**Introduction to Decision Theory** (6 credits – 42h.)

Fall – A.Y. 2019-20

Prof. Pierre Dehez – Prof. Pier Mario Pacini

The course is meant to introduce the student to the basic theoretical apparatus of Decision Theory: individual decisions and strategic decisions, both in a non-cooperative and cooperative framework. The course intends to provide the main tools and concepts to interpret many economic and social phenomena stemming out of individual and/or group strategic interaction and allow the student to deal with concepts as individual and group/social rationality, efficiency, equity, power. The course is tailored for a wide public of students both in economics and in social sciences; the mathematical tools are kept at the very basic level, but some knowledge of probability theory and of the methods and concepts introduced in a basic course in Microeconomics are highly advised.

– **Individual decisions**: the basic tools required to represent individual choices in different information context are presented

o Basic ingredients of decision theory: alternatives; constraints; objectives.

o Choices under certainty: preferences and utility; choice.

o Choices under ignorance: contingent results, maxmin, minmax and mixed rules.

o Choices under uncertainty; lotteries, Von Neuman-Morgestern Expected utility.

– **Non cooperative games:** the basic notions required to represent and analyse situations of strategic interaction are introduced, together with the main solution concepts:

o Basic ingredients of non-cooperative game theoretic situations.

o Representing games:

- the extensive form and backward induction;
- strategic (or normal) form. Strategies: pure/mixed, dominant/dominated, conservative, best response, rationalizability.

o Nash equilibrium: unicity, multiplicity, absence of equilibria in pure strategies, efficiency. Repeating a game.

– **Bargaining:** a bargaining situation between two parties will be introduced and analysed together with main solution concepts:

o Bargaining with non transferable utilities.

o The “Nash bargaining” axiomatization and solution.

o Other solution concepts.

– **Cooperative games (in coalitional form):** the basic notion of a characteristic function will be introduced together with key solution concepts, mainly the “core” and “Shapley” value

o Representation of cooperative games and its properties.

o Imputations.

o Stable allocations: the “core” of a cooperative game.

o The “Shapley” value.

o Applications.

*Main reading list*

Ø Dehez, Pierre (2017). *Theorie des Jeux – Conflict, Négociation, Cooperation et Pouvir*. Economica, Paris.

Ø Resnik Michael (1987). *Choices: An Introduction to Decision Theory*. University of Minnesota Press, Minneapolis.

*Further suggested readings*

- Maschler Michael, Eilon Solan and Schmuel Zamir (2013).
*Game theory*, Cambridge University Press, Cambridge MA. - Moulin Hervé (1995).
*Cooperative Microeconomics*. Princeton University Press, Princeton. - Myerson Roger (1991).
*Game theory, analysis of conflict*, Harvard University Press, Cambridge MA. - Osborne Martin (2009).
*An introduction to game theory*, Oxford University Press, Oxford. - Rubinstein Ariel and Martin Osborne (1994).
*A course in game theory*, MIT Press, Cambridge MA (see: arielrubinstein.tau.ac.il).