this was taken from game manual:
After all players have taken an action, we can start round 2
and I wonder, does this sentence mean the same:
After all players took an action, we can start round 2
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The first version ("have taken") sounds natural to this US English speaker and the second version ("took") sounds wrong. Let's break this sentence down to examine it. There are two main parts:
Because we're talking about something that is currently true, or is true in general, we use the present tense. The present perfect have taken matches this, because it is actually a present tense, describing the effects of a past action on the present.
The simple past took doesn't match, because the simple past means something that happened entirely in the past, but we want to talk about conditions in the present. If you were to begin the sentence "After all players took an action", it would only make sense to put the second part of the sentence in the past, like "we could start round two."
Quite often the difference between the simple past and the present perfect is simply an opinion. There are very few hard reasons why the simple past is preferred and the present perfect is not. The grammarians say that if a verb is in the simple past then it was true in the past but is not true now. And if a verb is in the present perfect then it was true in the past and still is true now. This rule is violated quite a lot.
The only difference between:
Is that in 2 it might also be true that the players will take no more actions. In 1 it might also be true that the player will take more actions. But notice I said 'might'. It is not a rule that is always observed.