The MVP reward is granted to individual Mechs, not players.
These Mechs were the most influential Mechs in the battle, and it's possible for all three MVP Mechs to belong to the same player.
MVP Mechs
You can also check these articles that can help you shed light on some unobvious situations:
- I won a battle but got no rewards. Why?
- Can I play the game offline?
- Battle Awards