How to customize the join table in Django

I am trying to find the best way to model this data structure. I want to have a Players table and a Games table so that every game has two or more players. For example.

Players

PlayerID | PlayerName
1        | John
2        | Sue
3        | Bob

      

        
        
        
      

    

Games

GameID | GameDate
1      | 1/1/2014
2      | 2/1/2014

      

        
        
        
      

    

GamePlayers (join table)

GamePlayerID | GameID | PlayerID 
1            | 1      | 1
2            | 1      | 2
3            | 1      | 3
4            | 2      | 2
5            | 2      | NULL

      

        
        
        
      

    

Note the NULL value. Basically it says that "Game 2" consists of player 2 and one undefined player . This functionality is what I need for replication in Django. This is what I have tried.

Models.py

class Player(models.Model):
    player_name = models.CharField(max_length=60)

class Game(models.Model):
    players = models.ManyToManyField(Player, blank=True)
    game_date = models.DateField(null=True, blank=True)

      

        
        
        
      

    

But with this setup, I cannot reproduce the functionality described above. How to do it?