It's well known that people shouldn't change playing style when playing at high stakes, but that they do (this is a classic Monty Hall style thing).
The really interesting game theoretic thing is that it goes further than just being relative to big blinds (if you have an infinite bankroll): it's all relative to the size of the pot. When you should be making or calling a bet is determined only by the relative size of the bet and the pot, not the blinds. The blinds just provide a natural escalation of pot size from 0.
Bankroll management comes into play with larger bets (at any stakes), and naturally affects pot odds decisions: if you have a $5,000 bankroll and you are facing a half-pot $1,000 bet, you should call that bet with a much tighter range than if you had a $20,000 bankroll. You can only afford to take so many coin flips. It is actually rational to be more conservative as bet sizes get closer to your bankroll size.
This means that people should be playing stakes relative to the size of their bankroll, which they don't always do (the average $1/$2 player doesn't usually have 1/5th the bankroll of the average $5/$10 player in my experience, it's closer to 1/3rd).
However, when the pot size is $0, people naturally treat the pot very differently than when it is even $1, since there are no bankroll considerations at all.
The really interesting game theoretic thing is that it goes further than just being relative to big blinds (if you have an infinite bankroll): it's all relative to the size of the pot. When you should be making or calling a bet is determined only by the relative size of the bet and the pot, not the blinds. The blinds just provide a natural escalation of pot size from 0.
Bankroll management comes into play with larger bets (at any stakes), and naturally affects pot odds decisions: if you have a $5,000 bankroll and you are facing a half-pot $1,000 bet, you should call that bet with a much tighter range than if you had a $20,000 bankroll. You can only afford to take so many coin flips. It is actually rational to be more conservative as bet sizes get closer to your bankroll size.
This means that people should be playing stakes relative to the size of their bankroll, which they don't always do (the average $1/$2 player doesn't usually have 1/5th the bankroll of the average $5/$10 player in my experience, it's closer to 1/3rd).
However, when the pot size is $0, people naturally treat the pot very differently than when it is even $1, since there are no bankroll considerations at all.