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

Abstract: 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.