The Asymptotic Theory of Stochastic Games
- 1 August 1976
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 1 (3) , 197-208
- https://doi.org/10.1287/moor.1.3.197
Abstract
We study two person, zero sum stochastic games. We prove that limn→∞{Vn/n} = limr→0rV(r), where Vn is the value of the n-stage game and V(r) is the value of the infinite-stage game with payoffs discounted at interest rate r > 0. We also show that V(r) may be expanded as a Laurent series in a fractional power of r. This expansion is valid for small positive r. A similar expansion exists for optimal strategies. Our main proof is an application of Tarski's principle for real closed fields.Keywords
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