Mr. and Mrs. Anderson and Mr. and Mrs. Barton competed in a chess tournament. Of the three games played:

(i) In only the first game were the two players married to each other.

(ii) The men won two games and the women won one game.

(iii) The Andersons won more games than the Bartons.

(iv) Anyone who lost a game did not play the subsequent game.

Who did not lose a game?