The 2021-22 Premier League season might just be two weeks old, but we've already seen why it's one of the most competitive leagues in world football. Brentford's victory against Arsenal set the ball rolling for the new season and since then it's been goals galore in the English top-flight.With the international break around the corner, players will look to sign off with a bang before going away to represent their countries. Matchday three of the Premier League kicks off with a tantalizing clash between Manchester City and Arsenal at the Etihad Stadium, as Pep Guardiola prepares to lock horns with his protege, Mikel Arteta.The standout fixture of the Premier League week, however, is at Anfield on Saturday, as Liverpool and Chelsea prepare to do battle in what could be one of the most important games of the season.So, what does the most exciting league in world football have in store for us this weekend? It's impossible to guess, but here are my predictions for each of the ten Premier League games on matchday three.Manchester City vs ArsenalManchester City v Norwich City - Premier LeagueI can only see one winner here and I’d be shocked if Arsenal got anything against Manchester City. They did well in the EFL Cup against West Bromwich Albion, but it was pretty much a full-strength squad against a Championship side, so this is a different kettle of fish in the Premier League.It would have been a good confidence boost nonetheless, but I just think Arsenal’s Premier League season will start after the international break. I can’t see them getting a positive result in this one, I just hope they aren’t on the wrong end of a huge scoreline.'These are early days, of course, but a trip to Manchester City before the international break suggests that things will get worse for Arteta and Arsenal before they get better.' / @Matt_Law_DT https://t.co/26bBvW46Yu— Telegraph Football (@TeleFootball) August 23, 2021If Arsenal get beaten badly, the international break could bring major trouble for Mikel Arteta, because this is the time managers get sacked. Arsenal will hurt Manchester City in attack and create chances, but Pep Guardiola and co should win this one easily.Prediction: Manchester City 3-1 ArsenalNewcastle United vs SouthamptonNewcastle United v Burnley - Carabao Cup Second RoundThese are two struggling teams in the grand scheme of things, but Southampton did alright against Manchester United. When it was 1-1, I thought it would be another one of those games where Southampton would lose after taking the lead, but they held on for a draw.As for Newcastle, there is major pressure on them after their recent run of form - they even lost to Burnley in the cup after playing a strong team! If they lose this, it’s three defeats in as many Premier League games against teams that aren’t from the top six, so that could turn out to be a problem for Steve Bruce.I predict goals in this one and the first goal could be crucial.Prediction: Newcastle United 2-2 SouthamptonBrighton & Hove Albion v EvertonLeeds United v Everton - Premier LeagueThis is a good game and a hard one to call. I like Brighton, I’ve said it so many times in the past that they are one of the best football playing sides in the Premier League at the moment. I fancied them to beat Watford and they did just that.Everton have done alright under Rafa Benitez and were involved in a thrilling game against Leeds United last weekend, so they will be a tough team to play against. I see goals in this one, but I think the two sides will share the spoils at the Amex Stadium.Prediction: Brighton 2-2 EvertonWest Ham United vs Crystal PalaceNewcastle United v West Ham United - Premier LeagueI watched West Ham play last weekend against Leicester City in the Premier League and I was absolutely blown away - they were outstanding! Leicester’s goal was completely and utterly against the run of play and the gulf of class between the two sides was apparent on the night.Michail Antonio has been sensational so far and was virtually unplayable that night. If he stays fit and plays 38 Premier League games this season, West Ham will emerge as massive dark horses this season and cause plenty of problems. They are in good form and I can’t see anything other than a home win.The one and only @Michailantonio 😍 pic.twitter.com/Kojzsosq9M— West Ham United (@WestHam) August 23, 2021I just can’t see where Palace are going to hurt West Ham, it’s been a hard start for Patrick Vieira at Selhurst Park.Prediction: West Ham United 3-0 Crystal PalaceAlso Read: Jim Beglin column - Ranking the 5 greatest central midfielders of all time