Abstract:

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k'geq 0$, of a stochastic game $'Gamma_'delta$ with stage duration $'delta$ is interpreted as the play in time $k'delta'leq t0$ as the stage duration $'delta$ 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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