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 "finals"
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 & 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.