Tauberian Theorem for Games with Unbounded Running Cost

Abstract

We study two game families with total payoffs that are defined either as the Cesàro average (the long run average game family) or Abel average (the discounting game family) of the running costs. We study value functions for all sufficiently small discounts and for all sufficiently large planning horizons (asymptotic approach), investigate a robust strategy that provides a near-optimal total payoff in this case (uniform approach). Assuming the Dynamic Programming Principle, we prove the corresponding Tauberian theorems without requiring the boundedness of the running cost.