Mo 22 november 2004, 3h-3h:
Introduction to the course.
Decision under certainty, risk and uncertainty.
Games in strategic form.
Game form.
Games in extensive form and strategies.
NOTE:
A good quick introduction to the strategic and extensive form models is the chapter of Hart (1992) in the Handbook of Game Theory (see: for details).
DOCUMENTS:
quadro concettuale IN ITALIAN. 21 november 2004 at 00.15
decisioni in condizione di certezza e rischio IN ITALIAN. 21 november 2004 at 00.15
decisions under certainty and under risk 22 november 2004 at 23.30
sommario decisioni in condizioni di incertezza IN ITALIAN. 21 november 2004 at 00.15

Mo 29 november 2004, no classes.
DOCUMENTS:
none

Mo 6 december 2004, 3h-6h:
Domination between strategies (three types of domination, just two names! domination and weak domination).
Dominating strategies.
Prisoner's dilemma.
Dominated strategies and iterated elimination of dominated strategies. Common knowledge of rationality.
Nash equilibrium, definition.
Properties and problems of Nash equilibria.
Best reply. Nash equilibrium as a fixed point for the best reply correspondence.
Mixed strategies and Nash's theorem.
Subgame perfect equilibrium. The extensive form matters.
DOCUMENTS:
Exercises, sheet no. 1. 13 december 2004 at 23.45

Mo 13 december 2004, Andreozzi, 2h:
ESS, replicator dynamics and evolutionary models; part 1.

Mo 13 december 2004, 3h-9h:
Duopoly (Cournot).
Battle of the sexes: looking for equilibria in mixed strategies.
Correlated equilibria.
Introduction to games with incomplete information.
DOCUMENTS:
A tree and a table for a game with incomplete information. 13 december 2004 at 23.45
Exercises, sheet no. 2. 13 december 2004 at 23.45

Tu 14 december 2004, Andreozzi, 2h:
ESS, replicator dynamics and evolutionary models; part 2.

Tu 11 january 2005, Mori, 4h:
Auctions.

We 12 january 2005, 2.5h-11.5h:
Types and beliefs.
A game tree representing a game with incomplete information.
Consistent beliefs.
Agreeing to disagree.
DOCUMENTS:
agreeing to disagree. 21 january 2005 at 8.00.

Th 13 january 2005, 2h-13.5h:
Cooperative vs. non-cooperative games: binding agreements.
Difficulties to convert a strategic game into a TU-game.
Formal definition of a TU-game.
Superadditivity.
Imputations.
The core.
Simple majority game: a (superadditive) game with an empty core.
Shapley value: four properties identify a unique point solution.
DOCUMENTS:
Exercises, sheet no. 3. 14 january 2005 at 8.00

Fr 14 january 2005, Parrachino, 3h:
TU-games and environmental applications.

Th 20 january 2005, 2h-15.5h:
Bargaining problem (cooperative version).
Correlated strategies and the set of possible cooperative agreements.
Difficulties to identify the disagreement point.
Divide 100$.
Axiomatic approach: the set of bargaining problems.
Conditions: symmetry, efficiency, covariance, independence from irrelevant alternatives (IIA).
The Nash solution and the Nash product.
Alternative routes: Kalai and Smorodinsky (utopia point; restricted monotonicity instead of IIA).
Non cooperative approach: alternating offers by Rubinstein.
Too many Nash equilibria; SPE are OK.
Convergence of the Rubinstein's solution to Nash's, when the time interval beween offers and counter-offers goes to zero.
DOCUMENTS:
ultimatum game and SPE. 21 january 2005 at 8.00.

Some point in the future?, 2h-17.5h:
Mechanisms.
Incentives.
Revelation principle.
DOCUMENTS:

ADDITIONAL RESOURCES:
A Game Theory course for PhD students, with video-recorded lessons and pdf notes. 22 november 2004 at 23.30

SOME EXERCISES:
Esempi di gioco in forma estesa e strategie; calcolo di equilibri in strategie miste IN ITALIAN. 21 november 2004 at 00.15

REFERENCES:
A short bibliography for Decision Theory. IN ITALIAN. 21 november 2004 at 00.15
An introductory bibliography for Game Theory, with comments. IN ITALIAN. 21 november 2004 at 00.15

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