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## Syllabus

### Updated A.Y. 2021-2022

This course is an introduction to Game Theory. In the first part, the course presents the theory
and applications for static and dynamic games of complete information.

Game theory is a formal and rigorous analysis of strategic interactions between two or
more players. Its use in economics is pervasive nowadays as it has prove itself useful to study
several problems involving conflict of interests, coordination issues, imperfect competition and
many others.

We will first investigate static games of complete information, that is, games in which agents
plays simultaneously. We will start by providing the formal definition of a game by introducing
the so-called normal-form representation. Then we will investigate various solution concepts for
those games of which we will focus on the most satisfactory one, namely, the Nash Equilibrium.

The course will then move to the study of dynamic games of complete information. In those
games, players play sequentially and can observe the past actions of other players. In a first
attempt, we will apply the Nash equilibrium as a solution concept and observe that it is not
anymore satisfactory in most cases. We will therefore have to develop a more appropriate
solution concept for dynamic games, namely, Subgame-perfect Nash Equilibrium.

Applications and famous examples will be presented along with the theoretical analysis
during the course. Additional exercises and applications will be more extensively discussed
during practice sessions.

A list of detailed topics can be found below.

1. Static games

Theory: Normal-form representation. Dominant and dominated strategies. Iterated elimination
of strictly dominated strategies. Best response correspondences. Nash Equilibrium. Mixed
Strategies. Existence of Nash equilibrium in finite games.

Applications and examples: Prisoner’s dilemma. Coordination games. Comparison with Pareto
efficient outcomes. Cournot Duopoly. Bertrand Duopoly.

2. Dynamic games

Theory: Normal and extensive form representations. Nash equilibrium and non-credible
threats. Subgames. Backward induction. Subgame-perfect Nash equilibrium.

Applications and examples: Stackelberg Duopoly. Entry Games. Sequential Bargaining.

References

Osborne, M. (2004). An Introduction to Game Theory, Oxford University Press.
Gibbons, R. (1992). Game Theory for Applied Economists, Princeton University Press.