28127 - Microeconomics and Games Theory

Learning outcomes

The first half of the course provides, together with standard knowledge of microeconomic theory, also instruments for decision making both (1) under uncertainty with non-additive beliefs, and (2) with respect to multiple criteria. The second half of the course is inteded to give an in-depth comprehension of key non-cooperative game-theoretical concepts such as information sets, pure and mixed strategies,  pure strategy (possibly strong) equilibrium, mixed strategy equilibrium and potential congestion) games. Additionally, cooperative games are also covered insofar as traditional solution concepts and coalition formation are concerned.

Course contents

The course is divided into Microeconomics, in the first semester, and Game Theory, in the second.
The textbook for the first part is
MICROECONOMIC THEORY
Mas-Colell, A. and Whinston, M. D. and Green, J. R.
Oxford University Press 1995

Covered topics are:

1) Individual preferences:
- complete and transitive binary relations
- representation through utility functions
- choice correspondences and the weak axiom of revealed preferences

2) Consumer choice:
- budget set and convexity
- preference relations and utility functions
- fundamental cases: Cobb-Douglas, Leontief, lineari
- optimization and demand functions

3) Aggregation of individual preferences
- Pareto-dominance and Pareto-optimality
- Preferences as linear orders or permutations

4) Pure exchange general equilibrium
- Aggregate excess demand functions
- Price simplex and fixed points
- Pareto-optimality at equilibrium
- Edgeworth box for the 2x2 case

5) Decisio under uncertainty
- choice over money lotteries
- lotteries as points in a simplex
- vN-M expected utility theory and Allais paradox
- non-additive probabilities and expectation as an aggregation issue
- Expected utility theory through Choquet discrete integral

References for the second part will be provided during classes.

Covered topics are:

1) Strategic or non-cooperative games:
- simultaneous move and multistage games
- extensive form, game tree and information sets
- pure strategies: dominated, rationalizable and best responses
- mixed strategies and expected utility
- equilibrium in pure and mixed strategies
- potential games
- congestion games
- conflict and coordination games

2) Cooperative games:
- coalitional games and solutions
- the distributive atomic lattice of subsets
- additive lattice functions and Moebius inversion
- random-order and probabilistic solutions
- the Shapley and Banzhaf values
- the core and convexity
- coalition formation potential games

Office hours

See the website of Giovanni Rossi