MT3040 Game theory (half course)
Either MT1174 Calculus or both MT105A Mathematics 1 and MT105B Mathematics 2.
This half course is an introduction to game theory. At the end of this half course, students should be familiar with the main concepts of non-cooperative game theory, and know how they are used in modelling and analysing an interactive situation. The key concepts are:
- Players are assumed to act out of self-interest (hence the term 'non-cooperative' game theory). This is not identical to monetary interest, but can be anything subjectively desirable. Mathematically, this is modelled by a utility function.
- Players should act strategically. This means that playing well does not mean being smarter than the rest, but assuming that everybody else is also 'rational' (acting out of self-interest). The game theorist's recommendation how to play must therefore be such that everybody would follow it. This is captured by the central concept of Nash equilibrium.
- It can be useful to randomise. In antagonistic situations, a player may play best by rolling a die that decides what to do next. In poker, for example, it may be useful to bet occasionally high even on a weak hand ('to bluff') so that one's opponent will take the bet even if you have a strong hand.
Topics covered are:
- Combinatorial games and Nim.
- Game trees with perfect information, backward induction.
- Extensive and strategic (normal) form of a game.
- Nash equilibrium.
- Mixed strategies and Nash equilibria in mixed strategies.
- Finding mixed-strategy equilibria for two-person games.
- Zero sum games, maxmin strategies.
- Extensive games with information sets, behaviour strategies, perfect recall.
- The Nash bargaining solution.
- Multistage bargaining.