Extensive and strategic (normal) form of a game.Game trees with perfect information, backward induction.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. In antagonistic situations, a player may play best by rolling a die that decides what to do next. This is captured by the central concept of Nash equilibrium. The game theorist’s recommendation how to play must therefore be such that everybody would follow it. 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). Mathematically, this is modelled by a utility function. This is not identical to monetary interest, but can be anything subjectively desirable. Players are assumed to act out of self-interest (hence the term ‘non-cooperative’ 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. This half-course is an introduction to game theory. or (MT105a Mathematics 1 and MT105b Mathematics 2).(MT2116 Abstract mathematics and MT1174 Calculus).You must pass the following before this half course may be attempted:
