On the Notion of Value for Games with Infinitely Many Stages
Shmuel Zamir · The Annals of Statistics · 1973
The value of a zero-sum two-person game with infinite number of stages can be defined either directly or as the limit of the values $v_n$ of the truncated games with $n$ stages. It is shown that these two concepts are not equivalent. There are games in which $\lim v_n$ exists but which do not have values as infinite stage games.