This paper investigates properties of Blackwell -optimal strategies in zero-sum stochastic games when the adversary is restricted to stationary strategies, motivated by applications to robust Markov decision processes. For a class of absorbing games, we show that Markovian Blackwell -optimal strategies may fail to exist, yet we prove the existence of Blackwell -optimal strategies that can be implemented by a two-state automaton whose internal transitions are independent of actions. For more general absorbing games, however, there need not exist Blackwell -optimal strategies that are independent of the adversary's decisions. Our findings point to a contrast between absorbing games and generalized Big Match games, and provide new insights into the properties of optimal policies for robust Markov decision processes.
Grand-Clément et al. (Wed,) studied this question.