Pre-requisite: MAST4004 (Linear Algebra) or MAST4005 (Linear Mathematics)
OverviewIn this module we study the fundamental concepts and results in game theory. We start by analysing combinatorial games, and discuss game trees, winning strategies, and the classification of positions in so called impartial combinatorial games. We then move on to discuss two-player zero-sum games and introduce security levels, pure and mixed strategies, and prove the famous von Neumann Minimax Theorem. We will see how to solve zero-sum two player games using domination and discuss a general method based on linear programming. Subsequently we analyse arbitrary sum two-player games and discuss utility, best responses, Nash equilibria, and the Nash Equilibrium Theorem. The final part of the module is devoted to multi-player games and cooperation; we analyse coalitions, the core of the game, and the Shapley value.
This module appears in:
Method of assessment
80% examination, 20% coursework
Game Theory: A playful introduction, M. DeVos and D.A. Kent, Student Mathematical Library, vol. 80, Amer. Math. Soc., 2016.
Playing for real: A text on game theory, K. Binmore, Oxford Univ. Press, 2007.
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate systematic understanding of key aspects of game theory;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of the material in the following areas: combinatorial games, two-player zero-sum games, general and multiplayer games, optimal strategies and equilibria in games;
3 apply key aspects of game theory in well-defined contexts, showing judgement in the selection and application of tools and techniques.
The intended generic learning outcomes. On successfully completing the module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.