## 经济代写|博弈论代写Game Theory代考|HOLD-UP EXAMPLE

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

## 经济代写|博弈论代写Game Theory代考|HOLD-UP EXAMPLE

For an illustration of the hold-up problem, consider a setting in which two people-Joel Dean (JD) and Brynn-interact in the development of a new product. JD is a scientist who can, with effort, design a new device for treating a particular medical condition. He is the only person with a deep knowledge of both the medical condition and physics sufficient to develop the innovative design. But JD has neither the engineering expertise nor the resources that are needed to construct the device. Brynn is the CEO of an engineering company; she is capable of implementing the design and creating a marketable product. Thus, success relies on JD’s and Brynn’s combined contributions.

Suppose JD and Brynn interact over three dates as follows. At Date 1, JD decides how much to invest in the design of the medical device. His investmentin fact, the complete design specifications-is observed by Brynn. Then, at Date 2, JD and Brynn meet to negotiate a contract that sets conditions (a price) under which Brynn can produce and market the device at Date 3. Commercial production of the device will generate revenue for Brynn, and this revenue will be a function of JD’s initial investment level. The key issue is whether JD has the incentive to invest efficiently, given that he has to later negotiate with Brynn to obtain the fruits of his investment.

Here, a bit more formally, is a description of the sequence of events: At Date 1, JD selects between “high investment” (abbreviated H), “low investment” (L), and “no investment.” If he chooses not to invest, then the game ends, and both parties get a payoff of 0 . In contrast, if JD chooses L or H, then JD pays a personal investment cost, and the game continues at Date 2. JD’s cost of low investment is 1 , whereas his cost of high investment is 10. Assume that JD’s investment choice is observed by Brynn but is not verifiable to the court, so that the investment cannot directly influence a legal action.

At Date 2, JD and Brynn negotiate over contracted monetary transfer $p$, which is a transfer from Brynn to JD to be compelled by the external enforcer (the court) if and only if Brynn elects to produce at Date 3 . The default price is $p$, which represents the legal default rule in case $\mathrm{JD}$ and Brynn do not establish an agreement. Assume that the court always compels a transfer of 0 if Brynn selects $\mathrm{N}^4{ }^4$ Also assume that the players have equal bargaining weights, so $\pi_{\mathrm{JD}}=\pi_{\mathrm{B}}=1 / 2$. At Date 3 , Brynn chooses whether to “produce” $(\mathrm{P})$ or not $(\mathrm{N})$. If Brynn chooses to produce, then $p$ is the amount transfered from Brynn to JD; if Brynn chooses not to produce, then the transfer is 0 . Thus, Brynn’s choice of whether to produce is verifiable, and the contract simply prescribes the transfer as a function of this selection. The time line of the game is pictured in Figure 21.1; note that this is not the extensive-form diagram, which you can draw as an exercise.

## 经济代写|博弈论代写Game Theory代考|UP-FRONT CONTRACTING AND OPTION CONTRACTS

Key aspects of the hold-up story are that (1) investments are unverifiable, so the court cannot condition transfers directly on these actions, and (2) there is some barrier to the parties writing a comprehensive contract prior to choosing investments. In the example that I just presented, item (2) is represented by the assumption that JD and Brynn meet only after JD makes his investment decision. This assumption may be a stretch, for in many real settings the contracting parties can negotiate and form a contract before they are required to make significant investments and take other productive actions.

Let us consider, therefore, a version of the model in which JD and Brynn meet and form a contract at Date 0 , with interaction continuing in Dates 1-3 just as described in the previous section. Think of the contract at Date 0 as the “initial contract,” and think of any contracting at Date 2 as “renegotiation.” At Date 0, JD and Brynn jointly select the value of $p$ (the amount Brynn will have to pay JD if she produces at Date 3), and they also may specify an up-front transfer. Then $p$ becomes the default value for renegotiation at Date 2. If the players keep $p$ in place at Date 2 , then we say that renegotiation of the contract did not occur. Otherwise, the parties will have renegotiated their initial contract to alter the production-contingent transfer. Assume that the default decision for negotiation at Date 0 is $p=20$, the legal default rule assumed in the previous section. The time line of the game is pictured in Figure 21.2.

Hold up is an issue even though contracting occurs at Date 0. Here’s why. Because JD’s investment decision is unverifiable, there is no way for the contract to give JD a high-powered incentive to invest (as was achieved for Carina in the example at the end of Chapter 20; see pp. 263-265. Instead, the contract can only be used to motivate Brynn in her choice between $\mathrm{P}$ and $\mathrm{N}$ at Date 3 (an action that is verifiable). One hopes that Brynn’s action can be made contingent on JD’s investment in such a way as to motivate JD to invest. Unfortunately, renegotiation at Date 2 may interfere with the whole plan because it may undo something to which the players wanted to commit at Date 0 .

# 博弈论代考

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|博弈论代写Game Theory代考|Dominance

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

## 经济代写|博弈论代写Game Theory代考|Dominance

Examine the game shown in Figure $6.1(\mathrm{a})$, and suppose that you are player 1. Regardless of your decision-making process, player 2 selects a strategy independently of your choice. She will pick either $\mathrm{L}$ or $\mathrm{R}$, and you cannot affect which she will choose. Of course, player 2 may base her choice on an assessment of what strategy you are likely to pick, but this is a matter of reason in the mind of player 2. Her decision-making process is independent of yours. ${ }^2$ A good way of thinking about this is to imagine that player 2 has already chosen her strategy but you have not observed it. You must select your own strategy.

In the game shown in Figure 6.1(a), strategy $U$ has an interesting property. Regardless of player 2’s choice, U gives you a strictly higher payoff than does D. If player 2 plays $L$, then you obtain 2 from playing $U$ and 1 from playing D. Obviously, $U$ is better in this case. Furthermore, if player 2 selects $R$, then you obtain 5 by playing $\mathrm{U}$ and 4 by playing D. Again, U is better. Technically, we say that strategy $\mathrm{D}$ is dominated by strategy $\mathrm{U}$, and thus D should never be played by a rational player 1 . Note that neither of player 2’s strategies is dominated. Strategy $L$ is better than $R$ if player 1 selects $U$, but the reverse is true if player 1 selects D.

Take another example, the game depicted in Figure 6.1(b). In this game, player 1’s strategy D is dominated by strategy M. Regardless of what player 2 does, M yields a higher payoff for player 1 than does $\mathrm{D}$. Strategy U is not dominated by $\mathrm{M}$, however, because, if player 2 were to play $\mathrm{L}$, then $\mathrm{U}$ would give player 1 a higher payoff than would $M$.

## 经济代写|博弈论代写Game Theory代考|The First Strategic Tension and the Prisoners’ Dilemma

Before enriching the theory, let’s use the concept of dominance to identify rational play in a simple application. Consider the prisoners’ dilemma game pictured in Figure 3.4 on page 29. For both players, strategy $\mathrm{C}$ is dominated by strategy D. We would therefore predict that neither player would select C. However, both players would be better off if they each selected C.

The prisoners’ dilemma illustrates one of the major tensions in strategic settings: the clash between individual and group interests. The players realize that they are jointly better off if they each select $\mathrm{C}$ rather than D. However, each has the individual incentive to defect by choosing D. Because the players select their strategies simultaneously and independently, individual incentives win. One can even imagine the players discussing at length the virtues of the $(\mathrm{C}, \mathrm{C})$ strategy profile, and they might even reach an oral agreement to play in accord with that profile. But when the players go their separate ways and submit their strategies individually, neither has the incentive to follow through on the agreement. Strong individual incentives can lead to group loss.

While we’re on the subject of conflicting interests, briefly consider two related issues. First, remember the meaning of payoff numbers. We take them to be utilities, as used generally in economics. As utilities, these numbers identify the players’ preferences. They do not necessarily signify profit or money. For example, all we mean by the payoff numbers 2 and 5 is that the player in question prefers the outcome yielding the payoff 5 to the outcome yielding the payoff $2 .^4$

# 博弈论代考

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|博弈论代写Game Theory代考|Uncertainty Degree and Inference Equilibrium

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Uncertainty Degree and Inference Equilibrium

To accurately estimate the expected payoff, the SCRC scheme defines the uncertainty degree of each strategy. Based on the $E P I(s)$, the uncertainty degree of a specific strategy $s_k\left(\delta\left(s_k\right)\right)$ is defined as follows.
$$\delta\left(s_k\right)=\frac{U_{\max }\left(s_k\right)-U_{\min }\left(s_k\right)}{\max {s \in S}\left{U{\max }(s)-U_{\min }(s)\right}} \text { s.t. }, 0 \leq \delta\left(s_k\right) \leq 1$$
In order to make adaptive decisions, the SCRC scheme needs a preference ordering for strategies. To estimate a strategy preference, the Expected Payoff for the strategy $s_k\left(E_{-} P\left(s_k\right)\right)$ is defined according to the $\operatorname{EPI}\left(s_k\right)$ and uncertainty degree $\left(\delta\left(s_k\right)\right)$.
$$E_{-} P\left(s_k\right)=U_{\min }\left(s_k\right)+\left[\left(1-\delta\left(s_k\right)\right) \times\left(U_{\max }\left(s_k\right)-U_{\min }\left(s_k\right)\right)\right]$$

At each strategy selection time, players select their strategy to maximize the $E_{-} P\left(s_k\right)$ (i.e., $\max {s \in S}\left{E{-} P(s)\right}$. According to the $E_{-} P(\bullet)$, each player can compute the selection probability for the strategy $s_k$ at the $(t+1)^{\mathrm{th}}$ round $\left(P_{r+1}\left(s_k\right)\right)$. It is given by
$$P_{t+1}\left(s_k\right)=P_{t+1}\left(e_k\right)=\frac{E_{-P} P\left(s_k\right)}{\sum_{s_j \in S} E_{-} P\left(s_j\right)}$$
$P_{t+1}\left(s_k\right)$ represents the preference of strategy $s_k$ at the $(t+1)^{\text {th }}$ game round. Therefore, based on the observation about the strategies’ past expected payoffs, players can update each strategy preference. With this information, the player can make a better decision for the next strategy selection.

As a solution concept of inference game, the SCRC scheme introduces the Inference-Equilibrium (IE), which is more general than the Nash equilibrium. To define the IE, the SCRC scheme introduces the concept of uncertainty regret $(U R)$; it is a method of comparing alternatives due to Savage (Savage, 1951). In this approach, the SCRC scheme first obtains the expected payoff for each strategy and then calculate the $U R$ for each alternative. If there are two strategies (i.e., $s_k, s_j \in S$ ), the $U R$ of strategy $s_j$ against the strategy $s_k\left(\Lambda_{s_j}^{s_k}\right)$ is given by
$$\Lambda_{s_j}^{s_k}=E_{-} P\left(s_k\right)-U_{\min }\left(s_j\right)$$
If $\Lambda_{s_j}^{s_k} \leq \Lambda_{s_k}^{s_j}$, the strategy $s_j$ is preferred to $s_k$ by players (Xiong, 2014). If the maximum regret of all players is within a pre-defined minimum bound $(\varepsilon)$, this strategy profile and the corresponding payoffs constitute the IE. Definition 2 mathematically expresses the IE.

## 经济代写|博弈论代写Game Theory代考|Utility Function for IoT Systems

In sensor communication, each machine device only sends or receives a small amount of data, and multiple devices can be grouped as clusters for certain management purposes. To manage such massive accesses, QoS requirements such as delay and throughput are needed for different types of sensor communication services. The SCRC scheme follows the assumption in (Yu, 2011) to implement the sensor services; a p-persistence CSMA/CA system with $L$ classes of devices – class 1 (or $L$ ) corresponds to the highest (or lowest) priority service. The system totally has $\sum_{i=1}^L n_i$ devices, where $n_i$ represents the number of the $i$-th class devices. The traffic activities of the $i$-th class devices follow the Poisson process with mean arrival rate $\lambda \mathrm{i}$ and departure rate $\mu \mathrm{i}$ In principle, the setting of parameter $p$ in $p$-persistent CSMA/CA is equivalently to tuning the size of backoff window in CSMA/CA. If the channel is idle, the device will transmit a packet with probability pi $w_h$ en new time slot commences. Otherwise, it will wait until the channel is idle. By varying the parameter pi $f_{\mathrm{r}}$ the $\mathrm{i}$-t $h$ class devices, differential QoS provisioning could be easily achieved. For simplicity, the SCRC scheme supposes an M/D/1 queuing model with no packet collisions. Therefore, the average output packet rate of the queuing system is equal to the input rate $\lambda \mathrm{i} .{ }L$ et $T_s^i$ denote the transmission time of a class i device, and the time fraction of that device occupies the channel is given by $\left(\lambda_i \times T_s^i\right)$. Let ei represent the probability that the channel is idle for a device of class $i$ in a given slot (Yu, 2011). $$\varrho_i=1-\sum{j=1, j \neq i}^L\left(n_j \times \lambda_j \times T_s^j\right)-\left(\left(n_i-1\right) \times \lambda_i \times T_s^i\right)$$
For the device of class $i$, the transmission probability in an arbitrary slot is represented by $\left(\rho{ }^{\circ}{ }x \mathrm{p} i{\text {. }}\right.$. Following the M/D/1 queuing model, the average service rate of the $i$-th class device $(\mu i)$ and the queuing delay $\left(W_Q^i\right)$ is given by
$$\mu_i=\frac{\varrho_i \times p_i}{T_s^i} \text { and } W_Q^i=\frac{\rho_i}{2 \times \mu_i \times\left(1-\rho_i\right)}$$

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|Uncertainty Degree and Inference Equilibrium

$$E_{-} P\left(s_k\right)=U_{\min }\left(s_k\right)+\left[\left(1-\delta\left(s_k\right)\right) \times\left(U_{\max }\left(s_k\right)-U_{\min }\left(s_k\right)\right)\right]$$

$$P_{t+1}\left(s_k\right)=P_{t+1}\left(e_k\right)=\frac{E_{-P} P\left(s_k\right)}{\sum_{s_j \in S} E_{-} P\left(s_j\right)}$$
$P_{t+1}\left(s_k\right)$ 代表策略偏好 $s_k$ 在 $(t+1)^{\text {th }}$ 游戏回合。因此，基于对策略过去预期收益的观察，玩家可以更 新每个策略偏好。有了这些信息，玩家就可以为接下来的策略选择做出更好的决策。

$$\Lambda_{s_j}^{s_k}=E_{-} P\left(s_k\right)-U_{\min }\left(s_j\right)$$

## 经济代写|博弈论代写Game Theory代考|Utility Function for IoT Systems

$$\varrho_i=1-\sum j=1, j \neq i^L\left(n_j \times \lambda_j \times T_s^j\right)-\left(\left(n_i-1\right) \times \lambda_i \times T_s^i\right)$$

$$\mu_i=\frac{\varrho_i \times p_i}{T_s^i} \text { and } W_Q^i=\frac{\rho_i}{2 \times \mu_i \times\left(1-\rho_i\right)}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|博弈论代写Game Theory代考|Cognitive Hierarchy Thinking Mechanism

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Cognitive Hierarchy Thinking Mechanism

Traditional game theory is a mathematical system for analyzing and predicting how game players behave in strategic situations. It assumes that all players form beliefs based on an analysis of what others might do, and choose the best response given those beliefs. However, this assumption is obviously not satisfied under the real world environment; experiments have shown that players do not always act rationally. To redeem this major shortcoming, the behavioral game theory offers a more realistic model for players with bounded rationality. The primary goal of behavioral game theory is to make accurate predictions (Camerer, 2004; Camerer, 2015). To satisfy this goal, the Cognitive Hierarchy (CH) mechanism was developed to provide initial conditions for models of learning while predicting behaviors in non-cooperative games (Camerer, 2004). For the player $i$, strategy attractions are mapped into probabilities; the selection probability for the $l$ th strategy $\left(\operatorname{Prob}i^l(t+1)\right.$ ) for the game round $t+1$ is defined as follows. $$\operatorname{Prob}_i^l(t+1)=\frac{\exp \left(\lambda \times A_i^l(t)\right)}{\sum{k \in S_1} \exp \left(\lambda \times A_i^k(t)\right)}, \text { s.t. }, l \in \boldsymbol{S}_i$$
where $\lambda$ is the response sensitivity, and $A_1^k(t)$ is the player $i$ ‘s attraction to choose the strategy $k$ at time $t$. The CHTPC scheme assumes that the players adjust their attractions for each strategy during the game process. If the $\lambda$ is infinite, a player gets greedy learning, in which only the action with the highest propensity is taken. If $\lambda$ approximates zero, all strategies have equal probability. Therefore, the key challenge is to find an adaptive value of $\lambda$ that achieves a reasonable trade-off (Camerer, 2003). In the CHTPC scheme, $\lambda$ is decided according to the player’s thinking level.

To compute a strategy attraction $(A(\bullet))$, the CHTPC scheme should know the other players’ decisions. Reasoning about other players might also be limited, because players are not certain about other players’ rationality. In the $\mathrm{CH}$ mechanism, the thinking mechanism is modelled by characterizing the number of levels of iterated thinking that subjects do, and their decision rules. If some players are zero-level thinkers, they do not reason strategically at all, and randomize equally over all strategies. Players, who do one-level of thinking, do reason strategically and believe others are all zero-level thinkers. Proceeding inductively, players who are $K$-level thinkers assume that all other players use zero to $K-1$ level thinking. The key issue in $\mathrm{CH}$ thinking mechanism is to decide the frequencies $(f(K))$ of $K$-level thinkers. From a common-sense standpoint, $f(K) / f(K-1)$ should be declining in $K$; in general $f(K) / f(K-1) \propto 1 / K$.

## 经济代写|博弈论代写Game Theory代考|Development Motivation

The rapid development of Internet of Things (IoT) technology makes it possible to connect various smart objects together through the Internet and to provide more data interoperability methods for application purposes. Recent research shows an increase in the number of potential applications of IoT in information-intensive industrial sectors. In various scenarios, IoT can be realized with the help of sensor communication, which provides ubiquitous networking to connect devices, so that they can communicate with each other to make collaborative decisions with limited, or without any, human intervention. Recently, the sensor communication paradigm has been considered as a new type of communication, empowering full mechanical automation that has the potential to change our life styles (Chen, 2012). However, enabling sensor communication in IoT is not straightforward. One major issue is how multiple machine-type devices should be connected in dynamic network situations. In addition, to achieve successful sensor communications, Quality-of-Service (QoS) provisioning is another important requirement. For machine devices, some applications require deterministic and hard timing constraints, and disasters occur when these are violated. For other applications, statistical and soft timing constraints are acceptable. Thus, one of the most challenging tasks is how to effectively multiplex massive accesses with enormously diverse QoS characteristics (Lien, 2011). Existing mechanisms do not adaptively tackle this QoS issue when services in IoT are performed. Until now, it is a complex and difficult work in a dynamically changing IoT environment (Giluka, 2014; Yu, 2011).

For IoT multimedia services, decisions that influence QoS are related to the packet rate control for application traffic. Based on real-time feedback, each machine device can adapt its behavior and make QoS decisions strategically to maximize its payoffs (Raazi, 2010). This strategic interaction among machine devices can be formally modeled as a decision-making mechanism. It is regarded as a process that results in the selection of a course of action from several alternatives. However, in real-world IoT operations, control decisions have to be made with only limited information. To address this issue, it is necessary to develop an effective control decision mechanism that works in situations involving uncertainty, which is caused by time pressure, lack of data, unknown factors, randomness outcome of certain attributes, etc. (Xiong, 2012; Xiong, 2014a; Xiong, 2014b).

The fundamental assumption of classical game theory is that the consequence or payoff of a strategy profile is determinate or precise (Dirani, 2006; Park, 2007). However, this assumption seems implausible and unreasonable under the real world environment. In view of realistic situations, game players may not be able to exactly expect their precise payoffs of strategy profiles. Due to limited information, players in real-life games have to make decisions under uncertainty. In canonical opinion, ‘uncertainty’ is referred to as a kind of ambiguity that describes situations where decision makers cannot determine a precise probability distribution over the possible consequences of an action (Xiong, 2014). Therefore, in games under uncertainty, the players could only assign a set of possible payoffs, rather than a precise payoff, and have an imprecise probability distribution over this set (Xiong, 2012; Xiong, 2014). To model this situation with indeterminate payoffs, some researchers have tried to apply some original ideas taken from decision theory to game models. However, this kind of work still assumes that the consequences in a game are accurate; it cannot adequately handle the problem concerning uncertain consequences and attitudes of players (Xiong, 2014).

By employing the rule of inferences, the SCRC scheme can allow a player belief concerning the possible payoffs, and determine a preference ordering over actions with respect to expected payoffs. Therefore, this game model can relax the rather stringent assumption of traditional game models. Based on the uncertainty-control game model, the SCRC scheme develops a new packet transmission rate control scheme for sensor communication. In interactive situations involving uncertainty, machine devices in the SCRC scheme can respond to current IoT system conditions for adaptive management. Therefore, they properly select the most adaptable strategy for packet transmissions while ensuring QoS for sensor communication. The distinct feature of the SCRC scheme is a more realistic game-based approach with the limited information.

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|Cognitive Hierarchy Thinking Mechanism

2004；Camerer，2015) 。为满足这一目标，开发了认知层次 (CH) 机制，为学习模型提供初始条件， 同时预测非合作博恋中的行为 (Camerer，2004)。 $i$ ，策略景点被映射为概率；的选择概率l策略 $\left(\operatorname{Prob} i^l(t+1)\right)$ 为游戏回合 $t+1$ 定义如下。
$$\operatorname{Prob}_i^l(t+1)=\frac{\exp \left(\lambda \times A_i^l(t)\right)}{\sum k \in S_1 \exp \left(\lambda \times A_i^k(t)\right)}, \text { s.t. }, l \in \boldsymbol{S}_i$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|博弈论代写Game Theory代考|Game Theory and Gaming Situation

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Game Theory and Gaming Situation

Game theory, one of the decision-making theories, began with the book Game Theory and Economic Behavior by John Von Neumann and Oskar Morgenstern (1947) in 1944. This theory is treated as a method of making decisions among plural persons, a type of decision-making that differs essentially from other decisions. In our study, we adopt an individual decision-making scenario for our purposes. The result depends not only on personal decision-making but also on other people’s decisions. Therefore, in game theory, even if a decision-making process is intended only for the purpose of one person, it always has to be made by considering the decisions of other people for their own purpose. This type of circumstances is considered a “gaming situation.”

Game theory began as a behavioral analysis of two decision makers with opposing interests. For instance, the theory is represented virtually by games such as chess. However, there are also numerous daily situations that involve gaming theory. These real-life situations include:

• Economic news such as the mergers or bankruptcies of companies,
• Salary negotiations between labor and management,
• The release of new products, and
• Changes in pricing, which are seen and heard on tv and in newspapers nearly every day.
Political examples include the division or junction of political parties, election results, and the formation of coalition governments. International examples include cross-national negotiations, territory negotiations and trade negotiations. Other applications include the construction or re-operation of
• nuclear power plants, the construction of dams, and the acceptance and processing of garbage. All of these situations involve competition and cooperation among various organizations in which the interests of companies, political parties, nations, groups, and local inhabitants are not always in accordance. In other words, they are generated from gaming situations among various decision makers.
• Gaming situations include various cases. For example, in the competition between companies, each company makes decisions individually without discussions among companies. In price setting, for example, the Fair Trade Commission would have started a collusion inquiry if it suspected that companies had talked with each other.
• However, when making decisions, companies do exhibit technical and business cooperation, merger negotiations, and contract discussions to reach agreements. Political parties negotiate during an election to increase their seats but also work and talk with opposing parties to reach compromises on bills and amendments. Moreover, in international relations, countries at war may search for a better solution through international conferences, diplomatic negotiations and trade negotiations.
• Game theory has also expanded widely to fields such as biology, information science, management engineering, social engineering, operations research, economics, political science, and sociology.

## 经济代写|博弈论代写Game Theory代考|Expression of Gaming Situations

1. Case of Non-Cooperative Game:
a. Strategic Form: The gaming situation is expressed by a method called “strategic form” when players act at the same time. In the strategic form, the gaming situation is expressed in the three elements of player, strategy and gain. First, a player is the main constituent of decisionmaking affecting a gaming situation. Next, the strategy is a plan that decided which option was taken previously when each player decides on an action. Finally, the gain is the result that occurs when each player acts according to each strategy.
b. Development Form: The gaming situation is expressed by a method called development form when decisions occur according to time. In development form, a tree structure is used for expressing who decides, when to decide and how to decide.
2. Cooperative Game: In cooperative games, the game situation is expressed by means of a special function. This special function expresses how much the group of players who contracted a collaborative relationship gains. These are called special function form or partner form in contrast to the terms strategic form or development form in non-cooperative games.
3. Cournot Model, Bertrand Model, and Stackelberg Model: The strategy which a company adopts is linked to the production output or the price of a product and divides competition into two parts. The Cournot competition is an oligopoly market in which two or two or more rival firms exist, and each company is in competition to attain profit maximization through the adjustment of production output. That is, it is competition of production output. Each company predicts a partner’s action from the market demand and supply, making decisions regarding production output used as the profit maximization of its company.

Unlike the Cournot competition, the point of competition of the Bertrand competition is not production output, but rather a price. Each company analyzes the price of a rival firm’s product and makes price decisions from which the profits of their own company become the maximum corresponding to the partner’s price. The Cournot competition and the Bertrand competition are examples of cases in which rival firms make decisions simultaneously. In the Stackelberg competition, decision-making occurs in turns (i.e., decisions are divided into leader and a Follower).

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|Game Theory and Gaming Situation

• 公司合并或破产等经济新闻，
• 劳资双方的薪酬谈判，
• 新产品的发布，以及
• 几乎每天都在电视和报纸上看到和听到的价格变化。
政治方面的例子包括政党的分裂或交汇、选举结果以及联合政府的形成。国际例子包括跨国谈判、领土谈判和贸易谈判。其他应用包括建造或重新运营
• 核电站、水坝的建设、垃圾的接收和处理。所有这些情况都涉及各种组织之间的竞争与合作，其中公司、政党、国家、团体和当地居民的利益并不总是一致的。换句话说，它们是从各种决策者之间的博弈情况中产生的。
• 游戏情况包括各种情况。例如，在公司之间的竞争中，每个公司都在不进行公司之间的讨论的情况下单独做出决定。例如，在定价方面，如果公平贸易委员会怀疑公司之间有过交谈，它就会启动串通调查。
• 但是，在决策时，企业确实会表现出技术和业务合作、合并谈判和合同讨论以达成协议。政党在选举期间谈判以增加席位，但也与反对党派进行工作和谈判，以就法案和修正案达成妥协。此外，在国际关系中，交战国可以通过国际会议、外交谈判和贸易谈判寻求更好的解决办法。
• 博弈论也广泛扩展到生物学、信息科学、管理工程、社会工程、运筹学、经济学、政治学和社会学等领域。

## 经济代写|博弈论代写Game Theory代考|Expression of Gaming Situations

1. 非合作博弈的情况
：战略形式：当玩家同时行动时，博弈情况通过一种称为“战略形式”的方法来表达。在策略形式上，博弈态势表现为玩家、策略和收益三个要素。首先，玩家是影响游戏情况的决策的主要组成部分。接下来，策略是一个计划，当每个参与者决定一个动作时，它决定了先前采取哪个选项。最后，收益是每个参与者根据每种策略行动时发生的结果。
b. 发展形式：当决策根据时间发生时，游戏情况通过称为发展形式的方法表示。在开发形式中，用树形结构来表示谁决定，什么时候决定，如何决定。
2. Cooperative Game：在合作博弈中，博弈的情况是通过一个特殊的函数来表示的。这个特殊函数表达了签订合作关系的玩家群体获得多少收益。这些被称为特殊功能形式或合作伙伴形式，与非合作博弈中的战略形式或发展形式形成对比。
3. Cournot模型、Bertrand模型和Stackelberg模型：公司采取的战略与生产量或产品价格挂钩，将竞争分为两部分。古诺竞争是一个寡头垄断市场，存在两个或两个或两个以上的竞争企业，每个企业都在竞争，通过调整生产产量来实现利润最大化。即是生产量的竞争。每个公司根据市场需求和供应预测合作伙伴的行动，做出有关生产产量的决策，作为公司利润最大化。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|博弈论代写Game Theory代考|LITERATURE REVIEW

statistics-lab™ 为您的留学生涯保驾护航 在代写博弈论Game Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写博弈论Game Theory代写方面经验极为丰富，各种代写博弈论Game Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|博弈论代写Game Theory代考|Real Option Literature

Steward Myers (1977, November) was the first who introduced “real options”. The real options approach applies the theory of financial option pricing to real assets while financial options deals with buying and selling contracts and obligations in the future. It referred the application of option pricing theory to the valuation of non-financial or “real” investments, such as multi-stage $R \& D$, manufacturing plant expansion. In strategic investments, a decision maker must understand the market evolves uncertainty. The real options method takes into consideration the managerial and strategic resilience in decision making and change the whole decision making process to a contingent one, which does not require the future investment decisions to be fixed at the outset. The managers can choose to expand if the market potential turns out to be large, or to contract if the past phases do not seem to be profitable. These options on strategy raise the value of the project, which have often been underestimated by the NPV approach. Many researchers have put great effort in the application of the real options approach to various industries and most of them proved helpful for managers to make contingent strategic decisions.

According to the limitations of such conventional methods as NPV, a project discount rate is the opportunity cost of capital. All risks are completely accounted for by the discount rate. Therefore, the traditional NPV method has serious shortcomings in analyzing projects when information concerning future investment decisions is not yet known. This leads most of decision makers to minimize the discount rate as much as possible in order to improve the payoff of the project. However, the uncertainty also means the opportunity to get more payoffs because the value of options is real, the greater the future uncertainty, the greater the project value should be. Dixit and Pindyck (1994) provide a systematic treatment of an approach to capital investment decision and the basic theory of irreversible investment under uncertainty. The study of the optimal timing of investment in an irreversible project where the benefits from the project and the investment cost follow continuous time stochastic processes can be found in (McDonald \& Siegel, 1986). The project value and the investment are assumed follow geometric Brownian motion (Dixit et al., 1994; McDonald et al., 1986).

For practitioners, the binomial tree model is the most widely used technique in the field of decision analysis. The details of such a technique can be found in (Trigeorgis, 1991). Trigeorgis develops a log-transformed variation of the Cox-Ross-Rubinstein binomial method. The major advantage of the procedure is that it can be flexibly applied to various real options problems encountered in corporate finance practices. This method is suitable for the situations that there are more than two options to be evaluated. In addition, there are multiple interacting options with the risk of rare event in the investment process (Trigeorgis, 1991; Cox et al., 1979, September).

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|Real Option Literature

Steward Myers（1977 年 11 月）是第一个引入“实物期权”的人。实物期权方法将金融期权定价理论应用于实物资产，而金融期权则处理未来的买卖合同和义务。它将期权定价理论应用于非金融或“真实”投资的估值，例如多阶段投资R&丁, 制造厂扩建。在战略投资中，决策者必须了解市场演变的不确定性。实物期权法考虑了决策过程中的管理弹性和战略弹性，将整个决策过程变为或有过程，不需要在一开始就确定未来的投资决策。如果市场潜力很大，管理者可以选择扩张，如果过去的阶段似乎没有盈利，管理者可以选择收缩。这些战略选择提高了项目的价值，而 NPV 方法常常低估了这些价值。许多研究人员在将实物期权方法应用于各个行业方面付出了巨大的努力，其中大多数被证明有助于管理者做出或有战略决策。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。