# Chapter 6 Stability of Industry level climate coalitions without enforcement policies

## 6.2 the Incentive To Change Memberships

This research investigates the potential for the success of self-enforcing environmental coalitions in the container shipping industry. Thus far, we have parameterized a game of environmental coalition formation. We assume that coalition membership decisions are taken within the first stage of the game, followed by the players’ optimal abatement strategies. However, the equilibrium concept that we need here extends beyond simply deriving vessel speeds and optimal fleet size’s \(PANE\) for all possible coalition structures. We also leverage ’ s concept of cartel stability under open membership to investigate the number and size of stable coalitions under the conditions of the maritime shipping industry.

As a game construct, coalition formation is often distinguished by the characteristics of its members. Restricted access (i.e. exclusive) games require consent from the coalition prior to changing membership decisions, whereas, open access games allow membership decisions to freely change without any restriction from the existing coalition’s members (). Our specific membership model assumes that abatement strategies and membership decisions are adopted simultaneously and that only a single member deviation from the coalition is investigated. So in the simulations, when a shipping firm flips its strategy and leaves the coalition to become a singleton, a smaller coalition survives among the remaining signatories. The latter is done for tractability, and we note that that coalition stability under exclusive memberships is beyond the scope of this research.

Subsequently, following cartel formations that can occur in a static oligopoly, Cournot-Nash framework, here a coalition structure \(C\) is only considered stable if it’s both internally and externally stable. Formally, internal stability implies that no signatories \(i \in C\) have an incentive to leave the coalition. External stability assumes that non-coalition members $ j C $, receive lower payoffs by switching their membership, and therefore, lack an incentive to join the extant coalition. \[\begin{equation} \begin{cases} \text{Internal Stability: } \Pi_i (C_{-i} ) \leq \Pi_i (C ) ~\ \forall i \in C \text{External Stability: } \Pi_j (C_{+i} ) \leq \Pi_j (C) ~\ \forall j \notin C \end{cases} \end{equation}\]

Furthermore, we leverage the individual rationality assumption and compute each members’ incentive to change membership \((ITCM)\). \(ITCM\) is affected by the payoff function. It quantifies gains, and therefore the incentives with switching membership, holding all else constant. When leaving the coalition, signatories with positive values receive higher payoffs whereas members with a negative $ITCM $ would be giving up their gains. Just as well, singletons with positive \(ITCM\) would benefit from joining the coalition. ( ; ; )

\[\begin{equation} ITCM_i (C)= \pi_i \bigg(C_{-i} \vee C_{+i} \bigg) - π_i \bigg(C\bigg) \end{equation}\]

Overall, considering $ N^{firms}$, we can derive \((2^{ N^{firms}})\) combinations of different abatement strategy vectors. However, one-firm coalitions convey the same structure as an all-singleton model. Therefore, we only need to investigate \((2^{ N^{firms}}- N^{firms})\) structures. The singleton structure is internally stable by definition, and since a single membership has no distinct meaning, the all-singleton structure is also externally stable ().

Once we numerically derive \(BAU\) emissions and abatement paths per firm, we need to iterate through the following procedure to compute the $ ITCM_i$ for every possible coalition structure:

## 6.3 Coalition stability analysis without taxation schemes

### 6.3.1 All singletons coalition structure

#### 6.3.1.1 Evaluation of the convergence of the coev-ga procedure

Insert a graph such that z =market strcuture ; Revenues / fuel comsimption cost and fixed cost per number of iteration

BAU emissions path / BAU pollution Stock / Damages

Insert a graph of emission path over the years by market structure for BAU

1000 | 5000 | 10k | 50k | 100k | 200k | 1000 | 5000 | 10k | 50k | 100k | 200k | 1000 | 5000 | 10k | 50k | 100k | 200k | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Net present value \(\Pi (USD)\) | ||||||||||||||||||

Total Fixed Cost \((USD)\) | ||||||||||||||||||

Total Fuel Consumption Cost \((USD)\) | ||||||||||||||||||

Average fleet size | ||||||||||||||||||

Average vessel speed | ||||||||||||||||||

BAU \(CO_2\) emissions | ||||||||||||||||||

BAU \(CO_2\) pollution stock | ||||||||||||||||||

BAU \(CO_2\) environmental damages | ||||||||||||||||||

BAU \(SO_x\) emissions | ||||||||||||||||||

BAU \(SO_x\) pollution stock | ||||||||||||||||||

BAU \(SO_x\) environmental damages |

#### 6.3.1.2 output analysis

convey the results of the non-cooperative case where all shippers act as singletons.

Industry Damages of \(CO_2\) in 2042 =

Industry Damages of \(SO_X\) in 2042 =

Firm | Annual abatement year 0 | Annual abatement year t | (NPV) of payoff | \(CO_2\) MAC in year 0 US /ton | \(SO_x\) MAC in year 0 US /ton |
---|---|---|---|---|---|

Firm 1 | |||||

Firm 2 | |||||

Firm 3 | |||||

Global |

illustrates the incentive structures of the different firms for the non-cooperative case where all players act as singletons.

Does The difference between annual abatement in the All Singletons case and in BAU decreases over time ?? and how much industry damages does it leads to by the year 2042 , This corresponds to about x times the Damage level in 2042 in BAU

Does Abatement differs across firms as the abatement level is determined by firm’s marginal benefits and marginal costs. In our model, bigger sized firms have a higher share of global benefits than the smaller firms ?

The big firm , having a low marginal abatement cost curve and high share of global benefits (think USA), will it havw an incentive to make substantial abatement efforts even in the All Singletons case .

How much each firm reduces its BAU emissions throought the years (get a graph of emissiob paths comparing the 2)

firms with higher marginal abatement costs and lower shares of global benefits will they have hardly any incentive to reduce emission on their own. ()

Even if a firm has a relatively high share of global benefits, could they not not make large abatement efforts due to their high marginal costs of abatement (a different market structure where firm 3 has high market share).

### 6.3.2 Grand coalition structure

Industry Damages of \(CO_2\) in 2042 =

Industry Damages of \(SO_X\) in 2042 =

Table displays the results for the Grand Coalition without taxation

Firm | Annual abatement year 0 | Annual abatement year final t | (NPV) of payoff | \(CO_2\) MAC in year 0 US /ton | \(SO_x\) MAC in year 0 US /ton | Incentive to change membership (NPV) |
---|---|---|---|---|---|---|

Firm 1 | ||||||

Firm 2 | ||||||

Firm 3 | ||||||

global |

In theory, with a Grand Coalition, marginal abatement costs equal the sum of marginal benefits among all firms.

The abatement allocation differs widely between firms ???

In the Grand Coalition, the total gain from cooperation in terms of the net present value of payoffs compared to the All Singletons case is: $Global_{NPV}^{GrandCoalition} - Global_{NPV}^{AllSingelton} $

Even though substantially higher global payoffs can be achieved,?? some firms will be worse off when the Grand Coalition is formed, maybe the firm that has the flattest abatement cost curve in our setting and has to contribute a lot to reduce emissions. This will probably leads to a large reduction in this firm’s net present value when comparing their All Singletons case to their NPV in the Grand Coalition.

The incentive to leave the coalition, i.e. the increase in payoffs by unilaterally changing the membership decision, is shown in the last column.

- In the case of the Grand Coalition where all firms are signatories, a positive number indicates an incentive to leave the coalition, while a negative number indicates the benefit from membership:
- which firms have no incentive to leave the Grand Coalition
- which firms have an incentive to leave the Grand Coalition , ie have stronger free-rider incentives and wisha to leave.

Compare damage values between the singeltons and grand coalition

### 6.3.3 Specific Characteristics coalition structure

We compute all possible cartel coalitions and examine stability of all 5 coalition structures We have 5 coalition structure to analyse under 5 different market structure Add a graph of MAC for each firm by percent reduction in Co2 and SOx ??

**is any of these colitions stable ??**

**Expectations**

check for the number of internaly stabile coalitions ? How many are also externally stable Without a taxation scheme, (xx or 0).

is the Larger coalitions (grand coalition ) not stable because free-rider incentives are strong and most firn are better off when they stay outside a coalition.

The following Table should reflect the results for any stable coalition - if they exist -

Further, we should look at firms’ abatement efforts , which firm is making the largest abatement ?? As a result of their cooperation, could firms obtain slightly higher payoffs than in the All Singletons case.

Why wont we have stable coalitions ??In equilibrium, the signatories have an interest in cooperating, because of their higher marginal benefits from abatement, while none of the singletons have an interest in joining, as their abatement costs would increase too much if they have to take the benefits of Japan and EU15 into account.

**Stable coalition of Firm x and Firm y -if it exists ??**

Industry Damages of \(CO_2\) in 2042 =

Industry Damages of \(SO_X\) in 2042 =

Firm | Annual abatement (year 0) | Annual abatement (final) | (NPV) of payoff | \(CO_2\) MAC in year 0 US/ton | \(SO_x\) MAC in year 0 US/ton | Incentive to change membership (NPV) |
---|---|---|---|---|---|---|

Firm 1 | ||||||

Firm 2 | ||||||

Firm 3 |