Abstract
We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage k, k≥0, of a stochastic game Γδ with stage duration δ is interpreted as the play in time kδ≤t 0 as the stage duration δ goes to 0, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.
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