  This paper is concerned with two-person dynamic zero-sum games. Let games for
some family have common dynamics, running costs and capabilities of players,
and let these games differ in densities only. We show that the Dynamic
Programming Principle directly leads to the General Tauberian Theorem---that
the existence of a uniform limit of the value functions for uniform
distribution or for exponential distribution implies that the value functions
uniformly converge to the same limit for arbitrary distribution from large
class. No assumptions on strategies are necessary. Applications to differential
games and stochastic statement are considered.
