Game theoretic analysis for an optimal stopping problem by means of moments of a distribution function

Let be mutually independent random variables with a common cdf F, which is unknown but belongs to some class of cdf's. The class is the set of all cdf's whose mean, variance and domain are , and respectively. It is assumed that they are known. Under an observation cost c, , the paper considers a stopping problem as a two-person zero-sum game in which the player 1 decides his stopping set , and the player 2 chooses her cdf F in . The paper analyzes the upper bound problem and the game problem to derive a simple and meaningful solution with the parameters c, μ, σ and M.