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

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## 经济代写|博弈论代考Game theory代写|Feasibility under Budget Balance

In many mechanism problems with several agents, the “principal” is not allowed to be a net source of funds to the agents. Moreover, the principal must raise enough revenue from the transfers to cover her cost. (In some applications, this cost is identically 0 .) This leads us to consider mechanisms that meet the additional constraint of budget balance:
(BB) $\sum_{i=1}^l t_i(\theta) \leq-C_0(x(\theta))$ for all $\theta .^{22}$
As in subsection 7.3.2, we say that an allocation $y=(x, t)$ is feasible if $x$ is implementable through $t$ and $y$ is individually rational; $y$ is feasible under budget balance if it satisfies BB as well.

One theme of this section will be that efficient allocations are typically not feasible under budget balance when there is incomplete information unless the individual-rationality constraints are very weak. (If budget balance is not required, individual-rationality constraints are irrelevant, as the principal can induce the agents to participate by giving them all very large positive transfers, and efficient allocations are usually feasible.) This kind of inefficiency is different from that in the monopoly-pricing example of section 7.1. There, the competitive outcome where price cquals the monopolist’s cost is both feasible and efficient; the monopolist’s optimal mechanism is inefficient because it is designed to maximize the monopolist’s profit and not social welfare. In contrast, the inefficiency results of this section pertain to all the allocations that are feasible under the budget-balance constraint.

## 经济代写|博弈论代考Game theory代写|Dominant Strategy vs. Bayesian Mechanisms

Mookherjee and Reichelstein (1989) identify a class of models in which dominant-strategy implementation involves no welfare loss relative to Bayesian implementation. ${ }^{23}$ Suppose that the agents have quasi-linear preferences, and that, for $i=1, \ldots, I$,
$$u_i(x, t, \theta)=V_i\left(x, \theta_i\right)+t_i,$$
where $t_i$ is the principal’s transfer to agent $i$. Mookherjec and Reichelstein allow $x$ to be multi-dimensional, but require that $V_i$ depend on $x$ only through a one-dimensional statistic $h_i(x)$ :
$$u_i(x, t, \theta)=V_i\left(h_i(x), \theta_i\right)+t_i .$$
They further assume that types are drawn independently, that the distribution $P_i(\cdot)$ of player $i$ ‘s type satisfies the monotone-hazard-rate condition $\left(p_i / 1-P_i\right)$ nondecrcasing) for cach $i$, and that preferences satisfy the sorting assumption $\lambda V_i / \partial \theta_i \partial h_i \geq 0$ and the condition that $\partial^2 V_i / \partial h_i \partial \theta_i$ is decreasing in $\theta_i$. Cnder these assumptions, they show that an allocation that maximizes the principal’s expected utility,
$$\mathrm{F}H\left(V_0(x, \theta)-\sum{i=1}^I t_i(\theta)\right),$$
subject to the constraints of Bayesian incentive compatibility (IC) and individual rationality,
(IR) $\mathrm{F}_\theta, u_i\left(y\left(\theta_i, \theta_i\right), \theta_i\right) \geq 0$ for all $\theta_i$.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Feasibility under Budget Balance

(BB) $\sum_{i=1}^l t_i(\theta) \leq-C_0(x(\theta))$为所有$\theta .^{22}$

## 经济代写|博弈论代考Game theory代写|Dominant Strategy vs. Bayesian Mechanisms

Mookherjee和Reichelstein(1989)确定了一类模型，其中优势策略的实施相对于贝叶斯策略的实施没有福利损失。${ }^{23}$假设agent具有准线性偏好，对于$i=1, \ldots, I$，
$$u_i(x, t, \theta)=V_i\left(x, \theta_i\right)+t_i,$$

$$u_i(x, t, \theta)=V_i\left(h_i(x), \theta_i\right)+t_i .$$

$$\mathrm{F}H\left(V_0(x, \theta)-\sum{i=1}^I t_i(\theta)\right),$$

(IR) $\mathrm{F}_\theta, u_i\left(y\left(\theta_i, \theta_i\right), \theta_i\right) \geq 0$为所有$\theta_i$。

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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## 经济代写|博弈论代考Game theory代写|The Notions of Type and Strategy

In the examples of sections 6.1 and 6.2 , a player’s “type”-his private information was simply his cost. More generally, the “type” of a player embodies any private information (more precisely, any information that is not common knowledge to all players) that is relevant to the player’s decision making. This may include, in addition to the player’s payoff function, his beliefs about other players’ payoff functions, his beliefs about what other players believe his beliefs are, and so on.

We have already seen examples where the players’ types are identified with their payoff functions. For an example where the type includes more than this, consider disarmament talks between two negotiators. Player 2 ‘s objective function is public information; player 1 is uncertain whether player 2 knows player 1 ‘s objectives. To model this, suppose that player 1 has two possible types a “tough” type, who prefers no agrement to making substantial concessions, and a “weak” type, who prefers any agreement to none at all-and that the probability that player 1 is tough is $p_1$. Furthermore, suppose that player 2 has two types – “informed,” who observes player 1’s type, and “uninformed,” who does not observe player 1’s type. The probability that player 2 is informed is $p_2$, and player 1 does not observe player 2’s type.

It is easy to construct more complicated versions of this game where, say, player 1’s prior beliefs about player 2 can be either $p_2$ or $p_2^{\prime}$, and player 2 docs not know which. In practice, though, these sorts of complications make the models difficult to work with, and in most applications a player’s beliefs about his opponent are assumed to be completely determined by his own payoff function.

More generally, Harsanyi assumed that the players’ types $\left{\theta_i\right}_{i=1}^I$ arc drawn from some objective distribution $p\left(\theta_1, \ldots, \theta_l\right)$, where $\theta_i$ belongs to some space $\Theta_i$. For simplicity, let us assume that $\Theta_i$ has a finite number $# \Theta_i$ of elements. $\theta_i$ is observed by player $i$ only. $p\left(\theta_{-i} \mid \theta_i\right)$ denotes player $i$ ‘s conditional probability about his opponent’s types $\theta_{-i}=\left(\theta_1, \ldots, \theta_{i-1}\right.$, $\left.\theta_{i+1}, \ldots, \theta_I\right)$ given his type $\theta_i$. Wc assume that the marginal $p_i\left(\theta_i\right)$ on each type $\theta_i \in \Theta_i$ is strictly positive.

## 经济代写|博弈论代考Game theory代写|Bayesian Equilibrium

Definition 6.1 A Bayesian equilibrium in a game of incomplete information with a finite number of types $\theta_i$ for each player $i$, prior distribution $p$, and pure-strategy spaces $S_i$ is a Nash equilibrium of the “expanded game” in which each player $i$ ‘s space of pure strategies is the set $S_i^{\Theta_1}$ of maps from $\Theta_i$ to $S_i{ }^6$

Given a strategy profile $s(\cdot)$, and an $s_i^{\prime}(\cdot) \in S_i^{\Theta_4}$, let $\left(s_i^{\prime}(\cdot), s_i(\cdot)\right)$ denote the profile where player $i$ plays $s_i^{\prime}(\cdot)$ and the other players follow $s(\cdot)$, and let
$$\left(s_i^{\prime}\left(\theta_i\right), s_i\left(\theta_{-i}\right)\right)=\left(s_1\left(\theta_1\right), \ldots, s_i{ }1\left(\theta{i-1}\right), s_i^{\prime}\left(\theta_i\right), s_{i+1}\left(\theta_{i+1}\right), \ldots, s_l\left(\theta_1\right)\right)$$
denote the value of this profile at $\theta=\left(\theta_i, \theta_{-i}\right)$. Then, profile $s(\cdot)$ is a (purestrategy) Bayesian equilibrium if, for each player $i$,
$$s_i(\cdot) \in \underset{s_i(\cdot) \subset s_i^{+,}}{\arg \max {\theta_i}} \sum{\theta, i} p\left(\theta_i, \theta_{, i}\right) u_i\left(s_i^{\prime}\left(\theta_i\right), s_{-i}\left(\theta_{-i}\right),\left(\theta_i, \theta_{-i}\right)\right) .$$
Because cach type has positive probability, this ex ante formulation is equivalent to player $i$ maximizing his expected utility conditional on $\theta_i$ for each $\theta_i$ :
$$s_i\left(\theta_i\right) \in \underset{s_i \in s_i}{\arg \max } \sum_{\theta i} p\left(\theta, i \theta_i\right) u_i\left(s_i^{\prime}, s_{-i}\left(\theta_{-i}\right),\left(\theta_i, \theta_{-i}\right)\right) .$$
The existence of a Bayesian equilibrium is an immediate consequence of the Nash existence theorem. (Since Bayesian equilibrium, like Nash equilibrium, is essentially a consistency check, players’ beliefs about others’ beliefs do not enter the definition – all that matters is each player’s own beliefs about the distribution of types and his opponents’ type-contingent strategies. Beliefs about belicfs, and so on, become relevant when one is considering the likelihood that play resembles a Bayesian equilibrium, and when one is considering equilibrium refinements.)

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Repeated Games with Imperfect Public Information

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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

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## 经济代写|博弈论代考Game theory代写|The Model

The building block of a repeated game, the game which is repeated, is called the staye game. Assume that the stage game is a finite I-player simultancous-move game with finite action spaces $A_i$ and stage-game payoff functions $g_i: A \rightarrow \mathbb{R}$, where $A=\times_{i \in}, A_i$. Let $\mathscr{A}_i$ be the space of probability distributions over $A_i$.

To define the repeated game, we must specify the playcrs’ strategy spaces and payoff functions. This section considers games in which the players obscrve the realized actions at the end of each period. Thus, let $a^t \equiv$ $\left(a_1^t \ldots, a_1^t\right)$ be the actions that are played in period $t$. Suppose that the game begins in period 0 , with the null history $h^0$. For $t \geq 1$, let $h^t=$ $\left(a^0, a^1, \ldots, a^{t-1}\right)$ be the realized choices of actions at all periods before $t$, and let $H^{\prime}=(A)^t$ be the space of all possible period-t histories.

Since all players observe $h^t$, a pure strategy $s_i$ for player $i$ in the repeated game is a sequence of maps $s_i^t$-one for each period $t$ that map possible period-t histories $h^t \in H^t$ to actions $a_i \in A_i$. (Remember that a strategy must specify play in all contingencies, even those that are not expected to occur.) A mixed (behavior) strategy $\sigma_i$ in the repeated game is a sequence of maps $\sigma_i^{\prime}$ from $H^{\prime}$ to mixed actions $\alpha_i \in \mathscr{X}i$. Note that a player’s strategy cannot depend on the past values of his opponents’ randomizing probabilities $\alpha{-i}$; it can depend only on the past values of $a_{{ }_i}$. Note also that each period of play begins a proper subgame. Moreover, since moves are simultaneous in the stage game, these are the only proper subgames, a fact that we will use in lesting for subgame perfection. ${ }^3$

This section considers infinitely repeated games; section 5.2 considers games with a fixed finite horizon. With a finite horizon, the set of subgameperfect equilibria is determined by backward-induction arguments that do not apply to the infinite-horizon model. The infinite-horizon case is a better description of situations where the players always think the game extends one more period with high probability; the finite-horizon model describes a situation where the terminal date is well and commonly foreseen. ${ }^4$

## 经济代写|博弈论代考Game theory代写|The Folk Theorem for Infinitely Repeated Games

The “folk thcorems” for repcated games assert that if the players are sufficiently patient then any fcasible, individually rational payoffs can be enforced by an equilibrium. Thus, in the limit of extreme patience, repeated play allows virtually any payoff to be an cquilibrium outcome.

To make this assertion precise, we must define “feasible” and “individuatly rational.” Define player is reservation utility or minmax value to be
$$r_i=\min {x_i}\left[\max {x_1} y_i\left(x_i, x_{-i}\right)\right] .$$
This is the lowest payoff player i’s opponents can hold him to by any choice of $x_i$, provided that player $i$ correctly foresees $x_{-i}$ and plays a best response 10it. I.et $m_{-i}^i$ be a strategy for player $i$ s opponents that attains the minimum in cquation 5.1. We call $m_{-i}^i$ the minmax profile against player $i$. Let $m_i^i$ be a strategy for player $i$ such that $g_i\left(m_i^i, m_{-i}^i\right)=v_i$.

To illustrate this definition, we compute the minmax values for the game in figure 5.1. To compute player 1 ‘s minmax value, we first compute his payoffs to $\mathrm{J}, \mathrm{M}$, and $\mathrm{D}$ as a function of the probability $q$ that player 2 assigns to $\mathrm{L}$; in the obvious notation, these payoffs are $v_{\mathrm{U}}(q)=-3 q+1$, $r_M(q)=3 q-2$. and $v_{\mathrm{D}}(q)=0$. Since player 1 can always attain a payoff of 0 by playing $D$, his minmax payoff is at lcast this large; the question is whether player 2 can hold player 1’s maximized payoff to 0 by some choice of $q$. Since $q$ does not enter into $v_D$, we can pick $q$ to minimize the maximum of $r_1$ and $r_M$, which occurs at the point where the two expressions are equal, i.e. $q=\frac{1}{2}$. Since $v_{\mathrm{L}}\left(\frac{1}{2}\right)=v_{\mathrm{M}}\left(\frac{1}{2}\right)=-\frac{1}{2}$, player 1 ‘s minmax value is the zero payoff he can achicve by playing D. (Note that $\max \left(v_{\mathrm{U}}(q), v_{\mathrm{M}}(q)\right) \leq 0$ for any $\left.q \in\left[\begin{array}{l}1 \ 3\end{array}-2\right] 3\right]$, so we can take player 2 ‘s minmax strategy against player $1, m_2$, to be any $q$ in this range.)

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|The Folk Theorem for Infinitely Repeated Games

$$r_i=\min {x_i}\left[\max {x_1} y_i\left(x_i, x_{-i}\right)\right] .$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 经济代写|博弈论代考Game theory代写|Applications of the Elimination of Dominated Strategies

In this subsection we present two classic games in which a single round of elimination of dominated strategies reduces the strategy set of each player to a single pure strategy. The first example uses the elimination of strictly dominated strategies, and the second uses the elimination of weakly dominated strategies.
Example 1.1: Prisoner’s Dilemma
One round of the elimination of strictly dominated strategies gives a unique answer in the famous “prisoner’s dilemma” game, depicted in figure 1.7. The story behind the game is that two people are arrested for a crime. The police lack sufficient evidence to convict either suspect and consequently need them to give testimony against each other. The police put each suspect in a different cell to prevent the two suspects from communicating with each other. The police tell each suspect that if he testifies against (doesn’t cooperate with) the other, he will be released and will receive a reward for testifying, provided the other suspect does not testify against him. If neither suspect testifies, both will be released on account of insufficient evidence, and no rewards will be paid. If onc testifies, the other will go to prison; if both testify, both will go to prison, but they will still collect rewards for testifying. In this game, both players simultaneously choose between two actions. If both players cooperate (C) (do not testify), they get 1 each. If they both play noncooperatively (D, for defect), they obtain 0 . If one cooperates and the other does not, the latter is rewarded (gets 2) and the former is punished (gets -1 ). Although cooperating would give each player a payoff of 1 , self-interest leads to an inefficient outcome with payoffs 0 . (To readers who feel this outcome is not reasonable, our response is that their intuition probably concerns a different game– perhaps one where players “feel guilty” if they defect, or where they fear that defecting will have bad consequences in the future. If the game is played repcatedly, other outcomes can be equilibria; this is discussed in chapters 4,5 , and 9.)

Many versions of the prisoner’s dilemma have appeared in the social sciences. One example is moral hazard in teams. Suppose that there are two workers, $i=1,2$, and that each can “work” $\left(s_i=1\right)$ or “shirk” $\left(s_i=0\right)$. The total output of the team is $4\left(s_1+s_2\right)$ and is shared equally between the two workers. Each worker incurs private cost 3 when working and 0 when shirking. With “work” identified with C and “shirk” with D, the payoff matrix for this moral-hazard-in-teams game is that of figure 1.7, and “work” is a strictly dominated strategy for each worker.

## 经济代写|博弈论代考Game theory代写|Definition of Nash Equilibrium

A Nash equilibrium is a profile of strategies such that each player’s strategy is an optimal response to the other players’ strategies.

Definition 1.2 A mixed-strategy profile $\sigma^$ is a Nash equilibrium if, for all players $i$, $$u_i\left(\sigma_i^, \sigma^\right) \geq u_i\left(s_i, \sigma_{-i}^\right) \text { for all } s_i \in S_i .$$
A pure-strategy Nash equilibrium is a pure-strategy profile that satisfies the same conditions. Since expected utilities are “linear in the probabilities,” if a player uses a nondegenerate mixed strategy in a Nash equilibrium (one that puts positive weight on more than one pure strategy) he must be indifferent between all pure strategies to which he assigns positive probability. (This linearity is why, in equation 1.2, it suffices to check that no player has a profitable pure-strategy deviation.)

A Nash equilibrium is strict (Harsanyi 1973b) if each player has a unique best response to his rivals’ strategies. That is, $s^*$ is a strict equi librium if and only if it is a Nash equilibrium and, for all $i$ and all $s_i \neq s_i^$, $$u_i\left(s_i^, s^{ }i\right)>u_i\left(s_i, s{-i}^\right)$$
By definition, a strict equilibrium is necessarily a pure-strategy equilibrium. Strict equilibria remain strict when the payoff functions are slightly perturbed, as the strict inequalities remain satisfied. 4.5

Strict equilibria may seem more compelling than equilibria where players are indifferent between their equilibrium strategy and a nonequilibrium response, as in the latter case we may wonder why players choose to conform to the equilibrium. Also, strict equilibria are robust to various small changes in the nature of the game, as is discussed in chapters 11 and 14. However, strict equilibria need not exist, as is shown by the “matching pennies” game of example 1.6 below: The unique equilibrium of that game is in (nondegenerate) mixed strategies, and no (nondegenerate) mixed-strategy equilibrium can be strict. ${ }^6$ (Even pure-strategy equilibria need not be strict; an example is the profile $(D, R)$ in figure 1.18 when $\lambda=0$.)

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|Definition of Nash Equilibrium

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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

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## 经济代写|博弈论代考Game theory代写|SETS

A set is any collection of distinct items. For example, the “days of the week” is a set comprising the following seven things: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Each member of a set is called an element of the set; the term point has the same meaning. One way of mathematically describing a set is to list its elements, separated by commas and surrounded by brackets, as such:
$${\mathrm{M}, \mathrm{Tu}, \mathrm{W}, \mathrm{Th}, \mathrm{F}, \mathrm{Sa}, \mathrm{Su}}$$
Note that for convenience, I use M to stand for Monday, Tu for Tuesday, and so on. Abbreviations such as these are often helpful.

Another example of a set is “integers from 1 to 100,” which can be represented as
$${1,2,3, \ldots, 100}$$
Note how an ellipsis $(\ldots)$ is used to signify the continuation of a pattern. The set of “positive odd integers” has no upper bound, so we represent it as
$${1,3,5, \ldots} .$$

## 经济代写|博弈论代考Game theory代写|FUNCTIONS AND CALCULUS

A function describes a way of associating the elements of one set $X$ with elements of another set $Y$. For each point $x \in X$, the function names a single point $y \in Y$; the point $y$ associated with $x$ is denoted by $y=f(x)$. For example,suppose $X={a, b}$ and $Y={3,4}$. A function $f$ might be defined by $f(a)=4$ and $f(b)=3$. Another function $g$ might be defined by $g(a)=3$ and $g(b)=3$. (A single $y$ value can be associated with more than one $x$ value.) To make clear between which sets a function relates, we usually write the expression $f: X \rightarrow Y$, which means ” $f$ maps $X$ into $Y$.” Here $X$ is called the domain and $Y$ is called the codomain. The set of points that $f$ can return, which is defined by
$${f(x) \mid x \in X}$$
is called the range of $f$. Many functions of interest map the real numbers into the same set. For example, we could define the function $f: \mathbf{R} \rightarrow \mathbf{R}$ by $f(x)=x^2$. In this case, if $x=3$ then $y=f(3)=9$, if $x=5$ then $y=25$, and so forth.
Real functions (those with real domains and ranges) can be graphed in the $\mathbf{R} \times \mathbf{R}$ product space-this is the usual $x / y$ plane. The graph plots the set of vectors of the form $(x, y)$, where $x \in \mathbf{R}$ and $y=f(x)$ is the value at $x$. The graph of $f(x)=x^2$ is depicted in Figure A.1. To determine the graph of a function, start by plugging in some numbers for $x$ and plotting the resulting $(x, y)$ vectors. Also find the $x$ – and $y$-intercepts, which are the vectors that correspond to $x=0$ in the first case and $y=0$ in the second case. Another useful exercise is to check what happens to $y$ as $x$ converges to positive and negative infinity. For example, as $x$ gets either very high or very low (large negative), $x^2$ becomes a very large positive number. Thus, the graph of $f(x)=x^2$ points upward on the right and the left.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|SETS

$${\mathrm{M}, \mathrm{Tu}, \mathrm{W}, \mathrm{Th}, \mathrm{F}, \mathrm{Sa}, \mathrm{Su}}$$

$${1,2,3, \ldots, 100}$$

$${1,3,5, \ldots} .$$

## 经济代写|博弈论代考Game theory代写|FUNCTIONS AND CALCULUS

$${f(x) \mid x \in X}$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。