That is a very interesting question. I often play at competitive festivals - as an accompanist rather than in my own right - and I know how nerve-wracking it can be if someone goes on before you (singly or as a duo) who you think is better than you. However, I prefer to stay and listen, because you can get ideas on how to deal with the piano, environment or acoustic - and you may see errors in stagecraft that you can correct in your own perfomance. But most important, if the adjudications are read out, you will know what the adjudicator is talking about when he/she discusses the performances of the players before you.