This is increasingly being used in live tournaments but my question is, if you are the big blind should you be calling open raises a bit wider if you are closing the action? You have already invested two big blinds into the pot. Or should you be thinking of the ante as a sunk cost and ignore it?

The difference between your big blind and your ante is that your big blind is a "live" bet and the ante is dead money. That is, when it's your turn to call, your big blind counts as part of your call, meaning that your further investment is less.

There are some games where anteing happens all the time, such as stud games, and it is common in home games to have one player post all the antes, so that you don't have to collect antes from each player, especially if there's not a dedicated dealer. Posting all the antes one hand per round is the same as posting one ante each hand, because the money is dead either way, but (bad) players often defended "their" ante posting heavily, which I personally loved.

Sunk cost. Take advantage of those who see it differently if you can.

Thanks both.

1. How much is your positional disadvantage worth?
2. How much equity does your hand have vs previous action?
3. What odds are you being presented?

These are the only important questions when defending your big blind as a call (you always want to ask yourself if the hand gains more ev as a 3bet). In an ante game, (3.) changes so that you will defend wider.

BB Ante defense is not solved. BB Ante short-handed is still being solved. I think you need to adjust for it.

Adjust holdings shorthanded before you become the bb ante.