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

Ivan Novikov ()
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Ivan Novikov: Université Paris Dauphine, PSL Research University

Dynamic Games and Applications, 2025, vol. 15, issue 3, No 13, 1094-1115

Abstract: 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.

Keywords: Stochastic games; Zero-sum stochastic games; State-blind stochastic games; Shapley operator; Varying stage duration; Viscosity solution; Continuous-time Markov games (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-024-00599-y

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