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Game Theory

Prof. S Modica

2018 Students please click here (December 28)

What we have done this year (2018)

We have done very little theory (proof of the expected utility theorem, characterization of the structure of zero-sum games, existence of subgame perfect equilibria, and little more); we have worked on finding solutions to non-trivial decision problems and equilibria in non-trivial games. In strategic form games we have worked on pure strategy equilibria, mixed equilibria, correlated equilibria and Bayes-Nash equilibria. In extensive form games we have done Nash and subgame-perfect equilibria, and we have only seen a couple of examples of imperfect information games (without going into the subleties of subgame-perfect refinements). In cooperative games we have computed the Core, Shapley value and the Nucleolus, with particular attention to the airport game and the bankruptcy game. We have finished off with a brief introduction to repeated games and the idea of cooperation opportunities in long run relationships. Thank you for attending the course!
S Modica

Syllabus (a superset of what we do each year)

Class material

The coach problem (from Dixit-Nalebuff Thinking Strategically)

Osborne-Rubinstein Proposition 22.2 (zero-sum games)
Mixed extension and Osborne-Rubinstein Lemma 33.2 (and equation 32.2)
Mixed extension of zero-sum games
The Rock-Paper-Scissors game
The bus game
A two-by-two simple game (hiring, from Gibbons)
A couple of exercises on normal form games by Joel Watson
The penalty game
Li Calzi exercise n.4.8 p.51 (last bit)
Battleships (based on Binmore's Fun and Games)
A voting game

Examples of correlated equilibria
Clarifications on correlated equilibrium

Battle of Sexes with Uncertainty (or: Yes, girls are definitely smarter than boys)

Definition of game tree gives equivalent definition of extensive form game
A bank deposit game
Three-way duels (or: the games of your life, Dixit-Nalebuff)
Fairness (Fehr-Schmidt-QJE1999)

Matching pennies with spying (Blackwell-Girshick)
Perfect Bayesian Equilibrium from MWG (ignore the word "weak")
Example of sequential equilibrium
More examples of PBE and sequential equilibria with solutions

Preliminaries on discountijng flows
Long Run Cooperation in oligopoly

Bankruptcy Solutions (Peyton Young in Equity)
Some basic points and examples about Core and Shapley Value
Shapley and Nucleolus in the bankruptcy game
Shapley and Nucleolus in the airport (or elevator) game
The heritage game
Nucleolus of the 4-player weighted majority game

More notes on games and decisions

Pareto Optima of the classical Tragedy of the Commons



20th January 2017, 26th January 2018