Is it possible for 16 players to play each other only once over four games?

No, it is not possible for 16 players to play each other only once over just four games. In a round-robin format, each player would need to play against every other player, which would require a total of 120 matches (since each pair of players constitutes one match). With only four games, it’s impossible to accommodate all possible matchups among 16 players.