Game theory - ranking of n players playing matches with m (>2) players each

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I am facing the following problem:

In two player games, a ranking of a pool of n players can be achieved by letting everyone play against every opponent, taking the result of each match and aggregate it to get the overall ranking. However, in my case a single match is played by m (e.g. 6) players. Every player is getting a score after a match. What would be a fair 'tournament format' that can be adjusted based on the total player count n and player count per match m to rank all the players from best to worst overall in a fair way?

I was searching for research in this area, but i am unable to find something fully covering this topic. I am probably using the wrong keywords. Can someone steer me in the right direction or suggest a solution to this problem? Thanks.