London School of Economics and Political Science (LSE)

40 Game theory (half unit)
Prerequisite

If taken as part of a BSc degree, 05a Mathematics 1 and 05B Mathematics 2.

Aims and objectives

The unit is designed to:
? To familiarise students with formal methods for strategic analysis.
? To develop the mathematical theory of games as used in economics.
Learning outcomes
Having followed this unit, students should have:
? 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.
Syllabus
This half-unit is an introduction to game theory. At the end of this half-unit,
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 modeled 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.
? 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.
Essential reading
The subject guide itself is the essential reading for this unit. Additional reading is
recommended. Assessment
This unit is assessed by a two hour unseen written examination.
All information in this document is subject to confirmation in the Programme Regulations for
degrees and diplomas in Economics, Management, Finance and the Social Sciences that are
reviewed annually. Notice is also given in the Regulations of any units which are being phased
out and students are advised to check unit availability.