Posted on Categories:Game theory , 博弈论, 经济代写

# 经济代写|博弈论代考Game theory代写|ECO467 The Coalition Formation Model

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## 经济代写|博弈论代考Game theory代写|The Coalition Formation Model

Consider that players have to take two decisions: whether or not to join an international fisheries agreement (IFA) and the level of fishing effort. This is modelled using a two-stage framework.

The First Stage
In the first stage, each player decides on its participation: join the IFA (coalition) or be a non-member and act as a singleton. It is assumed that only one coalition (IFA) forms and that any player (country) is allowed to join it. The assumption of only one coalition comes from the UN Fish Stocks Agreement (United Nations 1995), according to which internationally shared fish stocks should be managed through Regional Fisheries Management Organizations (RFMOs). The assumption of open membership is based on Article 8 of the UN Fish Stocks Agreement, which states that participation in an RFMO should be open to all countries with “a real interest in the fisheries concerned” (see Sect. 1.2.1 for a discussion on these legal aspects).
Thus, first-stage decisions lead to a coalition structure, a partition of the set of players. This coalition structure is represented by $C=\left{S, j_1, \ldots, j_{n-m}\right}$ where $S=$ $\left(i_1, \ldots, i_m\right)$ is a coalition (IFA) with $m$ members, $m \in{1, \ldots, n}$, and $j_1, \ldots, j_{n-m}$ represent the $n-m$ singletons (non-members). In this context in which there is only one coalition, a coalition structure is fully characterized by that coalition, $S$.

## 经济代写|博弈论代考Game theory代写|Second Stage

In the second stage, players choose their fishing effort strategies. Assume that a coalition, $S$, has formed in the first stage. The steady-state payoff of this coalition is given by the sum of the payoffs of its members:
$$\Pi_S(S)=\sum_{i \in S} \Pi_i(S)=p q E_S \frac{k}{r}\left(r-q E_S-q \sum_{j \notin S} E_j\right)-c E_S,$$
where $E_S=\sum_{i \in S} E_i$ stands for the aggregate effort of the coalition members, and $E_j$ for the fishing effort of a non-member of coalition $S$.
The payoff of each non-member, $j$, is given by
$$\Pi_j(S)=p q E_j \frac{k}{r}\left(r-q E_S-q E_j-\sum_{\ell \notin{S \cup j}} E_{\ell}\right)-c E_j$$

The problem of coalition $S$ is to maximize the sum of the payoffs of its members, $\operatorname{Max}{E_S} \Pi_S(S)$, and each non-member, $j$, maximizes its own payoff, $\operatorname{Max}{E_j} \Pi_j(S)$. The solution of the second-stage game is obtained by solving both problems simultaneously, which yields the Nash equilibrium fishing efforts:
$$E_S^(S)=E_j^(S)=\frac{r(1-b)}{(n-m+2) q},$$
where $b=\frac{c}{p q k}$, which always lies in the range $[0 ; 1],{ }^1$ is the “inverse efficiency parameter” presented in Chaps. 3 and 5.

# 博弈论代写

## 经济代写|博娈论代考Game theory代写|Second Stage

$$\Pi_S(S)=\sum_{i \in S} \Pi_i(S)=p q E_S \frac{k}{r}\left(r-q E_S-q \sum_{j \notin S} E_j\right)-c E_S$$

$$\Pi_j(S)=p q E_j \frac{k}{r}\left(r-q E_S-q E_j-\sum_{\ell \notin S \cup j} E_{\ell}\right)-c E_j$$

$$\left.\left.E_S^{(} S\right)=E_j^{(} S\right)=\frac{r(1-b)}{(n-m+2) q}$$

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## MATLAB代写

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