A note on semi-Markov perfect equilibria in discounted stochastic games

We establish that general discounted stochastic games with state transitions that are absolutely continuous with respect to a fixed, atomless measure admit stationary semi-Markov perfect equilibria, i.e., equilibria in which each player's action depends only on the current state and on the previous state and action profile. This resolves an open existence question stemming from an error in the proof of Theorem 4 of Chakrabarti [3]. Moreover, the result follows from “un-correlating” Nowak and Raghavan's [25] stationary correlated equilibrium, establishing that there is no need to resort to additional, unmodeled state variables.