It will be difficult for Arsenal to defeat Manchester City because both teams are playing well and scoring more than two goals in a single game. Arsenal, in particular, is capable of doing so against Manchester City because they are a dangerous team with better players than any other Premier League team. As per your statement, we shouldn't anticipate a draw in this game because both teams are strong and will compete to win; Arsenal leads both Liverpool and Manchester City by just one point, and if Arsenal loses, its point total will drop.
If you use the term "give up before the match" it seems like your statement is that Arsenal is not optimistic about the match hosting Man City, even though the match will be played at Man City's home ground, it doesn't mean that Arsenal just want to lose points. A draw is already beneficial for Arsenal because sharing points is the target. their main goal, but on the other hand, if a draw occurs then Liverpool has a chance to beat Arsenal, so like it or not, Arsenal in this match will fight tooth and nail even though they will be busy with various busy schedules to prepare against Bayer Munich in the Champions League, so I think Arsenal should win whatever the result when the match starts after the international break ends..
Yesterday, when Liverpool played against Man City, Arsenal had the advantage and now only Arsenal has to play against Man City. If the result is also a draw then Liverpool will benefit, but perhaps the result of this match will be a little different and Man City does not want to continue losing points. Against Arsenal is the only opportunity for The Citizen to take a little bit of the top of the standings. Until there is a wide enough difference in points, it will be very difficult to guess which one will win the trophy this season. Because the match will take place at Man City headquarters, it is automatically a tough challenge for the Gunners to come away with 3 points.