Markov games with unbounded rewards

2-person zero-sum Markov games with the total expected reward criterion are considered. The one period rewards are not supposed to be bounded. However, it is assumed that the values of the one period games in each state constitute a vector in a Banach space in which the transition probabilities are contracting. This game is proved to possess a value vector and optimal stationary strategies (in a weakened sense). Furthermore, it is exhibited how the value vector and optimal strategies may be computed using successive approximations.