If spellcaster A readies an action to cast time stop as soon as spellcaster B casts time stop, then on spellcaster B's turn they cast time stop, what happens? Who takes extra turns first? Also, can whoever goes first counterspell the other's time stop, and does doing so end their time stop early?
Reaction generally occur after their trigger and so cannot interrupt the casting of a spell
The Ready action is no exception to this rule so when Bob casts time stop Alice cannot actually interrupt the casting. This means that Bob's time stop will go off and he will receive the 1+1d4 turns while Alice cannot do anything.
Immediately afterwards Alice's Readied action will trigger and she will cast time stop, granting her 1+1d4 turns.
After Alice's turns it will go back to the rest of Bob's turn (the turn on which he cast time stop). This seemingly odd outcome (Bob acts, Alice acts and then we're back to Bob) is in accordance with answers to the following questions:
- When do the extra turns from Time Stop happen?
- If a caster readies Time Stop and casts it as a reaction during another creature's turn, what happens to that creature's turn?
However, castings can be interrupted using counterspell
Unlike the Ready action, counterspell takes place before a spell's effects; it explicitly allows you to interrupt the casting of a spell.
You attempt to interrupt a creature in the process of casting a spell. If the creature is casting a spell of 3rd level or lower, its spell fails and has no effect. [...]
As such Alice could interrupt Bob's time stop and Bob could interrupt Alice's time stop (also, either one could interrupt the other's counterspell assuming they hadn't already used their reaction in an attempt to interrupt time stop)
This is pointless.
Medix2's answer addresses why this doesn't work under the reaction rules. But there's also no reason to try it.
When you Ready a spell, you're already committed to expending the spell slot and any consumed material components. So if you're Alice and your intent is to cast time stop before Bob gets a chance to, and your turn is up first, then just cast the spell now. That's the great thing about winning initiative.
Even if you could Ready it in a way that would trigger before Bob casts his spell, you're only setting yourself up to waste a spell slot if Bob decides to do something else.