Final answer:
The maximum possible number of winners in this game is 4.
Step-by-step explanation:
To find the maximum possible number of winners in this game, we need to consider the skill levels of the 7 players and their pairings. Since each person will always defeat anybody with less skill, we want to make sure that each person is paired with someone of lower skill.
Let's assume that the players are labeled A, B, C, D, E, F, and G, in increasing order of skill.
In order to maximize the number of winners, we need to pair A with B, C with D, E with F, and G with the weakest player. This way, A, C, E, and G will each have two wins, making them the winners.
Therefore, the maximum possible number of winners in this game is 4.