?

Underlying Factorsdriving proximate causes

Causative interlinkages atproximate/underlying levels

Internal drivers

*If less than 5%of cases,not depicted here.

source:Geist &Lambin (Université Louvain)

5% 10% 50%

% of the cases

Modelling and Public Policy

System

EcologyEconomyPolitics

ScenariosDecisionMaker

Desired System

State

ExternalInfluences

Policy Options

Human-enviromental systems

[Ostrom, Science, 2005]

Types of goods

Source: E Ostrom (2005)

Institutional analysis

Old Settlements(more than

20 years)

Recent Settlements(less than 4

years)

Farms

Settlements 10 to 20 anos

Source: Escada, 2003

Identify different actors and try to model their actions

Institutional arrangments in Amazonia

Modeling PD games

Game theoretic problems: payoffs for each player depend on actions of both

Two possible strategies: A party cooperates when he performs value-increasing promises, and defects when he breaches

Cooperate

Player 1

Modeling Two-party choice

Defect

Player 1

Modeling Two-party choice

Cooperate

Player 2

Modeling Two-party choice: Player 2

Defect

Player 2

Modeling Two-party choice: Player 2

Cooperate Defect

CooperateBoth cooperate

Defect

Player 2

Player 1

Modeling Two-party Choice: Both Cooperate

Cooperate Defect

Cooperate

Defect Both defect

Player 2

Player 1

Modeling Two-party Choice:Both Defect

Cooperate Defect

Cooperate

Player 1 cooperates, Player 2 defects

Defect

Player 2

Player 1

Modeling Two-party Choice

Cooperate Defect

Cooperate

Defect

Player 1 defects, Player 2 cooperates

Player 2

Player 1


Cooperate Defect


Player 1 cooperates, Player 2 defects

Defect

Player 1 defects, Player 2 cooperates

Both defect

Player 2

Player 1


Cooperate Defect


Defect

Player 2

Player 1

Let’s examine Joint Cooperation

Joint Cooperation: Omerta as a substitute for contracting

Cooperate Defect

Cooperate

Defect Both defect

Player 2

Player 1

Joint Defection

Joint defection: Can these gentlemen be acting efficiently?

Player 2

Terminology

Where T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Sucker's payoff.

T > R > P > S

Where T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Sucker's payoff.

T > R > P > S

Prisoner’s Dilemma: Game Theory

Did you lie to Congress about WMD in Iraq?

Tragedy of the Commons?

How many animals can graze in a common area before degradation occurs?

Prisoner’s Dilemma: Game TheoryHow many animals do send to graze?

Strategy 1: Send only half of the maximum supported numberStrategy 2: Send as many animals as possible

Tragedy of the Commons?

Everybody’s property is nobody’s property

Brasil: compromisso de reduzir o desmatamento

NAMA: Reduzir o desmatamento da Amazônia em 80% até 2020

Smallest yearly increase since the 1970s

Yearly rates of deforestation: 2008-2009

Contribuição brasileira para as emissões globais

Amazonia

Redução anunciada pelos países desenvolvidos

30,5 Gt CO2eq

Os países desenvolvidos (Anexo I) propõem-se a cortar emissões em 15% com relação a 1990. Isto implica numa redução de 30,5 Gt CO2eq

Corte do desmatamento no Brasil

6,2 Gt CO2eq

A proposta brasileira é equivalente a 21% do compromisso anunciado pelos países do Anexo I.

21%

Brazilian contribution to GHG reduction

12% Amazonia

Reduction in developed countries50,8 Gt CO2eq

The Brazilian proposal is equivalent to 12% of the reductions proposed by the G77 countries to Annex I countries.

Reduction in Brazil6,2 Gt CO2eq

Como atingir as metas de redução de desmatamento?

(Getty Images, 2008)

+

POLÍTICAS PÚBLICAS MERCADOS

Trajetórias Tecnológicas da Região Norte

T4: Pecuária de corte

T1: Pecuária de leite

T5: Cultura permanente

T2: Agroflorestais

T6: Silvicultura

T3: Pecuária de corte (pequeno porte)

Trajetórias/Características

Trajetórias

Valores Absolutos em 1995

Sistemas camponeses: Sistemas patronais:

Queconverg

em para

pecuária

de Leite e

perman.(T1)

Que converge

m para

sistemas

agroflorest

(T2)

Queconver

g para

pecuária

de corte(T3)

Pecuária de Corte

(T4)

De culturas perma-nentes

(T5)

De Silvicultu

ra(T6)

Número de Estabelecimentos 171.292 130.593

109.405 27.831 4.444 3 443.568

Tamanho médio 54,47 23,04 62,23 1.196,00 472,62413.681,

7 125,74

VBP (R$1.000.000) 27% 21% 19% 25% 6% 2% 100%

Pessoal Ocupado 38,2% 26,6% 22,7% 10,5% 1,7% 0,2% 100%

Total de Terras Apropriadas 16,7% 5,4% 12,2% 59,7% 3,8% 2,2% 100%

Total de áreas degradadas 10,2% 3,5% 14,3% 70,4% 1,6% 0,0% 100%

Índice de Densidade Institucional - IDR 1 0,73 0,38 0,67 1,63 2,67 0,83

Emissão líquida de CO2 11,8% 2,6% 12,5% 70,5% 2,6% 0,0% 100%

Tx. de crescimento da renda líquida – 1995 e

20062,5% a.a. 7,9% a.a.

7,8% a.a. 8,4% a.a.

7,2% a.a.

-11,0% a.a.

6,4% a.a.

Taxa de crescimento do VBPR - 1995 e 2006 5% a.a 12% a.a.

7,0%a.a. 5,1%a.a.

2,5% a.a. -2,9% 5%

Incorporação do estoque adicional de

terras 13% 8% 7% 64% 5% 2% 100%


A pecuária de corte de grande porte emite 70% do CO2, emprega 10% do pessoal, e gera 25% da renda, sendo uma atividade predatória;

Os segmentos camponeses voltados para pecuária de leite e culturas permanentes tem 38% dos empregos, 27% da renda, 12% das emissões, sendo atividade de baixo carbono e alta relevância social;

Os segmentos camponeses agroflorestais (açaí e similares), de baixíssimo impacto sobre a biodiversidade e a emissão de CO2, cresceram 12% ao ano em renda líquida de 1991 a 2005.


Formação da Renda Líquida dos Produtores nas Trajetórias (Médias móveis de três anos, em R$ 1.000,00 constantes de 2005)

Índice de Densidade Institucionalidi = (Percentual de Crédito)/(Percentual de Valor Bruto de Produção)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,41

99

2

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

Índ

ice

de

Pre

val

ênci

a

TrajetóriaCamponês.T1 TrajetóriaCamponês.T2 TrajetóriaCamponês.T3

TrajetóriaPatronal.T4 TrajetóriaPatronal.T5 TrajetóriaPatronal.T6

Quanto maior o IDI, mais a trajetória se apropria do crédito disponível de forma desigual (Pecuária tem mais crédito do que

gera de renda)

O que aconteceria com a economia e com o balanço de CO2 se um programação de compensação por desmatamento evitado logra reduzir em 5 anos 50% da produção responsável pelo balanço de carbono verificado em 2004, por justa compensação dos proprietários dos estabelecimentos rurais no nível constatado de seus lucros?

Sucesso ecológico, fiasco econômico.

Val

or A

dici

onad

o R

$

Sal

ário

s R

$

Lucr

os R

$

Em

preg

o

Impo

stos

R$

Em

issã

o (G

t)

Seq

uest

ro (

Gt)

Bal

anço

CO

2 (G

t)

LocalEstadual

Nacional-700

-600

-500

-400

-300

-200

-100

0

100

O que aconteceria com a economia e seu balanço de carbono se um programa de compensação por emissão evitada lograsse induzir uma conversão na base produtiva dos sistemas que mostram os piores balanços de carbono pelos sistemas que mostraram os melhores. O que aconteceria, nesse caso, com a economia e seu balanço de CO2? Sucesso econômico, sucesso ecológico.

Val

or A

dici

onad

o R

$

Sal

ário

s R

$

Lucr

os R

$

Em

preg

o

Impo

stos

R$

Em

issã

o (G

t)

Seq

uest

ro (

Gt)

Bal

anço

CO

2 (G

t)

LocalEstadual

Nacional-200

-100

0

100

200

300

400

500

(Getty Images, 2008)

Incentivos a "boas" trajetórias (em termos ambientais e sociais), e apoio para reconversão das “ruins”.

Ostrom

“How best to limit the use of natural resources so as to ensure their long-term economic viability.”

“Neither the state nor the market is uniformly successful in enabling individuals to sustain long-term, productive use of natural resource systems.”

“Optimal equilibrium with centralized control is based on assumptions concerning accuracy of information, monitoring capabilities, sanctioning reliability, and zero costs of administration.”

Types of goods

Source: E Ostrom (2005)

7 “action situation” elements Participants Positions Actions Potential outcomes Transformation functions Information Payoffs

Games are the standard mathematical structure for representing an action situation

Introduction – IAD

Prisoner’s Dilemma

a a

b c

c b

d d

Player 2

Player 1

*

Prisioner’s Dilemma

a a

b c

c b

d d

b < d

a < c

*

a a

b c

c b

d d

b > d

*

a a

b c

c b

d d

a > c

*

a a

b c

c b

d d

**

*

F(2)/2 F(2)/2

F(1) w

w F(1)

w w

F(2)/2 F(2)/2

F(1) w

w F(1)

w w

Appropriation Externality [F(1) > w]

F(2)/2 F(2)/2

F(1) w

w F(1)

w w

P 2

P 1

w > F(2)/2

*

*

w < F(2)/2

*

*

Invest

Invest

~Invest

~Invest

v1/2 v1/2

v1 v2

v2 v1

v2/2 v2/2

v1/2 v1/2

v1 v2

v2 v1

v2/2 v2/2

v1/2 v1/2

v1 v2

v2 v1

v2/2 v2/2

Assignment Game [v1 > v2]

v1/2 v1/2

v1 v2

v2 v1

v2/2 v2/2

P 2

P 1

v1 > 2 * v2

*

**

*

v1 < 2 * v2v1 = 2 * v2

*

*

w(1,2) w(2,2)

v2 v1-c

v1-c v2

w(1,1)-c w(2,1)-c

Go to G1v1 v2

v2 v1

Go to G2

Fishing game

w(1,1) w(2,1)

v1 v2-c

v2-c v1

w(1,2)-c w(2,2)-c

G2G1

G

Spot 1 Spot 2

Spot 1

Spot 2

Stay Leave

Stay

Leave

Stay Leave

Stay

Leave

Monitoring

0 -C

0 0

B – P(F + B) PM-(C+(1-P)/B)

B -B

Monitor or not

Take the share or more

C: Cost of monitoring B: Benefit of taking more than the share P: Probability of detecting F: punishment for being detected M: bonus for successful monitoring

0 -C

0 0

B – P(F + B) PM-(C+(1-P)/B)

B -B

0 -C

0 0

B – P(F + B) PM-(C+(1-P)/B)

B -B

0 -C

0 0

B – P(F + B) PM-(C+(1-P)/B)

B -B

Monitoring

B < P(F+B)

*

*

B > P(F+B)

*

P(M+B)>C P(M+B)<C

0 -C

0 0

B – P(F + B) PM-(C+(1-P)/B)

B -B

*

Monitoring

2v 2v

v w + v

w + v v

w w

2v 2v

v w + v

w + v v

w w

Provision game, intermediate value

*

*

2v > v > w2v > w > v

2v 2v

0 w

w 0

w w

2v 2v

0 w

w 0

w w

Provision game, no intermediate value

*

* *

2v 2v

0 w

w 0

w w

*

2v > w

2v < w

CPR Experiments

8 undergraduate players Can invest in Market 1 with fixed returns Can invest in Market 2 with non-fixed returns:

Tokens invested by group

Units of Commodity produced

Average return per Token

20 360 0.18

40 520 0.13

60 480 0.08

80 240 0.03

100 -200 -0.02

120 -840 -0.07

160 -1680 -0.12

CPR Experiments with probabilistic destruction

Same as previous experiment LUB: lowest upper bound GLB: greatest lower bound Design 1: GLB = 0; LUB = 200 Design 2: GLB = 40; LUB = 200

Stable CPR arrangement requirements Clearly defined boundaries Congruence between appropriation and provision rules and local

conditions Collective-choice arrangements allowing for the participation of most

of the appropriators in the decision making process Effective monitoring by monitors who are part of or accountable to

the appropriators Graduated sanctions for appropriators who do not respect

community rules Conflict-resolution mechanisms which are cheap and easy of access Minimal recognition of rights to organize (e.g., by the government) In case of larger CPRs: Organisation in the form of multiple layers of

nested enterprises, with small, local CPRs at their bases.

Games, Rules, and Common Pool Resources

Pedro Ribeiro de AndradeDSSA/CCST/INPESão José dos Campos, 2010

Theory of Games and Common Pool Resources Pedro Ribeiro de Andrade DSSA/CCST/INPE São José dos...

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