An example of using of the Tauberian theorems for control and game-theoretical control problems

The talk is devoted to the asymptotic behavior of value functions of abstract control problem and games with the long-time and discounted averages. The Uniform Tauberian Theorem for abstract control problems states that the uniform convergence of value functions for long-time averages (as the horizon tends to infinity) is equivalent to the uniform convergence of value functions for discounted averages (as the discount tends to zero), and that the limits are identical. According to Miquel Oliu-Barton and Guillaume Vigeral, this assertion holds if the set of all feasible processes is closed with respect to concatenation. In this paper, we refine this condition.