Entry requirements

Mathematics 30 credit points or 60 credits in Science, Technology, Economics, Political Science or Philosophy.

Learning outcomes

In order to pass the course the student should be able to

• give an account of the following concepts: preference relation, utility function and expected utility;
• define the concept of strategic game and give an account of the concepts of mixed strategy, Nash equilibrium, maxmin strategy and dominance;
• characterise pure and mixed Nash equilibria, compute such equilibria in two person games, and solve games through iterated elimination of strictly dominated strategies;
• rewrite two-person zero-sum games as linear programming problems, and solve such games in simple cases;
• define the concept of extensive game, construct the game tree of an extensive game, determine the equivalent strategic form and compute subgame perfect equilibria;
• define the concept of coalitional game and give an account of the following concepts: imputation, core, nucleolus and Shapley value;
• compute the core, the nucleolus and the Shapley value of a game in simple cases;
• give an account of some game theoretic applications.

Content

Utility theory: preference relations, utility functions, expected utility, von Neumann–Morgenstern preferences.

Strategic games: pure and mixed strategies, Nash equilibrium, maxmin strategy, dominance, and iterated elimination of dominated strategies. Two-person zero-sum games: optimal strategy and optimal value, connection with linear programming.

Extensive games: game tree, perfect information, Nash equilibrium, subgame perfect equilibrium, chance moves, information set, incomplete information, perfect recall. Various oligopoly models.

Coalitional games: imputation, kernel, nucleolus and Shapley value. Coalitional games without transferable payoff exemplified by exchange economies.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. In addition, assignments may be given during the course.