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这是爱丁堡大学博弈论课程的代写成功案例。
CS4课程简介
This is an MSc (and 4th year) course that runs in Semester 2 (Spring 2023). The lecturer is Kousha Etessami. Some of the information below is still from the prior year, 2022. It will be updated during the course. The lecture times for the course are Mondays and Thursdays, 11:10-12:00 (Edinburgh time). The lectures will be recorded and posted online. There will also be weekly toturials, starting in Week 3. These will cover and discuss the contents of the weekly tutorial sheet. There is also a Piazza Discussion Forum for the course, accessible from the LEARN page, where you can post questions and discuss the course content with fellow students (but DO NOT share answers to coursework). The times are indicated under “Timetable” on the AGTA course DPT on the DRPS web pages the tutorial time slots may be subject change at the beginning of the course.
Prerequisites
No required reading.
Reference texts for the entire course see slides of lecture 1 for a more comprehensive list):
M. Maschler, E. Solan, and S. Zamir, Game Theory , Cambridge U. Press, 2013.
(Available online from the University Library.
K. Leyton-Brown and Y. Shoham, “Essentials of Game Theory”, 2008 . A short book, available electronically from the Edinburgh University Library.
N. Nisan, T. Roughgarden, E. Tardos, and V. Vazirani, Algorithmic Game Theory, Cambridge U. Press, 2007.
Available online from the University library.
Y. Shoham and K. Leyton-Brown, “Multi-agent Systems: algorithmic, game-theoretic, and logical foundations”, 2009. (MAS) A longer book on MAS, also available online. The main focus of the book is game theory.
T. Roughgarden. Twenty Lectures on Algorithmic Game Theory, Cambridge U. Press, 2016.
Available online from the University library.
CS4 Game theory HELP（EXAM HELP， ONLINE TUTOR）
Consider the following version of chess, in which there are three possible outcomes:
(a) Victory for White, if White captures the Black King,
(b) Victory for Black, if Black captures the White King.
(c) A draw, if:
i. if Black is stalemated,
ii. if White is stalemated,
iii. a position repeats.
Argue informally (or formally) that one and only one of the following must be true:
(a) White has a winning strategy.
(b) Black has a winning strategy.
(c) Each of the two players has a strategy guaranteeing at least a draw.
You may assume that chess is a finite game.
Consider the following bargaining problem: Two players must divide one unit of a perfectly divisible good into fractions $\alpha$ and $\beta$, such that $\alpha, \beta \geq 0$ and $\alpha+\beta=1$. If they cannot agree to a split, they get nothing. Player 1 has the utility function $u_1(\alpha)=\alpha$ and player 2 has the utility function $u_2(\alpha)=\sqrt{\alpha}$. How would you split the good so as to maximize the product of the player’s utilities?
Consider the roulette game in Vegas, where you bet on a number and the probability that you win is $\frac{1}{38}$, since there are 38 equi-probable outcomes. If the ball lands on the number you have chosen, you will be paid 35 times the amount that you bet and the bet itself.
(a) Formalize and visualize the decision problem in a decision matrix.
(b) Formalize and visualize the decision problem in a decision tree.
(c) How much can you expect to win on average, for every dollar you bet?
Explain in as much detail as you can (with examples), the differences between:
(a) Ordinal scales and Cardinal scales, and
(b) Interval scales and Ration scales.
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