Game theory

...

The course aims to present formally various topics in game theory. The course starts off with a recall of strategic or normal form game and definition of Nash equilibrium in pure and mixed strategies. We present a proof of Nash equilibrium existence using Kakutani fixed point theorem. Next, we define dominance and present a concept of rationalizability. If time allows, we also discuss evolutionary stable strategies and their relation to Nash equilibria. We also define a strategic form Bayesian game and game Bayes Nash equilibrium. Nest we define extensive form game and subgame perfection, followed by weak perfect Bayesian equilibrium and sequential equilibrium. Having that we provide students with a selection of current results from repeated games and folk theorems. Later we discuss communication in games. Hard vs. soft information, disclosure, cheap talk and Bayesian persuasion. Also, we present e review of current results for games on networks including learning. Simple topologies on networks: regular lattice, Erdos-Renyi graphs, small-world networks. A course ends with a Nash bargaining solution, selection of solutions for TU and NTU cooperative games and if time allows foundations of the Nash program.

During tutorials we discuss applications including Cournot and Bertrand games, supermodular games, bargaining games, symmetric information games, time-consistency games, mechanism design and auctions

Literatura podstawowa:

Fudenberg, D., and J. Tirole (2002): Game theory. MIT Press, Cambridge.

Osborne, M. J., and A. Rubinstein (1994): A course in game theory. MIT Press.

Maschler, M., E. Solan, and S. Zamir (2013): Game Theory. Cambridge University Press.

Literatura uzupełniająca:

Milgrom, P. (1989): ?Auctions and Bidding: A Primer,? Journal of Economic Perspectives,

3(3), 3?22.

Mailath, G., and L. Samuelson (2006): Repeated games and reputations. Long run relation-

ships. Oxford.

Wiedza: Student acquires knowledge of the formal tools necessary to study games ; Student understands the difference between various models, equilibria and solutions in games; Student knows classic games, their assumptions, implications, and limitations.

Umiejętności: Student can read and understand current reserach papers in game theory. ; Student is able to select appropriate tools to analyse various games.; Student is able to differentiate and solve for various concepts of equilibrium.

Kompetencje społeczne: Student recognizes, where using game theory is necessary.; Student sees the game theory implications in current discussions on the world economy

egzamin tradycyjny-pisemny: 0,60; kolokwium: 0; egzamin testowy: 0; referaty/eseje: 0; ćwiczenia: 0,40; egzamin ustny: 0; inne: 0