# 经济代写|博弈论代写Game Theory代考|ECON3050

## 经济代写|博弈论代写Game Theory代考|Traffic flows

A fundamental model for the analysis of flows in traffic networks goes back to WARDROP [45]. Let us look at a discrete version ${ }^2$ of it. It is based on a graph $G=(V, E)$ with a (finite) set $V$ of nodes and set $E$ of (directed) edges $e$ between nodes,
(v) $\stackrel{e}{\longrightarrow}$ (w),
representing directed connections from nodes to other nodes. The model assumes:
(W) There is a set $N$ of players. A player $i \in N$ wants to travel along a path in $G$ from a starting point $s_i$ to a destination $t_i$ and has a set $\mathcal{P}i$ of paths to choose from. Game-theoretically speaking, a strategic action $s$ of player $i \in N$ means a particular choice of a path $P \in \mathcal{P}_i$. Let us identify a path $P \in \mathcal{P}_i$ with its incidence vector in $\mathbb{R}^E$ with the components $$P_e= \begin{cases}1 & \text { if } P \text { passes through } e \ 0 & \text { otherwise. }\end{cases}$$ The joint travel path choice s of the players generates the traffic flow $$\mathbf{x}^{\mathbf{s}}=\sum{i \in N} \sum_{P \in \mathcal{P}_i} \lambda_P^{\mathbf{s}} P \quad \text { of size } \quad\left|\mathbf{x}^{\mathbf{s}}\right|=\sum_P \lambda_P^{\mathbf{s}} \leq n,$$
where $\lambda_P^{\mathrm{s}}$ is the number of players that choose path $P$ in s. The component $x_e^{\mathbf{s}}$ of $\mathbf{x}^{\mathbf{s}}$ is the amount of traffic on edge $e$ caused by the choice s.

## 经济代写|博弈论代写Game Theory代考|Potentials and Temperature

The temperature of a system depends on the measuring device in use, which is mathematically represented as a potential function. BoLTzMANN’s approach to the notion of temperature in statistical thermodynamics extends to general systems. Of particular interest are $n$-person matrix games where the temperature reflects the activity of the player set as a whole with respect to the total utility. The interpretation of the activity as a METROPOLIS process moreover indicates how the strategic decisions of individual players influence the expected value of the measuring device.
Consider a finite system $\mathfrak{S}$ that is in a state $\sigma$ with probability $\pi_\sigma$. Then $\mathfrak{S}$ has the entropy
$$H(\pi)=\sum_{\sigma \in \Sigma} \pi_\sigma \ln \left(1 / \pi_\sigma\right)=-\sum_{\sigma \in \Sigma} \pi_\sigma \ln \pi_\sigma .$$
The expected value of a potential $v \in \mathbb{R}^{\mathfrak{G}}$ will be
$$E(v, \pi)=\sum_{\sigma \in \mathfrak{S}} v_\sigma \pi_\sigma .$$
Let us think of $v$ as a numerical measuring device for a certain characteristic feature of $\mathfrak{S}$. In a physical model, the number $v_\sigma$ could describe the level of inherent “energy” of $\mathfrak{S}$ in the state $\sigma$, for example. In economics, the function $v: \mathfrak{S} \rightarrow \mathbb{R}$ could be a representative statistic for the general state of the economy. In the context of an $n$-person game, $v_\sigma$ could possibly measure a degree of “activity” of the set $N$ of players in the state $\sigma$, etc.

## 经济代写|博弈论代写博弈论代考|交通流

(v) $\stackrel{e}{\longrightarrow}$ (w)，

(W)有一个集合 $N$ 玩家。玩家 $i \in N$ 想要沿着一条路走进去 $G$ 从起点开始 $s_i$ 到达目的地 $t_i$ 有一套 $\mathcal{P}i$ 可供选择的道路。从理论上讲，博弈是一种战略行动 $s$ 球员的 $i \in N$ 指的是对某条道路的特定选择 $P \in \mathcal{P}i$。让我们来确定一条路径 $P \in \mathcal{P}_i$ 它的入射向量在 $\mathbb{R}^E$ 这些组件 $$P_e= \begin{cases}1 & \text { if } P \text { passes through } e \ 0 & \text { otherwise. }\end{cases}$$ 交通流量是由参与者的共同路径选择产生的 $$\mathbf{x}^{\mathbf{s}}=\sum{i \in N} \sum{P \in \mathcal{P}_i} \lambda_P^{\mathbf{s}} P \quad \text { of size } \quad\left|\mathbf{x}^{\mathbf{s}}\right|=\sum_P \lambda_P^{\mathbf{s}} \leq n,$$
where $\lambda_P^{\mathrm{s}}$ 选择路径的玩家数量是多少 $P$ s，分量 $x_e^{\mathbf{s}}$ 的 $\mathbf{x}^{\mathbf{s}}$ 流量是否处于边缘状态 $e$ 由选择s.

## 经济代写|博弈论代写博弈论代考|电位和温度

$$H(\pi)=\sum_{\sigma \in \Sigma} \pi_\sigma \ln \left(1 / \pi_\sigma\right)=-\sum_{\sigma \in \Sigma} \pi_\sigma \ln \pi_\sigma .$$

$$E(v, \pi)=\sum_{\sigma \in \mathfrak{S}} v_\sigma \pi_\sigma .$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: