The Asymptotic Solution of a Recursion Equation Occurring in Stochastic Games

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.

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