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# 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

Prerequisite: A course that you must have ordinarily attempted all elements of before you are permitted to register for another particular course.

You must attempt the following before this half course may be taken:

• (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).