Game Theory Modelling of Climate Change Aspects

Gbor Kutasi
assistant professor, Corvinus University of Budapest, Department of World Economy
supported by TAMOP-4.2.1/B/09/KMR-2010-0005


Abstract: The paper surveys the game theory modelling of behaviour of global players in the
mitigation and the adaptation related to the climate change. Three main fields, the behaviour
games, the CPR problem and the negotiation games are applied for the specific aspects of
temperature rise. The game theory instruments are useful to analyze strategies in uncertain
circumstances like the occurrence and impacts of climate change. To analyze the relations, the
actions, the attitude toward carbon emission, the negotiation power and motives of
international players, several games are applied for climate change in this paper. The overuse
of global natural resources also belongs to the circle of examined climate problems, as the
conflict between short term individual and long term community interest. The paper surveys,
also, the solution of externality problem, as the role and efficiency of international
organizations will be examined. International organizations shall be created to monitor the
actors and regulate the use of resources. The paper concludes, whether is there any saddle
point, or stable solution for the free riding and negative externalities of overuse of climate and
natural resource, or is it an instable game leading to collapse.

Key words: game theory, climate change, common pool resource, negotiation game

The issues of how best to govern natural resources used by many individuals
in common are no more settled in academia than in the world of politics
Elinor Ostrom (1990)

1. Introduction
As it is written by OHara (2009), [] global warming hypotheses have been a contested
terrain as advocates sparred with critics, resulting in controversy and analysis, but no firm
resolution either way at the level of public debate. All this has suddenly changed in the light
of the global warming thesis gaining the upper hand. The influence of [] publication of
the IPCC Report (2007a,b,c,d), the Stern Review (2007), the UNDP Report (2007), and the
Garnaut Report (2008) []have meshed with the election of more moderate governments in
several continents to change the public view of these matters. Climate change, as it is now
called, has become an accepted institution, even by most of those who previously argued
against global warming.
The climate change is a long-term challenge for the Earth, as action for prevention should be
started very soon before the impacts meanwhile it is very uncertain to forecast the exact far
future damages of different regions when exact scale of regional warming is an unsure
variable in the equation of economic impacts. The scenarios and action plans have been
developed, but there is an important factor what makes the execution questionable. This is the
hesitation of decision making stakeholders. Hesitation is rooted both in uncertainty and
expectations on each others strategy. Such a survey environment demands game theory, too,
to understand and forecast the strategy of stakeholders.
However Rubas et al. (2006) establish, that game theory has not been widely used in
applications of seasonal climate forecasts largely because of the increase in information
requirements and increased methodological knowledge necessary to develop and solve
games. [] Though rarely used in studies on climate forecast problems, game theory has
been used in climate related studies such as climate change studies (Ward 1996, Forgo et al.
2005) and climate variability studies (McKelvey et al. 2003). Rubas et al. (2006) quoted
previously gave a very broad view about economics and survey methodology of climate
change, detailing the game theory, too. Very specified modelling and surveys of negotiations
have been created, besides Forg et al. (2005), by Courtois, P. (2002), Yang (2003), Courtois
& Tazdat (2007), Pinto & Harrison (2003).
The study gives a view about application possibilities of game theory in climate change
aspects. The characteristics of games get adopted to the climate and carbon topics. Importance
of uncertainty, probability, marginal value of adaptation, common pool resource etc. get
settled into the context of international relations and the global challenge of warming.
The complexity of the theme demands to borrow some theses, also, from international
relations theories, behaviourism, ecological economics, international political economy. To
lead up the game theory, the general theses by Ostrom (1990), Owen (2008), Harsnyi &
Selten (1988), Olson (1965), Harding (1968) is applied.
2. Characteristics of games
In case of modelling of pro-actions and reactions for changing temperature, the characteristics
of events, actions and behaviours shall be know. In climate change, the uncertainty is a
dominant character. With technical terms, uncertainty means there is no saddle point in the
game. (Owen 2008) This means, the pay-off of the game is not sure, but dependent on actors
expectations and probable reactions on each others actions, or dependent on the probability
of certain external events. Especially in practice of climate change, the uncertainty is
accumulative.
1
(see figure 1) There are even scientific disputes, whether the change of
average temperature will really happen and, if it is, it has been caused by the CO2 emission
from human activities. About economic forecast challenges see Rubas et al. (2006).
If climate change got realized globally, it does not mean a generally same scale of change of
temperature in every region and territory of the Earth. (It is possible more or less rise in
temperature or even cooling down is a likely outcome in certain regions.) From differences,
the physical impact can be different. In some region, the rise of sea might will take costal
territories, in some region the hart illnesses might will rise by warmer climate, in other
territories the agricultural lands will dry out, somewhere else the disappearance of ice and
snow create land cultivation opportunities or ruin the winter tourism etc. But what is the
likelihood in a continent, a country, a county or a city/village level? If there are more
scenarios, what are the effective mitigation and adaptation actions? What is the critical mass
or scale of action? Will the actors wait for each other to act? Who should act first? Should the
state intervene, motivate, initiate? And so on. If such uncertain probabilities are accumulated
(namely multiplied) finally the likelihood of effective actions can be low.
Figure 1. Increasing uncertainty in climate change (CC)

Source: Simplified adaptation from Stern (2007) and OHara (2009)
The source of uncertainty can be asymmetry in information, moral hazard, irresponsibility (no
ability to carry out commitments), negative selection (counter selection), decentralized
governance, myopic self interest. Asymmetry in information can be rooted in technology and
science difference or different positions in information reception streams. The latter, in case
of climate change and the related carbon emission, is not very likely if we consider the global
information systems of the 21
st
century. Moral hazard, namely causing risk and cost for
someone else by ones behaviour or decision is a very typical occurrence in negative
externality situation just like environmental damage as CO2 emission. Irresponsibility can be
understood as sociopath behaviour, also adoptable into international relations just like North-
Korean nuclear threat and war threat psychosis. In case if carbon emission, irresponsibility
could mean the ignorance of negative global externalities from emission. Negative selection is
very theoretical in case of climate change games. Generally, it means that always the lower
quality, less credible, less able etc. option or actor is preferred. Among the behaviour games
we will see cases, when the smaller/weaker actor can enforce its own preference on the
bigger/stronger actor (see called bluff and suasion games). Decentralized governance is
relevant in game uncertainty and climate change as it increase the number of actors and move
further the scale of problem (global) and level of competence (regional) from each other.
Thus, the likelihood of free riding will increase. Possible occurrence of myopia as uncertainty

1
About circular and cumulative causation and irreversibility see Thorstein Veblen, Gunnar Myrdal, Nicholas
Kaldor, K. William Kapp and Nicholas Georgescu-Roegen refered in Berger 2008, 2009, about cumulative
uncertainity see Frank Knight (1921), J.M. Keynes (1921, 1936), and G.L.S. Shackle (1970)
factor means ignorance of long-term externalities for short-term profit, welfare, comfort etc.
The examples of peace treaties of World War I or absence of green-house-gases treatment can
be mentioned for myopia in international relations. (Keohane 1984:92-98)
The pay-off function of a game means the composition of probable individual cost-benefit
balances of different scenarios for the same problem. The total pay-off of a game can be
negative, zero and positive sum. It is possible also to have variable sum game if the sum of
total pay-offs are not constant in different scenarios (outcomes). Static and dynamic games
can be distinguished, as in static means constant, dynamic means changing preferences.
(Owen 2008) The exiting and challenging aspect of pay-off matrix definition related to
climate change is that it is the result of a national welfare optimization in relevance to green
house gas damage due geophysical and socioeconomic transformation.
In case of climate change, because of its complexity and high uncertainty, the variable sum
and dynamic approach is the most useful to model the behaviour of actors of international
relation. As certainty of occurrence and local/regional impact of temperature change gets
stronger, it has repercussion on the preference of decision makers in the international space.
Change in preferences can be caused, also, by change in political leadership or regime.
(Keohane 1984:116) For example, the end of Clinton governance and the beginning of G.W.
Bush governance had resulted significant difference in the U.S. attitude to the Kyoto protocol
in the presidency level. Very complex structure of possible choices can result also variable
international community pay-off in dependence of multi-country actions. And here comes the
question of timing dilemma: The further we are before the change of temperature and its
physical impact, the higher is the uncertainty of the occurrence of climate change, thus the
lower is the motivation to mitigate, however the cheaper and the more efficient is the
mitigation. The closer we get to the realization of climate change impacts, the higher is the
certainty but the mitigation or adaptation cost, too. Namely, the mix of probability, the scale
of temperature change, the current cost of adaptation and the expected damage will determine
a marginal value for the private and public and international actors as benchmark to decide the
timing of mitigation/adaptation.
In the timing of start-up the actions, there is an important factor, namely, when it does worth
to mitigate or adapt. This can be simply described by the net present value (NPV) calculation.
Just as generally, the aim of an economic actor is to maximize the net marginal benefit of the
action. (CEPS&ZEW 2010)
F = max{MB MC}
Until MB > MC, namely marginal benefit is bigger than marginal cost, there is no motivation
to start or extend the adaptation. For planning of timing of adaptation or mitigation to climate
change, this maximization should be dynamic, so the optimum NPV of adaptation cost and
climate damage is looked for. (Rubas et al. 2006)
NPV (climate change) = PV(adaptation cost) PV(climate damage)
According to the model of Hasson et al. (2010) with all-or-nothing trade-off between the
preventive mitigation and the reactive adaptation, the timing depends on the expected pay-off
for having and having not a disaster.
In Hassons et al. (2010) model, the expected pay-off depends on the probability of the
disaster, the vulnerability of the individual, the budget necessity of mitigation, budget
necessity of adaptation, existing financial instruments. Investment in mitigation lowers the
probability of a disaster for all subjects, while adaptation lowers the actual cost of a disaster
only for that individual subject. The total mitigation by the group is divided by the total
budget available to all subjects, so the more people that invest in mitigation, the lower the
probability of disaster.
Investment in adaptation may have on the economy other than preparing for a climate change
disaster. The cost of a disaster is also affected by the degree of vulnerability. The more
vulnerable are the actors, the higher will be the damage of a disaster. Likelihood of disaster is
determined by total mitigation and an element of chance, which means partly endogenous
and partly exogenous determination. It means, that the return from mitigation is largest if all
players mitigate, but there is still risk of a climate change disaster.
That is why the social dilemma is described by the marginal per capita return (MPCR) for
mitigation (m) and adaptation (a) in the followings:
MPCRm < MPCRa < n * MPCRm ,
where n is the total number of actors,
The relation between MPCR values means, that because of the exogenous chance for disaster,
the cost is too much, if every one mitigated, since it can not prevent absolute surely the
disaster. That is why it is expectable, that, depending on the above mentioned factors, there
will be some actors, who will and should not mitigate, if the community/society want to pay
the optimum cost for prevention.
The microeconomic game theory examines individual strategies in dependence of expectation
on other individuals behaviour. In the mainstream international political approaches (realism
by Morgenthau and Kenneth Waltz or constructivism by Alexander Wendt) consider the
actors of international relations just like rational individuals in the microeconomics. Thus,
games can be transplanted to international relations, like treating the global climate change
and regulation of carbon emission. In theses of Keohane (1984, 1989) and Keohane &
Hoffmann (1991) the application of game theory is to analyze the international relations is
exemplary. This literature uses variable sum games, dilemmas, dynamic preferences,
uncertainty, to explain cooperation, harmonization or conflicts. It is also important in
international relations theory, that Keohane (1984) apply the bounded rationality by Herbert
Simon when not maximization of net benefits, but satisfactory solutions are accepted, or the
empathy in relations, like humanitarianism, pacifism, Wilsons moralism, internationalism,
reciprocity as principals driving the participants decisions.
3. CPR problem in climate change
The examination of international relations with the instruments of microeconomics can be
started with a characteristic occurrence which is very often in the decentralized international
space. It is the common pool resource (CPR) problem. In the microeconomics, this problem
was described and explained by Garrett Hardin (1968) as the tragedy of commons. In the
common herding field in community ownership, the rational individual herders behaviour is
to add more and more animals onto the field and this way the cattle will overgraze, thus ruin
the grass field. This type of motivation to increase the using without limit in a limited world
(Hardin 1968:1244) is very often temptation in case of the international resources, just like the
climate. The climate, more precisely the average level of temperature in a region can be
understood as a resource for certain type of living, land cultivation, transportation, access to
costal territories, use of technologies, health conditions etc. This resource according to
natural sciences can be ruined by excessive carbon-dioxide emission. So, the common pool
resource and its possible overuse got identified. In optimum case, the users of the common
pool resource should agree, how to sustain and finance (or operate) this resource. But Olson
(1965) recognized according to the rational individual model of microeconomics, that if
someone can not be excluded from the use of the resource, he/she is not too much motivated
to contribute to the financing, sustaining of it, but to behave as a free rider.
Ostrom (1990:8-21) gathered the developed solutions for CPR problem: the Leviathan, the
Privatization, the self-financed contract-enforcement. The Leviathan model related to Hobbes,
who saw the solution of overuse of community resources in a strong central power, which
punishes the excessive access and this way change the original pay-off of excessive users.
This model has two weak points: the corrupt executives will cancel the penalty, and the
central authority might operate with incomplete information, thus can not effectively punish.
Besides, in international relations, in post-hegemonic cooperation (or multi-polar system, see
later) there is no chance to have and external strong power (the Leviathan) threatening the
carbon emitters with sure punishment. (Ostrom 1990: 12) The second option, the
privatization, according to Demsetz (1967) and Smith (1981), means that the common pool
resource should get distributed to private ownerships, and private owners will take care for the
completeness of own share. In case of climate impacts and temperature it is an irrelevant
option as this is an indivisible resource. The third solution, the self-financed contract-
enforcement means that the users watch and control each other, as they know mostly the
capacity of the resource, and as they are present in the use, they can have complete
information about the state of the resource and the behaviour of other users. In micro level,
this is a broadly used solution e.g. in case of issuing fishing, angling or hunting licences. That
is way what has been realized by the Kyoto protocol, too.
2

In case of the carbon emission as an international CPR problem, the emission can be
understood as negative CPR as more emission is worse, and its opposite CPR is the stable
temperature and all the economic and social opportunities related to this climate. The CPR
problem is that CO2 emitting countries do not want to bother with the level and impacts of
emission, do not want to join any reduction targeting or do not want to take the cost burden of
mitigation and adaptation with reference to uncertainty.
From the view of organization theory applied for international organizations, there is a very
general practice to try to solve international CPR problems. Namely, it is very close to
Coases ownership school approach that recommends the delegation of the ownership to those
who can distribute or trade the use and set the price of the resource in the most efficient way.
(Coase1960) In international relations, it means many cases, that countries create international
organisations who get the right to regulate, monitor, maybe penalize, make decisions, do
justice to disputing parties etc. In case of international oceans, external space, nuclear energy,
international trade or monetary regimes there are such international owners of the common
pool resources (many times with questionable efficiency). In case of carbon emission, such
international organisation (a Leviathan) has not been established, but the ownership has been
split among international country players who can have control over the private emitters and
trade quotas with each other, thus set the current global price of ton of CO2 emission.

2
However, the mentioned solutions tries to create a coordinated game on the use of CPR, Ostrom (1990:42-50)
still identified institutional problems rooted in uncertainty and difference in mobility, damage and dependency of
users. The problem of supply raises the question: Why would the members of a society be motivated to supply
the institutions governing the common pool resources? New institutions and rules, besides solving an existing
CPR problem, create new CPRs. The problem of credible commitments means, no one wants to be looser or as
written by Ostrom (1990) sucker, namely, no member is willing to contribute and risk any cost if other
members commitment got questionable. The problem of mutual monitoring enlightens the necessity of
voluntary activity which burden cost of punishment on the participants. The appropriation problem raise the
question, how to allocate spatial and temporal horizon. The provision problem points on the necessity of
appropriate construction and maintenance.
Table 1 and table 2 shows such prisoners dilemmas for CPR problem which are applied for
climate change mitigation/adaptation strategies. Table 1 illustrates a two countries (or two
groups of countries) situation, where the dilemma is to pay the cost of mitigation and
adaptation or not to do anything for lower carbon emission. If a country chose to mitigate and
adapt, she must pay the cost (C). Depending on strategies, in a simplified version, if both
players mitigate, there is no change of temperature, so cost of damage is zero (T0). If one of
them does not act, than at least 1 Celsius warming happens, so some economic damage will
be realized (T1). If no one acts, more serious, let us say, 4 Celsius warming occurs with
bigger economic damage.
Table 1. Climate change prisoners dilemma, country to country
Country A
STRATEGIES Mitigate and adapt No action
Mitigate and adapt C+(T0)
C+(T0)
T1
C+(T1) Country B
No action C+(T1)
T1
T4
T4
C= cost of mitigation and adaptation
T0= no temperature change, zero damage
T1= damage, caused by rising temperature by 1 Celsius
T4= damage, caused by rising temperature by 4 Celsius, T4 >> C, T4 >> T1
Source: author
Table 2 shows an intra-national situation with public and private group of players, where the
dilemma is to pay the cost of mitigation and adaptation or wait for the other type of national
actors. Namely, the public policy makers can decide whether they pay subsidies and introduce
green taxes to motivate lower carbon emission, or do not subsidize the private sector at all in
mitigation/adaptation. The private sector players can decide, whether they participate in
financing, they can share the cost (C/n + C/(1-n)), and they can reserve the current
temperature, in a simplified version, so they will not suffer damages (T0). If only on of the
types (public or private) is willing to finance, but the other one is reluctant, cost of adaptation
(C) will be levied on the willing player, but, let us say, the economic damages can be avoided
(T0). If no one is ready to finance, the economic damage will be extremely big (T5) for both
of them.
Table 2. Climate change prisoners dilemma, public to private players
Public Policy
STRATEGIES Subsidies the cost of
adaptation
No subsidies for
private sector
Pay the cost of
adaptation
C/n+(T0)
C/(1-n)+(T0)
T0
C+(T0)
Private Economic
Actors
Expect action from
Public Policy
C+(T0)
T0
T5
T5
C= cost of mitigation and adaptation, n + (1-n) = 1
T0= no temperature change, no damage
T5= damage, caused by rising temperature by 5 Celsius, T5 >> C
Source: author
These games are calibrated so, that both players no action strategy is so threatening, that it
must be avoided (if T4 damage is bigger, than C cost and bigger than T1 damage, and T5 >
C). But co-action is not secured. In table 1 the co-action depends on the C and T1 relation.
(T0 = 0). If T1 > C, it is worth to mitigate, other wise rational to wait for the other player. In
table 2, it is obvious that both C/n and C/(1-n) is bigger, than zero, so it is rational to wait for
the other player. This way of think lead us to the non action + non action pay-off in both
games, a heading for trouble, which can threaten both players to act at least individually. But
this result that they see each others to act, so they can return to passivity again etc.. It can be
established, that there is no saddle point in the two examples. Of course, the matrixes can be
rewritten in dynamic view, as time passes, T0 or T1 damage can not be limited, but will
increase. Same can happen with T4 and T5, or even with C, especially, if probability got
introduced, as either not constant variable.
4. Behaviour games for climate change practice
The climate change related behaviours can be easily modelled with two-player games. Game
theory is concerned with the actions of individuals who are conscious that their actions affect
each other (Rasmusen 1992:21) According to Ravenhill et al. (2005) the following two
games can be applied in international relations: with symmetric (equal) actors the basic
prisoners dilemma, the coordination game (also known as battle of sexes), the assurance game
(also known as stag hunt) and the chicken game; with asymmetric (weaker vs. stronger) actors
the called bluff, the harmony and the suasion.
The prisoners dilemma (see figure 2.) is a simple case to demonstrate the decision dilemma of
situation with different pay-offs depending on partners action. (Dawes 1973, Dawes 1975,
Harsnyi & Selten 1988) This is a no-communication game, when the players must derive
each others strategy from the past experience. This dilemma is the base of the following
modified situations. It could be good frame to model the followings: Shall a participating
country exceed the settled emission quotas? Cheat or not in emission reports? Do the short-
term individual and the long-term global interest meet each other in CO2 emission?
The coordination game is a situation when cooperation has added value. (see fig. 3.) The
original game is that the primary value for the husband and the wife is to be together, the
secondary is to enjoy their different favourite entertainment (football vs. opera). In this game,
the optimum (maximized total pay-off) can be achieved, if one of the partners is dominant or
selfish, the other one seeks the partners preference. Otherwise, the primary value will not be
realized. This is a good base game for following games when one of the actors must yield to
pressure. For example, rise of temperature might cause desert in Europe, but melt ice in
Siberia, thus European agriculture will be damaged, but Russian agricultural capacities will be
bigger. Someone must yield and give up own benefits for the partners favour. Climate
change can be prevented, but Russia will not have more lands for cultivation, or European
lands will become deserts (not cultivatable).
The assurance game
3
describes a state when players are unable to seize an opportunity for
cooperation that seems obvious. There is one best solution, and if it is spoiled, the worst pay-
off will be realised. That is why players are very cautious and do not act in uncertain
circumstance, but waiting for the others action or own certainty. However, after a while, cost
of passed time maters, so the players will accept the second best solution. (see fig. 4.) This is
a game without motivation for free riding. This game models e.g. the situation when small or
less developed economies waiting for large countries initiation or technologically first
comers advantage.

3
Briefly stag hunt means, stag is a very valuable trophy for the succeeding hunter and good meat for everyone,
but a missed shoot will threaten all other animal away. That is why players are very cautious. But if time is
passing without shouting, later any other type of successful meat will be good, and this will accept a second best
solution: les valuable meat and less valuable trophy.
The chicken game is a useful frame to describe a situation when two (ore more) opposite
approaches, opinions, interests are wanted to be realized for any price by the players. (see fig.
5.) The biggest damage (negative pay-off) will be realized, if all players insist on own ideas,
principles etc. and never give up their enforcement. The stubborn behaviour is motivated by
the cost, loss caused by giving up own preference. A climate example is when, during G.W.
Bush, the U.S. government insisted on market approach and market solutions of carbon
emission damages, while EU insisted on international regulation and quotas. The conflict
could have been cancelled only by change in U.S. governance (democrats returned to majority
in Congress and B. Obama became president).
The called bluff is the asymmetric game for free riding by weaker/less developed/smaller
player. There are cases when the weaker can enforce the stronger one to choose the weaker
ones preference and this way to avoid a bigger cost or loss. (see fig. 6) The weaker ones
preferred bargaining position must rooted in difference of vulnerability or resource
availability for the advantage of the weaker, in the given case. Just to enlighten it with general
international examples: The German and Japanese states defeated in the World War II could
use under valuated currency in the 1960s and this way gain higher growth financed by there
export markets. (Ravenhill et al. 2005) In the climate topic, the empirical example for called
bluff is the case when emerging countries like China or Brazil are asking compensation for
participation in the Kyoto protocol for CO2 reduction. This would mean extra costs and lower
pay-off for highly developed countries, but at least they could get closer to their objective, the
lower global carbon emission as a second best way. Meanwhile, the emission cut would be
cheaper for the emerging countries, besides they also could enjoy the benefits of less or zero
global warming, thus they (the less developed) could reach their own first best outcome. The
whole situation is derived that actually the highly developed countries are more vulnerable in
the mentioned case, as the emerging countries can blackmail them with ruing the mitigation
plans by remaining out of the carbon regulation.
The harmony (see fig. 7) and the suasion. (see fig. 8) games are specified asymmetric games
with communication between players. The games introduced before assumed no
communication, only individual deduction about the partners strategy. The harmony game is
the case when cooperation is the best solution. For a climate example, without mitigation
every big power of the Earth will lose costal territories as sea level would rise. Keohane
(1984) understood the harmony situation as an automatic, invisible hand operates the
international relation perfectly, because in that case there is no externality, so no motivation
for free riding. The suasion (convincing) means a called bluff with communication, when one
player can convince the other in negotiation to accept the second best pay-off to secure the
first best pay-off for the first one. E.g. China refers to the cost of change of the outdated
manufacturing technology as a reason to get financial compensation for Kyoto protocol
participation. A special case for suasion is the hegemonic stability, when there is one power
enforcing own first best pay-off and convincing allies to accept second best pay-off. In the
global order of 21
st
century not hegemonic, but post-hegemonic cooperation or multi-
polar/non-polar system can be mentioned. (see Haass 2008, Ikenberry 2008.)
Of course a multiplayer model is also possible by using matrixes or vectors as composition of
community or individual behaviour. (see Owen 2008, Osborne and Rubinstein (1996) and
Forg et al. (1999))

Figure 2. Prisoners dilemma

Source: Ravenhill et al. 2005
Figure 3. Coordination game

Source: Ravenhill et al. 2005
Figure 4. Assurance game (stag hunt)

Source: Ravenhill et al. 2005
Figure 5. Chicken game

Source: Ravenhill et al. 2005
Figure 6. Called Bluff

Source: Ravenhill et al. 2005
Figure 7. Harmony

Source: Ravenhill et al. 2005
Figure 8. Suasion

Source: Ravenhill et al. 2005

5. Negotiation games of climate change (3)
Negotiation games are about the enforcement of bargaining positions, namely, the relative
power. The enforcement demands to factors hand in hand: power and wealth. As Keohane
(1984) cited wealth definition by Karl Polnyi and power definition by Hans Joachim
Morgenthau, the wealth is the means of material want satisfaction, and exchange value of
marketable goods and services; the power is the control over minds and actions of others, or
control over other actors play in the process of satisfaction. The question is always: How to
use the power to enlarge wealth or how to use wealth to enlarge the power?
4
Negotiation
games can be used for modelling the process of carbon emission negotiations related to
climate change. Practically, it means in literature the modelling of strategies in the Kyoto
process.
In negotiation games, the significance of vulnerability of players and intensity of power
competition is high. The determinant factors of climate change negotiation games and the
pay-off of players are gathered by Hasson et al. (2010), which are the followings:
- Probability of warming or disaster, or expected change of temperature
- Marginal per capita cost of mitigation
- Marginal per capita cost of adaptation
- Share of cooperating partners from the total group of actors
There has been a lot of research devoted to bringing together game theory and climate
change negotiations. Simultaneous move non-cooperative (e.g. Nordhaus and Yang, 1996;
Peck and Tijsberg, 1999) and classical cooperative models (e.g. Barrett, 1994; Carraro and
Siniscalco, 1993; Chander and Tulkens, 1995) dominate the scene. Ciscar and Soria (2002)
were the first to suggest the use of sequential (extensive form) games to describe and analyze
the dynamics of the post- Kyoto negotiations in which reactions to previous moves of the
players are taken into account at any decision point. (Forg et al. 2003:252)
In the development of negotiation game models, two directions can be discovered in the
literature. The first is a sequential modelling of multi-participant decision making based on
Harsnyi model and Aumann model (Harsnyi 1967, Aumann 1974). The second one is
looking for the mapping of influence in negotiations.
Starting with sequential modelling, Forg et al. (2003) gives a good summary about the
Harsnyi model which is take the incomplete information into account. The Harsanyi model
calls for condensing all uncertainty a game might involve in defining different types of
players, each characterized by a specific information (attribute) vector whose actual
occurrence is governed by chance. Chance then determines which types of players will
actually play the game. Each player knows his own type but has only a subjective probability
distribution about the types of the rest of the players. Harsanyis basic assumption (usually
referred to as Harsanyis doctrine) is that there is a common prior distribution defined over
all possible types of all players whose conditional probabilities (conditioned on each players
own type) coincide with the posterior subjective probabilities of the players. Expected payoffs
can then be defined in terms of the common prior (or as shown by Harsanyi, equivalently in
terms of the posterior probabilities) and the game with incomplete information be reduced to
a game with complete information in which the Nash equilibrium will provide the same
solution we would have obtained in the original game (of incomplete information) if Bayesian

4
There are examples for both versions. The Nazi Germany in the 1930s or the USA in the cold war used the
power for economic advantages. Japan and West-Germany in period of 1960s-1980s used their economic wealth
to have international power as they were banned on keeping strong military force.
rationality is assumed of the players each player to maximize his own expected payoff using
his subjective (posterior) probabilities about the behaviour of the rest of the players. Forg
et al. (2003:255)
The Harsnyi model got developed and continued in the correlated equilibrium for two
players by Aumann (1974) and for multi players by Aumann (1987) with a bimatrix game.
The correlated equilibrium is based on the normal form of a noncooperative game. The
complex version has critical point, as when the game is originally defined in extensive form
and is given by the game tree, then going from the extensive form to the normal form entails
both a large growth in size and we also lose some of the direct, intuitive meaning of a CE
since the basic idea gets across through the mediation of the very complex strategies used in
the normal form. (Forg et al. 2003:259)
In the correlated equilibrium model adapted by Forg et al. (2003) from Aumann (1987), each
player can step once in a given sequence before any other player acts int he next round. Thus,
this assumption gives opportunity to draw the serial of decision options as a tree. This results
a so called tree-correlated equilibrium model derived by Forg et al. (2003) from the Aumann
model. The Forg Flp Prill model or tree-correlated equilibrium model (see figure 9)
assumes the followings: there is a game tree of an extensive game with perfect information
and probability distributions assigned to every non-terminal node, which probabilities are
known for each player. In the game there is a moderator, and the players react blindly for
moderators undercover proposal. Acceptance or rejection are the options. Forg et al. (2003)
have two way for game solution: Nash bargaining solution and Kalai-Smorodinsky bargaining
solution.
Figure 9. Example for tree-correlated equilibrium model

Source: Forg et al. (2003: 260, fig.3.)
Similar to the correlated equilibrium model, Rausser and Simon (1991) can be viewed as an
extension of Rubinstein (1982) developed the multilateral bargaining model in this model
there is no moderator, but player I does an offer, and player II can accept or reject the offer. In
case of rejection, game is repeated and bargaining can go on for an infinite number of times.
This model has been used by Pinto & Harrison (2003), where the players are the seven
regions/countries constituting the OECD. The countries choose among policy vectors and
create collations. The policy vector consists of a specific emission cut and a specific year to
attain it. The proposed coalition must be an admissible coalition as previously defined.
(Pinto & Harrison 2003:921) The model got specified for carbon regulation with and without
quota trade. The importance of
Table 3. TCCF model

Source: Courtois & Tazdat (2007:303)
The modelling of influence in climate change negotiations is made by the Tth Ciscar
Courtois Forg stochastic model (TCCF) by Tth et al. (2001) and used for simulation by
Courtois & Tazdat (2007), based on RICE model. RICE is Regional Integrated model of
Climate and the Economy (RICE), developed by Nordhaus & Yang (1996) and Nordhaus &
Boyer (1999). By the way, Yang (2003) made a coalition simulation based on RICE model for
climate change negotiations, and modelled the behaviour of big powers like China, USA etc.
In case of influence modelling, the methodological study of Courtois (2002) shall be
mentioned as an early mapping for climate change negotiations by vector and matrix
analysis.
5


5
Courtois & Tazdat (2007) illustrated the climate change negotiation games with the following situation: Each
country sends a delegate to a negotiation round. Each delegate knows to which coalition his country belongs. He
knows also his countrys payoff in any action profile. Consider pair wise interactions. The two countries
The TCCF model is built on an equilibrium framework using traditional economic concepts
regarding optimization and capital accumulation. It is a parameterized formulation of a
problem and allows the evaluation of countries pay-offs given key policy variables such as
capital accumulation and carbon emission control rates. Players optimize their economic
welfare taking into consideration the trade-off that the emission of greenhouse gases means
together production and damage, both expressible in economic terms. The model built in a
carbon-energy variable related to the energy intensity by carbon emissions. The geophysical
module of the TCCF model contains three groups of equations describing the causal chain:
emission concentration global change. Courtois & Tazdat (2007:303)
6. Conclusions
The game theory offers broad background for modelling and examination of stakeholders
behaviour affected by climate change challenges and damages. However, high number of
actors, variables, and high level of uncertainty limits the opportunities of game theory
modelling. Through the game theory, it is possible to illustrate the dilemmas and strategic
options of group of actors, thus making the very complex relation of industrial activity,
carbon emission, climate change, ecological end economic damages to be transparent for
decision makers either in economic diplomacy, or in public policy, or in private business
level.
We can conclude that the carbon emission and the climate can be surveyed the most efficient
way, if we consider them as common pool resource of the international relations. By this
approach and the well developed general theories and empirical experience on CPR problem,
we can create adequate strategies, recommendations, conclusions for the appropriate
mitigation and adaptation to global warming.
The negation games applied for climate negotiations have given opportunities to quantify and
compare the varied and diversified interests, cost, damages, benefits represented by hundreds
of countries and uncountable number of business, household, NGO etc. actors. Besides, the
negotiation games give opportunity to discover how to convince the reluctant players to
participate in mitigation and adaptation.
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