Under the initative phase it reads ".... Ties are rerolled."
There are certain rules lawyers out there and interpretation is quite subjective here and it might need a bit of revision in future versions (the text is the verbatim in my old BattleTech compendium too

)
With two "sides" this text in the initiative works, but when dealing with three or more initiative rollers a "fairness" may be an issue.
If I were to read this text as a new player I'd play and read this as:
While all parties are rolling initiative, everyone with a tie re-rolls until there are no ties and then everyone goes in that initiative order
The way that I've always been a party to games, It was any ties now "roll off" for the initiative for their roll
For example:
- Player 1 rolls a 7
- Player 2 rolls a 4
- Player 3 rolls a 10
- Player 4 rolls a 4
Now if one reads the text verbatim say Player 2 and Player 4 now re-roll:
- Player 2 rolls a 9
- and Player 4 rolls a 8
- Player 3 still has a 10
- and Player 1 still has a 7
Now Player 2 & 4 are no longer at the lower end of a pecking order and Player 1 & 4 are punished for rolling poorly... I know it's semantics as it's all random in the long run, but the player may have his/her feeling hurt.
How is this handled at Battle Royale games at tournaments?