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 Stable allocations: the “core” of a cooperative game.
o The “Shapley” value.
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).