The Asymptotic Solution of a Recursion Equation Occurring in Stochastic Games
- 1 November 1976
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 1 (4) , 321-336
- https://doi.org/10.1287/moor.1.4.321
Abstract
We show that there exists a Laurent series in a fractional power of n which approximates Vn up to log n, where Vn is the value of an n-stage two person zero sum stochastic game. We prove this result by showing that the Laurent series is an approximate solution of the dynamical programming equation for Vn, Vn+1 = f(Vn). It seems that our methods could be used to find approximate solutions to other difference equations. Our proof makes repeated use of Tarski's principle for real closed fields.Keywords
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