Summary: A game-theoretic model of two-person best-choice problem with non-complete information is proposed. The players (experts) observe a sequence of random vectors \((x_i, y_i)\), \(i=1,\ldots,n\) where the value of the first component \(x_i\) is known and the second value \(y_i\) is hidden. In each stage player can accept the object or reject it. The choice have to made on the base of the value of the first component. A player with maximal value of the sum of the components is winner in the game. The optimal strategies are derived for the dependent and correlated components.