This paper considers a game-theoretic model of a competition in which experts (players) seek to enrol two contestants into their own teams. The quality of the contestants is characterized by two random parameters, the first corresponding to the vocal talent of a contestant and the second to his appearance. The first quality parameter is known to the players, whereas the second is hidden from them. Each expert chooses an appropriate contestant based on the value of the known quality parameter only. The winner is the player whose team includes a contestant with the maximum sum of both quality parameters. This game is described by the best-choice model with incomplete information. The optimal strategies and payoffs of the players for different situations (subgames) of the game are found. The results of numerical simulation are presented.