How can we play Game of Thrones as a league game?
In simplest tournament form
In each round winners advance to next round, losers do not. If an alliance wins, they advance together for that round only. 2nd place matters not...
For a longer format
Everyone gets to play up to X games of Y game opportunities. Winners (individual or alliance) get 3 points each, losers get 1. After the Y
th opportunity has been played, count up total points. Top 4-6 players by points advance. If more than 6 are tied, have two tables, and divide the tied players between them, and then take the winners from both, and if needed the 2nd place players from both, to make a 3-6 player final.
In each of the x games, randomize from those present - I recommend using 3x5 cards with player names on them, and tracking of wins and losses.
2nd place - why not?
awarding points for non-victory is a complication that, while it can advance consistently passable players to finals, doesn't actually select for the best players. THe best players are good and consistent.
What If I want to push for solo wins?
In that case, Solo victory is a 3 point, alliance victory is a 2 point, and anything less is still 1 point
Why do losers get a point?
Because it pushes them up the rankings for being consistent in showing up. This is a benefit for league play.
Example
A 13 player league, players A-M, has 6 weeks and enough sets for 3 tables per week. The option to endorse solo wins over alliance wins is in place. Week 6 will be &quot;finals&quot;
Week 1, Everyone's present, and so the tables are 5, 4 and 4. AFGHM, BCIL, and DEJK are the table layouts. A wins solo, BC win as an alliance, and J wins
Week 2, A is sick. Tables are thus 6 each for two tables. BDFHJM and CEGIKL. KL win alliance, BD wins shared.
Week 3, D, K and M are stuck at work.  2 tables, 5 each. ACEIJ BFGHL. AC win shared, G wins solo.
Week 4,  N joins the league (late but enjoys play). there's a storm. Only ADGHN make it. H wins solo.
Week 5, Everyone shows. 5-5-4 tables. ADIKN BEGJM CFHL. A wins shared. BG win shared. H wins solo, as does N.
Final is H (with 9) G (with 8) A B (with 7), C &amp; J (with 6).
    Wk  A  B  C  D  E  F  G  H  I  J  K  L  M  N
    1:  3  2  2  1  1  1  1  1  1  3  1  1  1  -
    2:  0  2  1  2  1  1  1  1  1  1  2  2  1  -
    3:  2  1  2  0  1  1  3  1  1  1  0  1  1  -  
    4:  1  0  0  1  0  0  1  3  0  0  0  0  0  1
    5:  1  2  1  1  1  1  2  3  1  1  1  1  1  3
  Tot:  7  7  6  5  4  4  8  9  4  6  4  5  4  4

Now, if run without the penalty for shared, the numbers look like this:
    Wk  A  B  C  D  E  F  G  H  I  J  K  L  M  N
    1:  3  3  3  1  1  1  1  1  1  3  1  1  1  -
    3:  0  3  1  3  1  1  1  1  1  1  3  3  1  -
    3:  3  1  3  0  1  1  3  1  1  1  0  1  1  -  
    4:  1  0  0  1  0  0  1  3  0  0  0  0  0  1
    5:  1  3  1  1  1  1  3  3  1  1  1  1  1  3
  tot:  8 10  8  6  4  4  9  9  4  6  5  6  4  4

The finals would be B (10), GH (9) AC (8). we don't go to the 6's because that would trigger a second table.
Note that the longer the league plays, the more important consistent play is.