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

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## 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.

# 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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