**Objectives: **Most of the decision problems in economics are taken under uncertainty: the decision maker does *not know with certainty the results* that each *alternative* action will lead (for instance, several problems related to portfolio selection and insurance).

The goal of this course is to offer an overview of some classical analytical models and concepts in decision-making situations under uncertainty, and to introduce some basic notions of game theory, a mathematical theory aimed at studying interaction situations among multiple intelligent and rational decision-makers, and where the outcome of an agent's choices also depends upon the choices of other agents.

**Contents:**

*Decision theory*:

- Introduction: concepts of uncertainty and risk, preferences
- Decision under risk: expected value model, von Neuman-Morgenstern's expected utility theory, risk-aversion and risk-loving, decision tree, solution of a decision tree
- Decision under uncertainty: criteria for decision-making under uncertainty (Wald, Hurwicz, Laplace,...), objective and subjective probability, Savage's model.

*Game theory*:

- An introduction to decision making models in interaction situations (games in strategic form, mixed extensions, the notion of Nash equilibrium; overview of bargaining games; transferable utility games, the notion of core and the axiomatic approach)

**References:**

- von Neumann, John and Oskar Morgenstern,Theory of Games and Economic Behaviour, Princetown University Press, 1947.
- Gilboa, Itzhak, Theory of decision under Uncertainty, Cambridge University Press, 2009.
- Savage, Leonard J., The Foundations of Statistics, Dover, 1954.
- Myerson, Roger B., Game Theory: Analysis of Conflict, Harvard University Press, Cambridge (MA), 1991.
- Osborne, Martin and Ariel Rubinstein, A course in Game Theory, MIT Press, Cambridge (MA), 1994. (freely downloadable:http://theory.economics.utoronto.ca/books/)
- Owen, Guillermo: Game Theory, III edition, Academic Press, New York, 1995.