28127 - MICROECONOMIA E TEORIA DEI GIOCHI

Conoscenze e abilità da conseguire

Al termine del corso, lo studente apprende giochi strategici o non-cooperativi, forma estesa e forma normale, strategie razionalizzabili e best responses, l'equilibrio di nash in strategie pure e miste.

Contenuti

The course extends over both fall and spring semesters, thereby naturally dividing into Microeconomics and Auction Theory in the former as well as Game Theory in the latter. Covered topics are:

Fall

1) Choice and individual preferences:
- Complete and transitive binary relations
- Representation via utility functions
- Choice correspondences and weak axiom of revealed preferences

2) Consumer choice:
- Budget set and hyperplane and convexity
- Preferences over consumption bundles
- Main types: Cobb-Douglas, Leontief, linear
- Utility maximization and demand function
 
3) Preference representation and aggregation:
- Preferences as subsets of ordered pairs of alternatives
- Preferences and linear orders or permutations
- Pareto-dominance and optimality

4) Pure exchange general equilibrium:
- Aggregate excess demand
- Price simplex and fixed points
- Equilibrium and Pareto-optimality

5) Decision under uncertainty and risk:
- Choosing among lotteries
- Stochastic dominance
- vN-M expected utility theory
- Allais and Ellsberg paradoxes
- Non-additive probabilities
- Expectation and aggregation
- Choquet expected utility theory

6) Auctions:
- Single-good auctions and objectives in mechanism design
- Second-price sealed-bid and generalizations: VCG mechanisms
- Combinatorial auctions
- Sponsored search auctions

Spring

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

2) Coalitions and coordinated behavior:
- Strong equilibrium
- Correlated equilibrium
- Mediated equilibrium
- Conflict and coordination games

3) Potential and congestion games:
- Potentials: ordinal, weighted exact
- Improvement paths, local optima and equilibrium
- Symmetric congestion games
- Singleton strategies and generalizations 

4) Cooperative games 1 (coalitions):
- From strategic (TU) games to coalitional ones
- Coalitional games and the subset lattice
- Moebius inversion, additive games and solutions
- Random-order and probabilistic solutions
- The Shapley and Banzhaf values
- Core and convexity

5) Cooperative games 2 (partitions):
- Coalition structures and the partition lattice
- Games in partition function form
- Global games and generalizations

6) Coalition formation:
- Coalition formation potential games
- Coalition structure generation in multi-agent systems (AI)
- Global task performance in multi-agent systems (AI)

Orario di ricevimento

Consulta il sito web di Giovanni Rossi