A game is considered in which at timesn=0,1,Players I and II choose non-negative random variablesUn, Vnrespectively, and I pays to II the amount (VnXn)/Unwhere X = {Xn, n≧0} is a given sequence of non-negative random variables. The random variables Un, Vn, Xnare adapted to a given filtration and are restricted so thatfor given β>0 and γ≧1. The solution of this gameleads to the investigation of a certain recursive stochastic equation and to an approximation scheme for the Snell envelope of the processX.