Games with Dynamic Externalities
and Climate Change
Tatsuyoshi Saijo*, Katerina
Sherstyuk**, Nori Tarui** and MajahLeah V. Ravago**
*Osaka University and
**University of Hawaii at Manoa
Moscow -- June 2009
Science of Global warming
 Human
activities (primarily
the burning or fossil fuels)
intensify the warming effect
by releasing GHG into the
atmosphere.
Buildup is slow to reverse itself.
Source: http://science.nationalgeographic.com/science/environment/global-warming/gw-overview-interactive.html
Nature of the CC problem

Global public good (bad) – total GHG stock is what
matters


Huge potential cost and effects worldwide
Unilateral emission reduction favors all countries =>
=> Free-rider problem

Irreversibility – GHG accumulate faster and deplete
slowly, effect of emission today can be felt into the
distant future =>
=> Dynamic externalities
Thus, a social dilemma setting and dynamic
externalities are essential features of the problem.
Static externalities are less pronounced.
Research focus and questions

Games with dynamic externalities



Inter-generational aspect
Applied to climate change


Current action of each player affects not only the
players’ payoff this period but also the payoff level of
the game that will be played tomorrow.
The benefits derived by the future generations depend
on the stock of GHG buildup, with higher current
emissions resulting in lower future payoffs
Research questions:


Can socially optimal actions be sustained in this
setting without an explicit enforcement mechanism?
Does access to history and advice from previous
generations help to achieve and sustain optimality?
Some earlier exper. studies

Fischer et al (JEEM 2004)




Study altruistic restrain in common pool
resource setting with dynamic externalitites
Chains of groups of subjects, each subject
only made one decision
Report “optimistic free-riding”
Chaudhuri et al (ReStud 2006)


Study social learning and norms in a public
good setting with intergenerational advice
Report that common knowledge of advice had
a significant and positive effect on
contributions
Model (close to Dutta and Radner)
G  

- (non-overlapping) generation of players,
starts with g=0

i = 1..N - players (countries)
Each player’s payoff depends on the benefit from
current activity xig and damage from the total emissions
stock Sg:
,
where d is the damage from stock
Emissions stock for gen (g+1) depends on emissions by
gen g



Stock retention rate:

First best solution:
Benchmark solutions

Myopic Nash (MN):


Constant Markov Perfect (MP)


A subgame perfect equilibrium of the dynamic
game played by countries across generations
First Best (FB)


Each generation ignores dynamic externalities,
maximizes own payoff
A cooperative solution with discounting δ<1
Sustainable (Sus)

A cooperative solution with no discounting
Experimental Design
Dynamic externalities only, no static
 Instead of choosing emission levels,
subjects choose tokens, bounded [1,11]
 3-subject groups in each generation
(“series”)
 Total group tokens in this series determine
the payoff level in the next series; this is

emphasized in the instructions
Series 1 starts at the first best steady state
stock
 Extensive training before the actual play

Payoff Scenarios
Payoff Scenarios Continued
Experimental Design Continued



At the end of each series, each subject sends a
suggested number of tokens and verbal advice for
the next series
Advice and history from previous series is available
Each series is continued to the next series with
probability ¾ (determined by a roll of a die)
Experimental Treatments

Baseline Long-Lived (LL)



The same group of subjects makes decisions in all series
represents an idealistic setting where long lived social planners
make decision over a long time horizon and are motivated by longterm welfare for their countries
Intergenerational Selfish (IS)


In each series, decisions are made by a separate group of
subjects, who are paid based on own series payoffs only.
Groups are linked in chains.
represents a more realistic setting in which the countries’ decisionmakers are motivated more by their countries’ immediate welfare
and may care at most partially about the future generations’
payoffs

Intergenerational “Long-Sighted” (IL)

In each series, decisions are made by a separate group of
subjects, who are paid based on own series payoffs and all the
followers’ payoffs
Results

We conducted Baseline Long-Lived (LL),
Intergenerational Selfish (IS) and
Intergenerational Long-Sighted (IL)
treatments, with


4-5 independent chains for each treatment,
4-9 series (generations) per chain
Group Tokens by Series
Group Tokens: LL treatment
Group Tokens: IS treatment
25
25
25
22
22
22
MN
19
MN =
FB
10
Sus
7
16
13
13
FB
Chain 1
Chain 2
Chain 3
Chain 4
Sus
Chain 1
Chain 2
Chain 3
Chain 4
2
3
4
series
5
6
7
8
9
Chain 1
Chain 2
Chain 4
Chain 5
Chain 3
4
1
1
1
Sus = 9
7
4
1
FB = 12
10
10
7
4
MP = 18
MP =
16
13
MN = 21
19
19
MP
16
Group Tokens: IL treatment
1
2
series
3
4
5
1
2
3
series
4
5
6
7
Changes in Stock Level
Stock Level: IS treatment
LL treatment
70
70
70
Stock Level: IL treatment
MN =
MN =
65
65
65
60
MP =60
55
55
55
50
50
50
45
45
60MP =
45
35
35
Chain 1
Chain 3
25
1
2
3
4
Series
5
6
7
30
30
Chain 2
Chain 4
8
25
9
Sus =34.3
Sus
Sus =34.3
30
FB = 42.9
40
40
35
MP = 60
FB =
FB = 42.9
40
MN = 68.6
1
Chain 1
Chain 2
Chain 3
Chain 4
2
3
4
series
5
25
Chain 1
Chain 2
Chain 4
Chain 5
1
2
3
4
series
5
Chain 3
6
7
Recommended Group Tokens
Recommended Group Tokens
Recommended Group Tokens
Recommended Group Tokens
25
25
25
22
22
22
MN = 21
19
MP = 18
16
MN = 21
19
19
MP = 18
FB = 12 13
10
FB = 12
Chain 1
Chain 2
Chain 3
4
Chain 1
1
1
2
3
4
5
6
Baseline Series
7
8
9
Sus = 9
7
4
Chain 4
FB = 12
`
Sus = 9
7
4
13
10
Sus = 9 10
7
MP = 18
16
16
13
MN = 21
Chain 2
Chain 3
Chain 1
Chain 2
Chain 4
Chain 5
Chain 3
Chain 4
1
1
1
1
2
3
4
Intergenerational Series
2
3
4
5
5
IL Cumulative
6
7
Summary of Results

Baseline LL (Long-Lived) treatment:



IS (Intergenerational Selfish) treatment:




All groups were able to avoid myopic Nash solution and were
converging to the First Best group tokens and stock levels
Verbal advice was used as an effective communication device
Group tokens and stock levels quickly increased to just under
(but still below) the Myopic Nash levels
Attempts made by some subjects to cut down group tokens
were largely unsuccessful
IL (Intergenerational Long-Sighted) treatment exhibited
mixed dynamics in between the FB and MP benchmarks
Based on the estimates of convergence levels, the
difference between the treatments is significant in both
actual decisions and stock, and advices
Advice from Baseline LL, Chain 2
Series
Subject
Advise
Series 1
1
2
6 as next token order
we started out really high this past one. maybe we can go lower for the next trials.
3
Start with small orders and gradually order more for each subsequent trial. The loss
we take early will give us bigger payoffs in the later series.
1
I agree with ID#3's advice on starting on smaller orders and gradually ordering more
for each trial. I suffered from a loss in the beginning, but my payoffs increased as we
went on. Let'
better, much better. If we can keep it lower or about the same for next round then our
payoff will be greater in the subsequent trials.
Series 2
2
Series 3
1
2
3
Series 4
1
2
3
Series 5
1
2
Good, it seems to be getting better and better. Let's keep it at the same or even lower.
Let's just not go greater
Hmm...the tokens were around the same ballpark. Maybe keep it the same for one
more series then start to push our luck and slowly increase in token counts.
Let's stay with this order one more round. It gives us a good balance between payout
and upping the payoff level for the next series.
Payoff did increase, but I think we should increase our token rather than stay at 4.
Let's try increasing it a bit
I say slowly up the token count…
The benefit from 4 to 5 is only a 100 point difference (50 cents) so let's stay with 4.
Let's just stay at 4...doesn't look like it's increasing by much. 4 would be the best
token order. 4 everyone!
...I don't know what to say now. We seem to be doing whats best.
Advice from IS Chain 4
Series
Subject
Advise
Series 1
4
5
6
For me I try to choose the tokens which has the highest payoff.
Series 2
4
5
6
Do not choose a number beyond 6. Otherwise, our total payoff will decrease.
The greatest payoff calculated against the results for the subsequent group is 6
for maxmin payoff for your series, but the payoff decreases for the later series
Series 3
4
5
6
Do not choose higher than 5. Otherwise your optimal payoff will decrease.
keep it fairly low until later rounds
choose 7
Series 4
4
5
6
never go beyond 5 to save your future generations
for everyone's best
choose 6 b/c you make money plus earn more money in the following rounds.
Series 5
4
5
go between 6 and 8 tokens to gain max payoff and prediction bonus
for your own benefit, choose the maximal payoff, ie 7; the rest is not worth considering, it's just a
diversion.
Get the most out of it NOW!
6
the next set you should choose a low amount of tokens so your payoff level will increase. In the long
run, as the pay off level increases, you will have a higher payoff schedule. I chose 4 because its not
too low and not too high but just right.
Advice from IL Chain 3
Conclusions



We obtain evidence that self-interested individuals
can resolve dynamic social dilemmas when
interacting in small groups over a long time horizon
(LL Treatment)
In an intergenerational setting without explicit
motivation for caring for the future, (IS treatment),
individual’s decisions are largely myopic
The evidence from the intergenerational IL treatment
with full motivation for caring about the future is
mixed; social dilemmas are not fully resolved
This suggests that international dynamic enforcement
mechanisms (treaties) are necessary to control GHG
emissions
Decision Screen
Trial Results Screen
Series Results Screen
Waiting Screen with Advice
Advice from Previous Series