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经济代写|博弈论代考Game theory代写|ECON7062 An Asymmetric Cooperative Game

如果你也在 怎样代写博弈论Game theory ECON7062这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。博弈论Game theory在20世纪50年代被许多学者广泛地发展。它在20世纪70年代被明确地应用于进化论,尽管类似的发展至少可以追溯到20世纪30年代。博弈论已被广泛认为是许多领域的重要工具。截至2020年,随着诺贝尔经济学纪念奖被授予博弈理论家保罗-米尔格伦和罗伯特-B-威尔逊,已有15位博弈理论家获得了诺贝尔经济学奖。约翰-梅纳德-史密斯因其对进化博弈论的应用而被授予克拉福德奖。

博弈论Game theory是对理性主体之间战略互动的数学模型的研究。它在社会科学的所有领域,以及逻辑学、系统科学和计算机科学中都有应用。最初,它针对的是两人的零和博弈,其中每个参与者的收益或损失都与其他参与者的收益或损失完全平衡。在21世纪,博弈论适用于广泛的行为关系;它现在是人类、动物以及计算机的逻辑决策科学的一个总称。

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经济代写|博弈论代考Game theory代写|ECON7062 An Asymmetric Cooperative Game

经济代写|博弈论代考Game theory代写|An Asymmetric Cooperative Game

In this asymmetric game, it will be assumed that the two coastal states, players 1 and 2 , are identical in all respects, except with regards to fishing effort costs, which we will denote by $c_1$ and $c_2$, respectively. It shall be assumed that $c_1<c_2$. If we return to Chap. 3, we will be reminded, given our model, that for any level of $X$ we shall have $c_1(X)<c_2(X)$, which in turn implies that, in contrast to the symmetric case, the perception of the optimal level of $X$ will differ between 1 and 2 . We shall have $X_1^ \cdot 11$

It is not immediately clear that there would be scope for cooperation that the Core of a potential cooperative game would in fact be other than empty. We know from Chap. 3 that, if players 1 and 2 refused to cooperate, there would be three possibilities, namely, $X_1^=X_2^{O A}$ and $X_1^*>X_2^{O A}$. If either of the first two possibilities were to occur, there would be no basis for cooperation. ${ }^{12}$

Let it be supposed that the third possibility, $X_1^*>X_2^{O A}$, occurs. It is by far the most likely of the three. Now, there is clearly scope for cooperation.

One can see at once that side payments could play a role. Indeed, if side payments were feasible, global harvesting cost minimization, and thus global resource rent maximization would demand that all of the harvesting of the resource should be done by player 1 . In such circumstances, one could think of player 2 importing the harvesting services of player 1 . By assumption, however, players 1 and 2 are not prepared to contemplate side payments. Let us see what can be done.

In this asymmetric game without side payments, the payoff to player 1 will depend upon both player 1’s share of the harvest through time and upon the resource management policy through time that is adopted. There is no assurance whatsoever that the resource management policy adopted will be the one that player 1 deems to be the optimum. What applies to player 1 , applies with equal force to player 2.

In following the lead of Hnyilicza and Pindyck (1976), we first look at harvest shares. ${ }^{13}$ Let us denote 1’s harvest share as $\alpha$, and 2’s share simply as $(1-\alpha)$. There is no necessary reason why these shares should be constant through time. Both the cases of $\alpha$ being constant over time and that of $\alpha=\alpha(t)$ will be considered.

With respect to the first step, let us start with the case of $\alpha$ being constant over time. We then, in effect, have a two stage game. Stage one, determine $\alpha$; stage two determine the resource management policy through time.

As for stage one, what we can say right off is that with $\alpha$ constant through time, it is obvious that $0<\alpha<1$, if the individual rationality constraints are to be satisfied. Beyond this, we will simplify further by looking at the real world. In the real world, the determination of $\alpha$ is typically done without excessive negotiation, being usually done on the basis of some formula such as harvesting histories or zonal attachment-the amount of the resource to be found in EEZ ${ }_1$ and $E E Z_2$, respectively. ${ }^{14}$

经济代写|博弈论代考Game theory代写|Two-Player Cooperative Fishery Games with Side Payments

In examining two-player cooperative fishery games with side payments, we continue with the specific fishery model from Sect. 4.2, but now assume that the players overcome their objections to side payments. With side payments allowed, the objective becomes that of maximizing the global net economic returns from the fishery through time, and then bargaining over the division of these net economic returns between 1 and 2 .

With regards to the symmetric cooperative game, nothing changes. With regards to the asymmetric cooperative game (Sect. 4.2.2) a great deal changes. Return to Eq. (4.6). Maximizing the global returns from the fishery means giving equal weight to $\mathrm{PV}1$ and $\mathrm{PV}_2$ (set $\beta=1 / 2$ ), and then “letting the chips fall where they may”. In so doing, there are no difficulties in allowing $\alpha$ to be function of time-to the contrary. Part of “letting the chips fall where they may” involves optimizing with respect to $\alpha(t){ }^{24}$ As Munro (1979) demonstrates, this drives us to the not unexpected conclusion that the optimal $\alpha(t)$ is $\alpha(t)=1$, for all $t, 0{\text {comp }}^* \equiv X_1^*$. 2’s harvesting costs are simply irrelevant. 1 , and 1 alone, determines the optimal resource management policy.

Two comments are immediately required, both obvious. The first is that this is clearly optimal, if one’s objective is to maximize the net economic returns from the fishery through time. If the 2 fleet does any of the harvesting, the net economic returns from the fishery will not be maximized. The second is that the policy is feasible, if and only if side payments can be employed.

In Chap. 1, reference was made to the Compensation Principle. The Principle states that where there are differences in management objectives between/among the players, it is all but inevitable that one player places a higher value on the fishery resource than does (do) the other(s). Optimal policy calls for allowing that player to dominate the resource management regime, and then compensate the other(s) through the use of side payments. Here one can see the Principle at work. The low-cost player 1 obviously places a higher value on the resource than does high

cost 2 . The optimal policy described brings with it the complete dominance of 1 ‘s management preferences. Indeed, all of the harvesting is undertaken by 1 . 1 then compensates 2 through side payments.

Consider Fig. 4.3, which shows the Pareto Frontier without side payments, and the Pareto Frontier with side payments. The Pareto Frontier with side payment lies everywhere above the Pareto Frontier without side payment. Why? If there are no side payments, 2 must do some of the harvesting for there to be a stable solution to the cooperative game, which in turn means that the global net economic returns from the fishery will not be maximized.

经济代写|博弈论代考Game theory代写|ECON7062 An Asymmetric Cooperative Game

博弈论代写

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

我们现在将探讨参与者不对称的情况。我们通过假设玩家在所有方面都是相同的来引入不对称性,除了捕鱼努力成本。 双人博亦
不失一般性,假设玩家 1 的捕鱼努力成本低于玩家 2 。我们因此有 $c_1<c_2$. 正如我们所说,我们一直在展示的模型是 GordonSchaefer 模型的动态版本。在那个模型中,捕捞成本对种群大小很敏感, $X(t)$. 正如我们对方程式的讨论所回忆的那样。
(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。
这意味着,对于任何给定的水平 $X(t)$ ,玩家 1 的单位收获成本将低于玩家 2 的单位收获成本。反过来,这样做的结果是 额外的闭式大括号或缺少开式大括号 $\quad$ 和 $X_1^{O A}<X_2^{O A}$
雞放器的问题 $i$ 可以表示如下:
$$
\max _{E_i(t)} P V_i\left(E_i(t), E_j(t)\right)=\int_0^{+\infty} e^{-\delta t}\left(p q X(t)-c_i\right) E_i(t) \mathrm{d} t \text { s.t. } \frac{\mathrm{d} X}{\mathrm{~d} t}=F(X(t))-q E_i(t) X(t)-q E_j(t) X(t) X(0)=X_0, X(t) \geq 00 \leq E_i(t) \leq E^{\max }
$$

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

本章介绍的两个经典游戏已被用于模拟不同背景下的渔业。静态博弈通过关注稳态、可持续收益、收益,比动态博弈简单得多。出于这个原因,静态博弈在理论研究中得到广泛应用,尤其是在与联盟形成相结合时,如第 2 章中所示。5 和 6。动态博弈的优势在于允许捕捞努力量通过反馈策略随时间变化,其中捕捞努力量取决于库存水平。因此,动态博弈通常在实证应用中更受欢迎。

两场比赛的结果如何比较?两者都预测不合作将产生次优结果,合作确实很重要。两者都预测不对称会减轻不合作的影响,并且在某些情况下会导致最佳状态,即效率更高的参与者将效率较低的参与者赶出渔业。然而,动态博弈的结果比静态博弈的结果更具戏剧性。这在对称博弈的情况下最为明显。

任何理论、任何模型的检验都取决于其预测能力。在渔业资源快速增长的情况下,静态模型很可能发挥作用。在第一章 2、以秘鲁和智利共享鳀鱼资源为例,双人非合作博弈。结果显然是次优的,但并不是灾难性的——静态游戏类型的结果。该资源是一种增长非常快的资源。接下来的案例研究将针对一个增长非常缓慢的资源。在本案例研究中,可以看出动态对称非合作博弈的预测非常出色。

经济代写|博弈论代考Game theory代写

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现代博弈论始于约翰-冯-诺伊曼(John von Neumann)提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理,这成为博弈论和数学经济学的标准方法。在他的论文之后,1944年,他与奥斯卡-莫根斯特恩(Oskar Morgenstern)共同撰写了《游戏和经济行为理论》一书,该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论,使数理统计学家和经济学家能够处理不确定性下的决策。

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它有两个主要分支,微分和积分;微分涉及瞬时变化率和曲线的斜率,而积分涉及数量的累积,以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系,它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。

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什么是计量经济学?
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