Strategic games

Notices

The course will start on 4th of February 2011. It will take place at Science Park in the room G.05.

Lecturer

Krzysztof R. Apt

Website of the course

website

Objectives

To introduce the basic concepts of the theory of strategic games.

Prerequisites

Really basic knowledge of linear algebra and calculus. Some maturity in following the mathematical arguments.

The aim of this course is to introduce the main concepts concerned with strategic games (sometimes called non-cooperative games). This branch of game theory deals with the analysis of interaction between rational players, where rationality is understood as utility maximization. In strategic games the players take their actions simultaneously and the utility (payoff) for each player depends on the resulting joint action.

The course will deal with the following concepts: best response, Nash equilibrium, pure and mixed strategies, strictly and weakly dominated strategies, Pareto efficient outcomes, social optimum, rationalizability, pre-Bayesian games, and Bayesian games.

We shall discuss such well-known examples as the prisoner's dilemma, the beauty contest games, and the tragedy of the commons. Also, we shall use the introduced concepts to analyze some well-known examples of strategic games studied in the economics: Cournot competition, Bernard competition and location game. We shall also study special classes of games, including zero-sum games, congestion games and network sharing games.

Finally, we shall consider mechanism design, the aim of which is to arrange the economic interactions in such a way that when everyone behaves in a self-interested manner, the result is satisfactory for everybody.

Grading Information

5 problems 2 solve @ home; each worth 5 points.
Midterm exam: 25 points. It will take place Friday 25 March at 9:45.
Final exam: 50 points. It will take place Thursday 26 May, 13:00 - 16:00 in F1.02
Results so far (May 18, 2011)

Problems 2 solve

will be posted here.
Note: you are welcome to send your solutions to me by email, to
apt at cwi.nl,
subject: Solution to an assignment
or hand them in at the beginning of the lecture.
I shall acknowledge all email submissions by email. So if you don't get any acknowledgement, please yell.

Assignment 1	Solution
Assignment 2	Solution
Assignment 3	Solution
Assignment 4	Solution
Assignment 5	Deadline: 26 May, 2011, 12:58

Course material

- Resources on Game Theory

A course in game theory, M.J. Osborne and A. Rubinstein (MIT Press, 1994) (free download)
Game Theory .net ('A resource for educators and students of game theory')
Game Theory, R. Aumann (An excellent survey of game theory, with fragments about strategic games)
Potential Games (Chapter 8 from
S. Tijs, Introduction to Game Theory, Hindustan Book Agency, 2003.)
Best-Response Dynamics and Nash equilibria (pages 690-700 from
J. Kleinberg and E. Tardos, Algorithm Design. Addison-Wesley, 2005.)
D. Easley and J. Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World
(Cambridge University Press, 2010.)
Modeling Network Traffic using Game Theory (Chapter 8 from
D. Easley and J. Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.)
Y. Shoham and K. Leyton-Brown, Multiagent Systems Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2009.
(Has a number of chapters on game theory, in particular about strategic games.)
Graduate-Level Course in Game Theory, Jim Ratliff (On-line course notes.)
Game Theory Text, T. S. Ferguson (Parts II and III are about strategic games.)
Rock-Paper-Scissors: You vs. the Computer (A website from New York Times.)
Auctions (Chapter 9 from Klein and Bouwman, The Cartoon Introduction to Economics.)

- Lecture Notes

from most of the lectures will be added here.

Nash Equilibrium	notes
Nash Equilibria and Pareto Efficient Outcomes	notes
Strict Dominance	notes
Weak Dominance and Never Best Responses	notes
Regret Minimization and Security Strategies	notes
Strictly Competitive Games	notes
Sealed Bid Auctions	notes
Repeated Games	notes
Mixed Extensions	notes
Elimination by Mixed Strategies	notes
Mechanism Design	notes
Pre-Bayesian Games	notes
Alternative Concepts	notes

Lecture Notes as one file

- Slides

from some of the lectures will be added here.

Nash Equilibria and Pareto Efficient Outcomes	slides
Potential Games	slides
Mixed Strategies	slides
Mechanism Design	slides
Pre-Bayesian Games	slides

- Handouts

will be given during some lectures.