If we run a restaurant and are considering adding delivery, and think adding delivery will eat into our take$-$out sales, but note that the nearby restaurant is adding delivery and will probably cause us to lose those sales if we don't have delivery, should we include this in our decision process?,

The lost take$-$out sales will be gone either way, so they should be excluded from the analysis.

The lost take$-$out sales should be counted as a cost against the delivery project due to cannibalization.