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.
Original language | English |
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Pages (from-to) | 236-278 |
Number of pages | 43 |
Journal | Dynamic Games and Applications |
Volume | 3 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2013 |
Keywords
- Continuous-time stochastic games
- Equilibrium of stochastic games
- Multistage games with short-stage duration
- Stochastic games
- Uniform equilibrium payoffs
- Uniform value