L9: International Environmental Problems

Question 1

What conditions are necessary for international cooperation according to Game Theory? (useful for evaluation points) 13

Answer 1

(i) The existence of an international political institution
(ii) Output of agreement yields private goods
(iii) A large proportion of nation specific benefits
(iv) A small number of cooperating countries
(v) Relatively high cultural similarity
(vi) A leadership role
(vii) A small degree of uncertainty about costs and benefits
(viii) The agreement is self-enforcing
(ix) It is a continuous relationship
(x) The existence of linked benefits
(xi) Short-run costs of implementation are low
(xii) A high proportion of available benefits are obtained currently
(xiii) The costs of bargaining are small relative to the expected gains

Question 2

How many international treaties have been created?

Answer 2

170

Question 3

Why is Game theory appropriate for international behaviour?

Answer 3

This interdependence is evident in environmental problems. For example, where pollution spills over national boundaries, expenditures by any one country on pollution abatement will give benefits not only to the abating country but also to others as well.

▪ Similarly, if a country chooses to spend nothing on pollution control, it can obtain benefits if others do so.

So, in general, the pay-off to doing pollution control (or not doing it) depends not only on one’s own choice
but also on the choices of others.

Question 4

What determines if cooperation can be sustained? 3

Answer 4

The communications between countries,

The number of interactions/repetitions

The self-interests/preferences of each country

Question 5

In the simple game theory prisoner’s dilemma game, what are the large assumptions? 3

Answer 5

Pollution abatement is assumed to be a public good that benefits both countries equally.

There is no cost to both countries polluting

Symmetry

Question 6

The chicken game advances on from the simple PD game in that…

Is there a nash equilibrium in the PD game?

Answer 6

it assumes a cost from both countries both not abating and ‘doing nothing’

Yes, the solution (both pollute is a nash equilbrium but not cost efficient because they could both do better if they both abated)

Question 7

Chicken Game; what represents main course and what represenets swerve?

What is the assumption that has changed for this game?

Is there a Nash Equilibrium?

Answer 7

MC = pollute
swerve = abate

That there is a cost for both countries chossing to pollute. The game is still played simultaneously.

Yes, two nash equilibriums (abate, pollute) x2

Question 8

▪ Countries could only be forced to keep to their promises if there was a ___ ____ that could enforce the agreement

▪ No such enforcer as states are ____ so agreements must be ___-____

▪ If the situation resembled a game of chicken then there would be some form of protective action but there is some doubt about who will do it

Answer 8

▪ Countries could only be forced to keep to their promises if there was a third party that could enforce the agreement

▪ No such enforcer as states are sovereign so agreements must be self-enforcing

▪ If the situation resembled a game of chicken then there would be some form of protective action but there is some doubt about who will do it

Question 9

How is the game different if it takes the extensive form?

Answer 9

The game is played sequentially, therefore one player chooses a move and the other chooses after.

This game is different because (assuming rationality and common knowledge of BR’s) the game’s nash equilibrium can now be found using backward induction.

There is a first mover advantage but struggle to determine what constitutes pre-commitment

Question 10

The assurance game involves threshold benefits, what are these?

Answer 10

Threshold benefits are when the benefits are only enjoyed once a certain level of commitment is reached - in the assurance game is this means the benefits of abatement are only realised once both players commit to abating. This is arguably most representative of reality.

eg: controlling of infectuous disease

Question 11

In a one-shot scenairo of the assurance game (with threshold benefits) is there a dominant strategy ?

What could change this?

Answer 11

Looking first at non-cooperative behaviour, there is no dominant strategy for either player, two NE. Which is more likely to occur? Clear that game theory may not be of much help in a one-shot scenario.

▪ If repeated (Abate, Abate) is more likely.

Question 12

What makes the Cooperative solution stable?

Answer 12

The cooperative solution is that in which both contribute. This solution is stable because (Abate, Abate) is self-enforcing: In the interest of one to
cooperate if the other does. Once here, non will wish to renege or renegotiate

• change structure of pay-offs
• simultaneous or sequential moves?
• which country moves first?
• what constitutes pre-commitment/reputation?

Question 13

When there are multiple players (as in practice) what is critical in determining whether cooperation can be achieved?

Answer 13

▪ The structure of pay-offs is critical in determining whether cooperation can be sustained. Consider pay-offs to choices in a more general way

Question 14

How can the net benefits/payoffs for Abating and polluting be written when there are multiple players?

What is the outcome of this?

Answer 14

NB^p = a + bK

NB^a = c + d(K+1)

These parameters determine the number of countries that cooperate

Outcome is two stable equilibria: either all
will abate, or none will.

Question 15

Why are the two equilibria of the multiple players game stable?

Answer 15

The two equilibria are stable because
(i) With no abaters, no country can individually improve its pay-off by abating rather than polluting (i.e., 12 > 0).

(ii) If every country abates, no country can individually improve its pay-off by polluting rather than abating (12 < 63).

▪ No other combination of polluting and abating countries is stable, e.g., if you are polluting and two others are abating (i.e., the remaining 7 pollute), you get 18 and they each get 14.
▪ But the abaters have an incentive to switch (pollute) as the pay-off rises

Question 16

If the structure of the payoff means that there is a higher payoff if more countries cooperate then, what is the outcome?

Answer 16

If the structure of the payoff means that there is a higher payoff if more countries cooperate then, despite higher payoffs when just a few cooperate, the large marjority will pollute

Question 17

Continuous Payoffs:

▪ The situation has been unrealistic thus far because we have focused on a ____ decision

▪ In practice it’s usually a non-discrete decision (not an all-or-nothing choice). Three types of discrete outcome:

Answer 17

Continuous Payoffs:

▪ The situation has been unrealistic thus far because we have focused on a binary decision

▪ In practice it’s usually a non-discrete decision (not an all-or-nothing choice). Three types of discrete outcome: none abate, all do, or some do and some
don’t

Question 18

What is the Payoff for each country i:

Answer 18

Pi i = B (Z) - C (zi)

Where Z is the total abatement and zi is the abatement for each individual country

Still assume symetry between countries

Question 19

▪ Given the assumption of symmetry, all countries’ efficient _____ are identical

▪ Each country abates to the point where …

▪ Full cooperative behavior is where the N countries jointly choose their levels of ____ to maximise their ____ pay-off. Abatement in i is chosen to max
the ___ pay-off

Answer 19

▪ Given the assumption of symmetry, all countries’ efficient abatement are identical

▪ Each country abates to the point where MBA=MCA

▪ Full cooperative behavior is where the N countries jointly choose their levels of abatement to maximise their collective pay-off. Abatement in i is chosen to max
the collective pay-of

Question 20

Full cooperation is collectively rational/welfare-maximising for all N countries treated as a single entity (e.g., EU).

Efficiency gain is the shaded area, the size of which depends on:’

(i)
(ii)

Answer 20

Full cooperation is collectively rational/welfare-maximising for all N countries treated as
a single entity (e.g., EU).

Efficiency gain is the shaded area, the size of which depends on:’

(i) slopes of MBAi and MCAi,
and (ii) the number of countries

Question 21

The world consists of two countries X which is poor and Y which is rich. The total benefits (B) and total costs (C) of emissions abatement (A) are given by
the functions:

How do you solve for the :

(a) Obtain the non-cooperative =m levels of abatement for X and Y
(b) Obtain the cooperative =m levels of abatement for X and Y

Answer 21

a)

Subtract the cost function from the benefits function for X and Y separately. And then differentiate and make equal to zero, separately.

b) In the cooperative outcome, the benefit and cost functions are combined (U = Ux + Uy)

this is then differentiated wrt the Ax and Ay

Question 22

▪ A third possibility is ____ cooperation: some countries agree to abate pollution (by negotiated amounts), while others act independently, doing the best they can given what the cooperators have agreed.

▪ This could be described as an ___ environmental agreement

▪ Self-enforcing international agreements: create incentives for all parties to adhere to the agreement, once it has come into effect.

▪ If a country cooperates the signatories will ___ their abatement (rewarding ____). If a country cheats they will ___ their abatement (punishing
____)

Answer 22

▪ A third possibility is partial cooperation: some countries agree to abate pollution (by negotiated amounts), while others act independently, doing the best they can given what the cooperators have agreed.

▪ This could be described as an incomplete environmental agreement

▪ Self-enforcing international agreements: create incentives for all parties to adhere to the agreement, once it has come into effect.

▪ If a country cooperates the signatories will increase their abatement (rewarding cooperation). If a country cheats they will reduce their abatement (punishing
defection)

Question 23

What kind of self-enforcing IEA do we expect to see – if any – under a variety of different circumstances?

5

Answer 23

What kind of self-enforcing IEA do we expect to see – if any – under a variety of different circumstances?

(i) Non-signatories and signatories would do better if they cooperated (PD?)
(ii) Non-signatories do better than signatories (Chicken?)
(iii) Full cooperation is not usually stable
(iv) High degree of cooperation only if the difference between global net benefits
under the full and non-cooperative solutions are small
(v) Self-enforcement cannot support a large number of countries, no matter how
many signatories there are. Difficult to secure agreement among a large number
of countries.

Question 24

▪ The larger the potential gains from cooperation, the larger the gains from ___-___ and so the larger are the incentives to ___.

▪ But the larger are the incentives to defect, the ____ will be the number of signatories.

▪When N is large, defection or accession will have only a small effect on total ___ of the other cooperators. There the gains from cooperation are very large, so there is an incentive to defect.

• Thus, it will be difficult to secure agreement among a large number of countries

Answer 24

▪ The larger the potential gains from cooperation, the larger the gains from free-riding and so the larger are the incentives to defect.

▪ But the larger are the incentives to defect, the smaller will be the number of signatories.

▪When N is large, defection or accession will have only a small effect on total abatement of the other cooperators. There the gains from cooperation are very large, so there is an incentive to defect.

• Thus, it will be difficult to secure agreement among a large number of countries

Question 25

What other mechanisms exist to achieve cooperation?

4

Answer 25

Role of commitment: Countries may make voluntary commitments irrespective of what others do. Giving up the right to change abatement levels in response to changes in number of cooperators. If the commitments are regarded as credible, then possible to achieve and
sustain a full (complete) IEA.

(ii) Transfer and side payments: Suppose an agreement can only support a small number of signatories. Signatories can offer side-payments to non-signatories to enter. Side-payments must be greater than original
inducements

(iii) Linking benefits and costs: Joint consideration of benefits e.g. national debt, so that agreements link different objectives, creating overall positive net benefits for the entire set of participants. Willingness
to act in the common interest in one respect may secure benefits in another respect. Some costs though. If large, the smaller are the net gains from cooperation

(iv) Repeated games: Observation of actual cases and experimental games suggest cooperation is commonplace, especially in the face of communication is allowed. Likelihood of cooperation also increases
greatly with continuous interaction or unknown end point. For example tit-for-tat strategies tend to encourage cooperation.