Intensive Course on Repeated Games

Organized by Robert J. Aumann, Jean-François Mertens, and Abraham Neyman

July 12 to July 16, 1993
Stony Brook, New York


Monday, July 12, to Friday, July 16: Earth and Space Sciences 001
Each day there will be four one-hour lectures: at 10:00, 11:30, 2:30, and 4:00.

Part A: Games with Complete Information

A.1 general model of repeated games, definition of Ginfinity, Gn, Glambda, or generally Gtheta
A.2 max min and min max and individually rational payoffs of the repeated game
A.3 equilibria in Gn, Glambda, Ginfinity
A.4 subgame perfect equilibria in Gn, Glambda, Ginfinity
A.5 Blackwell's approachability theorems

Part B: Stochastic Games

B.1 general motivations and model
B.2 basic results in the discounted and undiscounted cases:
  • finite games, algebraic aspects, lim(nu)
  • zero-sum case, contraction mapping
  • general existence theorem
B.3 study of the Big Match
B.4 existence of nuinfinity
B.5 existence of equilibria

Part C: Games with Incomplete Information

C.1 general motivation and model
C.2 lack of information on one side: infinite stage game and limit of finitely many stages
C.3 lack of information on both sides: min max and max min
C.4 equilibria: characterization and bimartingales, existence theorem