The approachability theorem of Blackwell (1956b) is extended to infinite dimensional spaces. Two players play a sequential game whose payoffs are random variables. A set C of random variables is said to be approachable by player 1 if he has a strategy that ensures that the difference between the...

We introduce the concept of -consistent equilibrium where each player plays a -best response after every history reached with positive probability. In particular, an -consistent equilibrium induces an -equilibrium in any subgame reached along the play path. The existence of -consistent...

The notion of mediated talk in which players communicate through a mediator before starting the game is introduced. It shows that a deterministic mechanized mediator receiving private inputs and producing public outputs can generate any rational correlated equilibrium with rational probabilities...

This note studies relations between lim "V [subscript n]" and the lower long-run average value ("V" [underlined]) in dynamic programming. It is shown that a certain bounded variation conditions of {"V [subscript n]} implies that lim "V [subscript n] [is equal to] "V" [underlined].