While Mitchell Starc showed in this World Cup that Gayle can be pushed back with genuine pace, he has gone after a few not-so-fast bowlers.
These days his preferred style is to give himself a bit of time to get warmed up and then go after anything that is pitching and/or finishing within the stumps. The only exception is the fast bouncer close to his shoulders; those cramp him regularly and he doesn't seem to have a successful plan to counter them. Anything that is in the mid-130s pace-wise, and doesn't get up above the waist, will get dispatched in the midwicket or long-on region.
Against most opening batsmen you could bowl a good-length delivery with the intent of it being a dot ball, or using it as a set-up delivery for a possible wicket-taking ball, but not against Gayle. While you might be able to get away with that length initially, the risk is that if he survives the initial spell, even the good balls will start getting put away.
Every ball you bowl to Gayle should be an attempt to dismiss him. The ideal way to attack is to use mostly two lengths - really full and really short - at high pace. The short ball should be used to push him back and the full ball (even as full as a yorker) to either go through his defence or find the outside edge.
I think a bowler's body language while bowling to Gayle is as important as the ball he's going to bowl. It's important to send a message that it's a battle of equals - even after you've been hit for demoralising sixes.
Bringing spin in is a good move too, but you need to be careful about the timing of it. If India had an offspinner, Kohli could probably have started with spin from one end, with Jasprit Bumrah on at the other. But since they don't, it'll be tricky to bring in Kuldeep Yadav or Yuzvendra Chahal after Gayle has been around for eight or ten overs. It's a given that he will go after the spinners and Hardik Pandya, but they must bowl with the intent to dismiss him. There's no place to hide against a batsman like him, and that makes the contest compelling to watch.
He is the most compact batsman in the West Indies squad, and if they are to do well against India, their batting must revolve around him. He is equally competent against pace and spin, and that makes him a batsman to watch out for.
While Hope is good at driving off the front foot, we have seen him get troubled by balls that dart back in to him after pitching. Mohammed Shami could be the man for him, for Shami's upright seam at the point of release gives no hint about the movement off the surface; in such cases, batsmen often end up playing down the wrong line.
The other option would be to bring in spin from one end as soon as he walks out and bowl slow and full to him. If you bowl quick to him, he is quite capable of rotating the strike, but bowling slow might force him to manufacture shots, since easy singles won't be available because of the lack of pace.
He is all arms and legs in his action and looks a little less synchronised than most of his compatriots. He also has a fairly roundarm action that suggests he will be trying to swing the ball back into the Indian top order, which is all right-handers.
While Cottrell has been successful in patches, he is also guilty of spraying the ball around. From a batsman's perspective, it's an uncomfortable thought that you can't guess where the next ball is likely to be. It could be a bouncer, full toss, down the leg side, or a peach that will dismiss you. Most bowlers have a set pattern - Jofra Archer usually bowls a shortish length; Trent Boult and Mitchell Starc a little fuller, looking for swing; Cummins a little short but not as short as Archer.
Like with the length, even the lines are mostly predictable with most international bowlers, but not with Cottrell. The plan against him should be to play every ball as one from a brand-new bowler. Though it is tough not to plan and prepare, that approach is advisable against him.
Watching the seam out of the hand is important. Some balls will wobble on the way down - those will leave the right-hand batsmen. The rest will be bowled with the intention of swinging it in. Once in a while Cottrell has also managed to get extra bounce off the surface, and one must account for that while attempting vertical-bat shots off the back foot.
This big fast bowler has all the ingredients to become a top-flight pacer in coming years. He is strategically used by Jason Holder to push the batsman back, for he is the tallest of the lot and the fastest. While he has the ability to bowl a decent full ball, his primary length of attack in this World Cup has been short.
However, he doesn't necessarily have to bowl short to bowl a bouncer, for his height allows him to get the ball to lift pretty high from short of a good length. With Thomas, you will generally find the ball hitting the bat higher than you expect it to.
One thing you might want to keep in mind against bowlers who get extra bounce is to not hit along the ground while playing horizontal-bat shots. Keeping the ball down needs you to make sure that the bat is higher than the bounce of the ball. Since doing that is a little tough against Thomas, attempting to keep the ball down will mostly lead to feeble shots. Play the horizontal-bat shot only after you've weighed your options of lofting the ball.