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What happens if there is a new rollup deployed today and there is no nodes ready to check their commitments in the next two weeks? Will they be automatically cemented after 2 weeks, even nobody checked it?

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I don't have enough reputation to answer in the thread so I'll try to answer at everything here:

What happens if there is a new rollup deployed today and there is no nodes ready to check their commitments in the next two weeks?

The rollup will advance no matter if there is another node checking its commitments (unless there's a conflict of course).

Will they be automatically cemented after 2 weeks, even nobody checked it?

Not automatically but the rollup publishing the commitments will cement them via L1 operations (so it's not automatic but the rollup node will do it programmatically).

But what is the economic incentive for the honest participant to check what other rollups are doing? I can imagine that the chances of detecting a bad participant and getting the 5k tez bonus are rather low, so they will be consuming their CPUs for nothing?

Expect for the 5k tez reward, there is no really incentive to check what other rollups are doing. However, it's important to check what the rollup you're operating and/or using is safe (i.e., multiple nodes checking the commitments). Are you willing to deposit money on a rollup that is operated and checked by a single individual? Would you trust it?

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Yes. A single node is enough to make a rollup progress. Security is ensured only if there is at least one honest participant, it can be this one!

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  • Q: But what is the economic incentive for the honest participant to check what other rollups are doing? I can imagine that the chances of detecting a bad participant and getting the 5k tez bonus are rather low, so they will be consuming their CPUs for nothing?
    – user9011
    Commented Apr 5, 2023 at 11:19

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