Introductory description

The focus of the module is on algorithmic and computational complexity aspects of game-theoretic models.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Game models: Strategic form, extensive form, games of incomplete information (eg auctions), succinct representations, market equilibria, network games, co-operative games;
Solution concepts: Nash equilibria, subgame perfection, correlated equilibria, Bayesian equilibria, core and Shapley value;
Quality of equilibria: Price of anarchy, price of stability, fairness;
Finding equilibria: Linear programming algorithms, Lemke-Howson algorithm, finding all equilibria;
Complexity results: Efficient algorithms, NP-completeness of decision problems relating to set of equilibria, PPAD-completeness;
Some parts of the module will be research-led, so some topics will vary from year to year.

Learning outcomes

By the end of the module, students should be able to:

• Understand a variety of advanced algorithmic techniques and complexity results for computing game-theoretic solution concepts (equilibria).
• Apply solution concepts, algorithms, and complexity results to unseen games that are variants of known examples.
• Understand the state of the art in some areas of algorithmic research, including new developments and open problems.
• Understand the fundamental concepts of non-cooperative and co-operative game theory, in particular standard game models and solution concepts.

Indicative reading list

Osborne and Rubinstein, A Course in Game Theory;
Roughgarden, Selfish Routing and the Price of Anarchy;
Nisan, Roughgarden, Tardos and Vazirani (eds), Algorithmic Game Theory;
Selected research papers.

Subject specific skills

Advanced algorithmic techniques;

Transferable skills

Problem Solving;
Communication skills