BSc Computer Science and Mathematics

The main contents of this module include:

1. What is a game? (Definition of game, pay-off function, representations in normal form, and extensive form.)

2. What is a plan for decision-making in a game context? (Definition of strategy, representations of strategy.)

3. What does it mean to play a game well? (Definition of best-response strategy, equilibrium point, discussion of the validity of these concepts, discussion of alternatives.)

4. Properties of the Nash equilibrium. (How it incentivizes bad outcomes to prevent opponents from taking advantage.)

5. How do we find good game plans? (Complexity of finding equilibrium points, minimax algorithm, alpha-beta pruning, discussion of the components of a typical game playing program via evaluation function and alpha-beta search)

6. How do we learn good game plans? (Introduction to reinforcement learning, learning through "self-play", TD-learning, Monte Carlo Tree Search.)

The aim of the course is to introduce students to the main concepts of non-cooperative game theory and the game solution concept of the Nash equilibrium. Different categories of games and different approaches to effective play in games is developed. During the first six weeks of the course, conceptual and theoretical material is developed. During the final 5 weeks, the students put this material into practice by developing an AI agent which plays a particular game.