Lectures
2 sessions / week, 2 hours / session.
Description
This course is an introduction to the fundamentals of cooperative and noncooperative game theory. Motivations are drawn from engineered/networked systems (dynamic resource allocation, multi-agent systems, cyber-physical systems), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.
The course is organised in three main topic areas.
Noncooperative games
Cooperative games
Evolutionary games
We will make use of numerical examples and MATLAB coding to illustrate the concepts in practice.
Class will be a mix of lectures and tutorials.
Learning outcomes
At the end of the course the student is able to:
Choose and implement the most appropriate models and methods to address competition in engineering systems
Analyse the performance measures and optimally design the inputs under deterministic or stochastic, known and unknown parameters of multi-agent systems and perform numerical analysis and design of small-scale examples on paper
Develop a code using computational language (MATLAB) to perform numerical analysis and design on large-scale examples in game theoretic engineering applications
Grading
Final Exam (60%). A final exam at the end of the course will cover all topic areas. The class textbook and a reasonable amount of lecture notes will be allowed.
Week 4 Group presentations of a research paper (35%).
Week 9 Project report (5%). During the 2 sessions of computer Lab (4 hours per week) in week 7 and 8, each student will need to solve a set of Problems and develop a simulation code in MATLAB. The student will write a brief report which is due end of week 9.
Topics
Week 1
Lecture 1: Introduction, types of games (sequential, simultaneous), Prisoner's Dilemma, Nash Equilibrium (NE), Dominant Strategies
Lecture 2: Zero-sum games, conservative strategies, existence and properties of saddle points, mixed strategies, min-max theorem, Equilibrium point theorem, more on mixed strategies and saddle points, examples, computation of saddle points via linear programming problems, computation of NEs via Linear complementarity problems
Week 2
Lecture 3: Refinement on equilibria, Payoff dominance, Risk dominance, Subgame perfect equilibrium points, Non-credible threats, Stackelberg equilibrium, Pareto optimality, examples & exercises
Tutorial 1: Internet Service Providers (ISPs) routing game, Market Price Competition, Asymmetric Cournot Duopoly, and Bertrand Duopoly
Week 3
Lecture 4: Cooperative game theory, coalitional games with transferable utilities (TU games), Operational Research games, properties, Imputation set, Core, Nucleolus, examples & exercises
Lecture 5: Evolutionary Game Theory, Evolutionary Stable Strategies (ESS) Replicator dynamics, Asymptotically stable solutions, Learning in Games, Fictitious Play
Week 4
Tutorial 2: Computation of saddle-points and Nash equilibria
Tutorial 3 on Cooperative Games
Week 5
Group presentations 1
Group presentations 2
Week 6
Tutorial 4 on Evolutionary Game Theory
Week 7- 8
(deadline 29 January 2023, 23:59) the deadline for the Project is tight and please do not ask for exceptions. Please upload your project (one pdf file up to 5 pages) to Nestor. Make sure the name of your file reads: "WMIE009-05 Project - Albert Einstein"
Data are available here
Latex template for your report here and guidelines
Mock exam with guideline solutions
Readings
Textbook
Bauso, Dario, Game Theory with Engineering Applications, SIAM Series: Advances in Design and Control 2016
Additional material
Osborne, Martin J., and Ariel Rubinstein. A Course in Game Theory. Cambridge, MA: MIT Press, 1994. ISBN: 9780262650403. Free download here.
Maschler, Michael, Eilon Solan, and Shmuel Zamir. Game Theory, Cambridge University Press, 2013. ISBN-10: 1107005485. ISBN-13: 978-1107005488.
Basar, Tamer, and Geert Jan Olsder. Dynamic Noncooperative Game Theory. Philadelphia, PA: SIAM, 1999. ISBN: 9780898714296.
Basar, Tamer. Lecture Notes on Non-cooperative Game Theory, 2010. Free download here.
Bressan, Alberto. Noncooperative Differential Games. A Tutorial, 2010. Free download here.