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# 博弈论代写代考| Variable-Sum Games 数学代写

## 博弈论代考

With constant-sum games, we introduced mixed strategies as a way to handle games that were not strictly determined; that is, they had no saddle points, which were the same things as pure strategy Nash equilibria. The same idea works for variable-sum games. It is quite possible that a variable-sum game has no pure-strategy Nash equilibrium. Yet Nash proved that every game has at least one equilibrium point, so there must be a way to find one using mixed strategies. We’ll show an example presently, but before embarking on the example, we caution the reader not to get his or her hopes up too much. In the example of the last subsection, we did find a Nash equilibrium (even one using pure strategies), yet we had reason to possibly reject that outcome as an alleged “solution” to the game.
Consider the game with the following payoff matrix:
$$A=\left[\begin{array}{ll} (3,5) & (6,1) \ (7,2) & (5,7) \end{array}\right]$$
The reader should check that none of the four outcomes is a Nash equilibrium (for example, draw a movement diagram). The concept of a mixed strategy is the same as before, as is the notation. Thus, playing $p=[0.4,0.6]$ can be interpreted as playing the first row $40 \%$ of the time in the long run with repeated play or, equally well, as saying that on any one play of the game, the first row is played with probability $0.4$. So, for example, if $p=[0.4,0.6]$ and $q=\left[\begin{array}{l}0.7 \ 0.3\end{array}\right]$, how do we determine the expected payoff to each player? The formula $E(p, q)=p A q$ is still valid (assuming that the players choose simultaneously and independently, as usual), only this time, we must be careful about what we use for $A$. If you want the row players payoffs, you use just the first coordinates in the payoffs in A. To obtain the column players payoffs, in the constant-sum case, this time using the second coordinates in $A$. So for the given example:

$$A=\left[\begin{数组}{ll} (3,5) & (6,1) \ (7,2) & (5,7) \end{数组}\right]$$

## 博弈论代写

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## 编码理论代写

1. 数据压缩（或信源编码
2. 前向错误更正（或信道编码
3. 加密编码
4. 线路码

## 复分析代考

(1) 提到复变函数 ，首先需要了解复数的基本性左和四则运算规则。怎么样计算复数的平方根， 极坐标与 $x y$ 坐标的转换，复数的模之类的。这些在高中的时候囸本上都会学过。
(2) 复变函数自然是在复平面上来研究问题，此时数学分析里面的求导数之尖的运算就会很自然的 引入到复平面里面，从而引出解析函数的定义。那/研究解析函数的性贡就是关楗所在。最关键的 地方就是所谓的Cauchy一Riemann公式，这个是判断一个函数是否是解析函数的关键所在。
(3) 明白解析函数的定义以及性质之后，就会把数学分析里面的曲线积分 $a$ 的概念引入复分析中， 定义几乎是一致的。在引入了闭曲线和曲线积分之后，就会有出现复分析中的重要的定理: Cauchy 积分公式。 这个是易分析的第一个重要定理。