I think this is a bit better:
"Collusion is two or more players acting with a common agreed-upon strategy, usually in secret, to gain an advantage over one or more other players."
Otherwise, for instance, if two players were to verbally agree out loud to check it down against another all-in player, it would still not be collusion per the definition you quoted.
A warning for first instance would do nothing to stop the behavior of agreeing to move all-in blind in the case of these re-entry tournaments. It is, by nature, something that happens just the one time during the tournament. Keep in mind:
Re-entry is on the next Day 1 of the tournament.
Players do not have to have zero chips left to re-enter. In most cases, they abandon their chipstack to play the next Day 1. In some cases, whichever Day 1 chipstack is largest advances to Day 2.
Only a severe penalty, such as disqualification, or a penalty that removes any incentive from the action, such as removing all chips won in the hand as I propose, will deter the behavior.
There are other types of pre-agreed action for which a warning and then escalating penalties are appropriate. Current rules already cover this sufficiently. It is only this special situation which needs the more severe treatment of a specialized penalty. Current common penalties, such as sitting out one orbit, won't do anything to stop it - it's worth it for the pot winner and doesn't make a difference to the pot losers. Disqualification of the players might work, but there is little chance of implementation or enforcement by poker rooms, since that cuts into their house fees (the players can't re-enter).