On a randomized strategy in Neveu's stopping problem

In Neveu's variant of the stopping problem, a randomized strategy is considered in order to relax a condition on values of two stochastic sequences. We shall describe the variant of the problem as a zero sum two person sequential game and show that a solution for a recursive equation of the game value exists. Neveu's condition reduces the equilibrium solution to a Markov time among the class of randomized strategies.