# Game theory MT3040

## Half course

This half course is an introduction to the main concepts of non-cooperative game theory, and know how they are used in modelling and analysing an interactive situation.

### Prerequisites

You must pass the following before this half course may be attempted:

• (MT2116 Abstract mathematics and MT1174 Calculus)
• or (MT105a Mathematics 1 and MT105b Mathematics 2)
• or MT1186 Mathematical methods).

### Topics covered

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 your opponent will take the bet even if you have a strong hand.
• Combinatorial games and Nim.
• Game trees with perfect information, backward induction.
• Extensive and strategic (normal) form of a game.
• Nash equilibrium.
• Commitment.
• 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.

### Learning outcomes

If you complete the course successfully, you should be able to:

• Knowledge of fundamental concepts of non-cooperative game theory
• The ability to apply solution concepts to examples of games, and to state and explain them precisely
• The ability to solve unseen games that are variants of known examples.

### Assessment

Unseen written examination (2 hrs).