Theory of Games and Common Pool Resources Pedro Ribeiro de Andrade DSSA/CCST/INPE São José dos...
Transcript of Theory of Games and Common Pool Resources Pedro Ribeiro de Andrade DSSA/CCST/INPE São José dos...
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Theory of Games and Common Pool Resources
Pedro Ribeiro de AndradeDSSA/CCST/INPESão José dos Campos, 2010
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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
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Modelling and Public Policy
System
EcologyEconomyPolitics
ScenariosDecisionMaker
Desired System
State
ExternalInfluences
Policy Options
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Human-enviromental systems
[Ostrom, Science, 2005]
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Types of goods
Source: E Ostrom (2005)
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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
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Institutional arrangments in Amazonia
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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
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Cooperate
Player 1
Modeling Two-party choice
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Defect
Player 1
Modeling Two-party choice
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Cooperate
Player 2
Modeling Two-party choice: Player 2
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Defect
Player 2
Modeling Two-party choice: Player 2
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Cooperate Defect
CooperateBoth cooperate
Defect
Player 2
Player 1
Modeling Two-party Choice: Both Cooperate
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Cooperate Defect
Cooperate
Defect Both defect
Player 2
Player 1
Modeling Two-party Choice:Both Defect
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Cooperate Defect
Cooperate
Player 1 cooperates, Player 2 defects
Defect
Player 2
Player 1
Modeling Two-party Choice
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Cooperate Defect
Cooperate
Defect
Player 1 defects, Player 2 cooperates
Player 2
Player 1
Modeling Two-party Choice
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Cooperate Defect
CooperateBoth cooperate
Player 1 cooperates, Player 2 defects
Defect
Player 1 defects, Player 2 cooperates
Both defect
Player 2
Player 1
Modeling Two-party Choice
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Cooperate Defect
CooperateBoth cooperate
Defect
Player 2
Player 1
Let’s examine Joint Cooperation
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Joint Cooperation: Omerta as a substitute for contracting
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Cooperate Defect
Cooperate
Defect Both defect
Player 2
Player 1
Joint Defection
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Joint defection: Can these gentlemen be acting efficiently?
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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
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Prisoner’s Dilemma: Game Theory
Did you lie to Congress about WMD in Iraq?
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Tragedy of the Commons?
How many animals can graze in a common area before degradation occurs?
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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
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Tragedy of the Commons?
Everybody’s property is nobody’s property
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Brasil: compromisso de reduzir o desmatamento
NAMA: Reduzir o desmatamento da Amazônia em 80% até 2020
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Smallest yearly increase since the 1970s
Yearly rates of deforestation: 2008-2009
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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%
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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%
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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
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Como atingir as metas de redução de desmatamento?
(Getty Images, 2008)
+
POLÍTICAS PÚBLICAS MERCADOS
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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)
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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$1.000.000) 27% 21% 19% 25% 6% 2% 100%
Pessoal Ocupado 38,2% 26,6% 22,7% 10,5% 1,7% 0,2% 100%
Total de Terras Apropriadas 16,7% 5,4% 12,2% 59,7% 3,8% 2,2% 100%
Total de áreas degradadas 10,2% 3,5% 14,3% 70,4% 1,6% 0,0% 100%
Índice de Densidade Institucional - IDR 1 0,73 0,38 0,67 1,63 2,67 0,83
Emissão líquida de CO2 11,8% 2,6% 12,5% 70,5% 2,6% 0,0% 100%
Tx. de crescimento da renda líquida – 1995 e
20062,5% a.a. 7,9% a.a.
7,8% a.a. 8,4% a.a.
7,2% a.a.
-11,0% a.a.
6,4% a.a.
Taxa de crescimento do VBPR - 1995 e 2006 5% a.a 12% a.a.
7,0%a.a. 5,1%a.a.
2,5% a.a. -2,9% 5%
Incorporação do estoque adicional de
terras 13% 8% 7% 64% 5% 2% 100%
Trajetórias Tecnológicas da Região Norte
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A pecuária de corte de grande porte emite 70% do CO2, emprega 10% do pessoal, e gera 25% da renda, sendo uma atividade predatória;
Os segmentos camponeses voltados para pecuária de leite e culturas permanentes tem 38% dos empregos, 27% da renda, 12% das emissões, sendo atividade de baixo carbono e alta relevância social;
Os segmentos camponeses agroflorestais (açaí e similares), de baixíssimo impacto sobre a biodiversidade e a emissão de CO2, cresceram 12% ao ano em renda líquida de 1991 a 2005.
Trajetórias Tecnológicas da Região Norte
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Formação da Renda Líquida dos Produtores nas Trajetórias (Médias móveis de três anos, em R$ 1.000,00 constantes de 2005)
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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)
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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
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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
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(Getty Images, 2008)
Incentivos a "boas" trajetórias (em termos ambientais e sociais), e apoio para reconversão das “ruins”.
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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.”
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Types of goods
Source: E Ostrom (2005)
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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
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Prisoner’s Dilemma
a a
b c
c b
d d
Player 2
Player 1
*
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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
**
*
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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
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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
*
*
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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
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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
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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
*
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Monitoring
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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
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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
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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
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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
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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.
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Games, Rules, and Common Pool Resources
Pedro Ribeiro de AndradeDSSA/CCST/INPESão José dos Campos, 2010