1. Antpool does not want to be "liable" for a 2+ block chainsplit that could appear as an attempt to reorg blocks (its a way to guard reputation as an "honest" pool)
I don't think AntPool mining on it's own block could easily cause a 2+ block chainsplit. If they find a block on their own block, their side of the split wins by having the most work chain. All other pools will switch to it no matter where they mined before.
  1. Antpool is using the Tit for Tat Strategy (its a long-term strategy of mutual cooperation)
In this case, the Tit for Tat Strategy isn't working out against Foundry. It's known that Foundry will switch and mine on their own block (see e.g.
).
Do you have a theory why a pool would mine on the competing fork?
My guess is that they are either not aware of the game theory (doubtful as they've been in the industry for quite long), or they don't care enough. After all, there's maybe one or two forks a month involving AntPool, and even fewer ones where they end up loosing due to not mining on their own.