Zero-Sum State-Blind Stochastic Games with Vanishing Stage Duration

In stochastic games with stage duration h, players act at times 0, h, 2h, and so on. The payoff and leaving probabilities are proportional to h. As h approaches 0, such discrete-time games approximate games played in continuous time. The behavior of the values when h tends to 0 was already studied in the case of stochastic games with perfect observation of the state. We examine the same question for the case of state-blind stochastic games. Our main finding is that, as h approaches 0, the value of any state-blind stochastic game with stage duration h converges to the unique viscosity solution of a partial differential equation.