Pointwise and Uniformly Good Stationary Strategies for Dynamic Programming Models

This paper considers discrete time countable state Markovian decision problems with the total reward criterion. The main results are the following: a method for reducing the size of action sets for the given model without a loss in value, proof of the existence of pointwise good stationary strategies in the given model if such strategies exist in the embedded negative model and proof of the existence of uniformly good stationary strategies if pointwise good stationary strategies exist in the model.