Log Limerick

Instructions

This is a closed book exam, but you will have an access to computers to check your calculations.
You have 45 minutes.
Both questions have equal weights (30 points).
You may be able to receive partial credit for intermediate calculations.

Soft

The online Game Theory Explorer tool, which allows you to build and solve games interactively in your web browser. (If nothing happens, open the link in another browser (Chrome, IE, Firefox) or try to install Adobe FlashPlayer)
An interactive guide to voiting systems
The telegram bot to create a poll @ubervotebot
This pivot tool can be used to solve linear programming problems.
A Bimatrix Games solver

Topics

Classification of the games (antagonistic, bimatix, zero\positive\negative sum, simultaneous, etc)
Maximin and Minimax Algorithms (saddle points in pure strategies)
Payoff matrix (Strategic form) <-> Tree view (Extended form) transformations
Strickly and weakly dominant and dominated strategies
Game patterns (Stag hunt, Chicken, The battle of the sexes, Prisoner's Dilemma, Rock, Scissors and Paper, Coins Matching, Hide and Seek)
Games against nature. Laplace, Savage, Wald, Hurwitz criterions.
Nash equilibria in mixed strategies. Formulas for 2x2 and 3x3 matrices.
Simplex Method (saddle points in mixed strategies). Duality.

Demo of Examination Sheets

Example A

Describe Stag hunting game: fill in a payoff matrix, find optimal strategies (30 points)
Consider the following tree view of a game. Create a payoff matrix and describe the game. (30 points).

Example B

Use the linear programming method to find a solution of the game manually (10 points), in Excel (10 points), in R (10 points).
Consider the following game: [5, 2] [3, 4]. Draw a tree and compute optimal strategies (30 points).

Books

Kevin Leyton-Brown, Yoav Shoham Essentials of game theory. A concise, multidisciplinary introduction. 2008.
Martin J. Osborne, Ariel Rubinstein A course in game theory. 1994.
Robert Gibbons A Primer in Game Theory. 1992.
Jean Tirole The theory of industrial organizations. 1988.
Avinash K. Dixit, Barry J. Nalebuff The Art of strategy: a game theorist's guide to success in business and life. 2008 (Russian translation 2015).
James W. Friedman Game theory with applications to economics. 1990.
Samuel Karlin Mathematical methods and theory in games, programming, and economics. 1959.

There once was a log named Lynn
Whose life was devoted to sin.
She came from a tree
Whose base was shaped like an e.
She's the most natural log I've seen.

There once was a number named pi
Who frequently liked to get high.
All he did every day
Was sit in his room and play
With his imaginary friend named i.

Pi Limerick

Moebius Strip Limerick

A burleycque dancer, a pip
Named Virginia, could peel in a zip
But she read science fiction
and died of constriction
Attempting a Moebius strip.

Miscellaneous

Лекции и семинары

Lecture Matrix games and their forms

Seminar Strategic & Extended Forms of Games in the GTE tool

Lecture Minimax&Maximin Algorithms