Stochastic Games with Short-Stage Duration

Abraham Neyman ()

Dynamic Games and Applications, 2013, vol. 3, issue 2, 236-278

Abstract: We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage k, k≥0, of a stochastic game Γ δ with stage duration δ is interpreted as the play in time kδ≤t>(k+1)δ and, therefore, the average payoff of the n-stage play per unit of time is the sum of the payoffs in the first n stages divided by nδ, and the λ-discounted present value of a payoff g in stage k is λ kδ g. We define convergence, strong convergence, and exact convergence of the data of a family (Γ δ ) δ>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. Copyright Springer Science+Business Media New York 2013

Keywords: Stochastic games; Equilibrium of stochastic games; Continuous-time stochastic games; Multistage games with short-stage duration; Uniform value; Uniform equilibrium payoffs (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s13235-013-0083-x

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