·      To explore, from a game-theoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur.

·      To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc..

·      To treat fully a number of specific games including the famous examples of "The Prisoners'' Dilemma" and "The Battle of the Sexes".

·      To treat in detail two-person zero-sum and non-zero-sum games.

·      To give a brief review of n-person games.

·      In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved.   To see how the Prisoner''s Dilemma arises in the context of public goods.

After completing the module students should:

·      Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences.

·      Be able to formulate, in game-theoretic terms, situations of conflict and cooperation.

·      Be able to solve mathematically a variety of standard problems in the theory of games.

·      To understand the relevance of such solutions in real situations.

Simple examples of games.

Von Neumann-Morgenstern theory of utility.

Concepts:   Conflict and cooperation; game-trees, normal and extensive form; domination, Nash equilibrium.

Two-player, zero-sum games:  statement of maximin theorem and its consequences;  solution (2 x 2, 2 x 3, 3 x 3).

Two-player, non-zero-sum, non-cooperative games: solution concepts and implication for Prisoners'' Dilemma.

Two-player cooperative games:  Bargaining and threat concepts.

N-player cooperative games: coalitions, characteristic function, imputations and the core.

Microeconomic theory. Edgeworth Box, public go ods.