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# 经济代写|博弈论代考Game theory代写|ECO467 Asymmetric Game

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## 经济代写|博弈论代考Game theory代写|Asymmetric Game

We will now explore the case in which the players are asymmetric. We introduce asymmetry by assuming that the players are identical in all respects, except with regards to fishing effort costs.
Two-Player Game
Without loss of generality, it will be assumed that player 1 has lower fishing effort costs than does player 2 . We thus have $c_1<c_2$. The model that we have been presenting is, as we have stated, a dynamic version of the Gordon-Schaefer model. In that model, harvesting costs are sensitive to the size of the stock, $X(t)$. As will be recalled from our discussion of Eq. (3.51), we can express unit harvesting costs as $c(X)=\frac{c}{q X}$, where the sensitivity of harvesting costs to the size of $X$ is obvious.
The implication is that, for any given level of $X(t)$, player 1’s unit harvesting costs will be lower than those of player 2 . The consequence of this, in turn, is that $X_1^ 20}$ and $X_1^{O A}<X_2^{O A}$
The problem of player $i$ can be expressed as follows:
$$\begin{gathered} \max _{E_i(t)} P V_i\left(E_i(t), E_j(t)\right)=\int_0^{+\infty} e^{-\delta t}\left(p q X(t)-c_i\right) E_i(t) \mathrm{d} t \ \text { s.t. } \frac{\mathrm{d} X}{\mathrm{~d} t}=F(X(t))-q E_i(t) X(t)-q E_j(t) X(t) \ X(0)=X_0, X(t) \geq 0 \ 0 \leq E_i(t) \leq E^{\max } \end{gathered}$$

## 经济代写|博弈论代考Game theory代写|Comparison of Static and Dynamic Games

The two classical games presented in this chapter have been used to model fisheries in different contexts. The static game, by focusing on steady state, sustainable yield, payoffs is far, far simpler than the dynamic game. For that reason, the static game is widely used in theoretical studies, especially when combined with coalition formation, as will be shown in Chaps. 5 and 6 . The dynamic game has the advantage of allowing the fishing effort to vary over time through feedback strategies, in which the fishing effort depends on the stock level. Thus, the dynamic game is usually preferred in empirical applications.

How do the outcomes of the two games compare? Both predict that noncooperation will produce sub-optimal results, that cooperation does indeed matter. Both predict that asymmetry will mitigate the effects of non-cooperation and can in some cases lead to an optimum, in which the more efficient player drives the less efficient one(s) out of the fishery. The outcomes of the dynamic game are, however, much more dramatic than those of the static game. This is most apparent in the case of symmetric games.

The test of any theory, of any model, rests upon its predictive power. In those cases in which the fishery resource is a fast-growing one, the static model is likely to come into its own. In Chap. 2, case study on the anchovy resource shared by Peru and Chile, the two-player game is non-cooperative. The results are clearly sub-optimal, but not disastrously so-a static game type outcome. The resource is a very fast-growing one. ${ }^{23}$ The case study to follow will be on a very slow-growing resource. In this case study, it will be seen that the dynamic symmetric non-cooperative game predicted brilliantly.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Asymmetric Game

(3.51)，我们可以将单位收获成本表示为 $c(X)=\frac{c}{q X}$ ，其中收获成本对大小的敏感性 $X$ 很明显。

$$\max _{E_i(t)} P V_i\left(E_i(t), E_j(t)\right)=\int_0^{+\infty} e^{-\delta t}\left(p q X(t)-c_i\right) E_i(t) \mathrm{d} t \text { s.t. } \frac{\mathrm{d} X}{\mathrm{~d} t}=F(X(t))-q E_i(t) X(t)-q E_j(t) X(t) X(0)=X_0, X(t) \geq 00 \leq E_i(t) \leq E^{\max }$$

## 经济代写|博弈论代考Game theory代写|Comparison of Static and Dynamic Games

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。