Multiple rows or column array
Given the information in the question I would start out with something like:

CREATE TABLE players
( player char(8) not null primary key
, additional attributes );

CREATE TABLE games
( game_id int not null primary key
, additional attributes );

CREATE TABLE player_games (match?)
( player char(8) not null
     references players (player)
, game_id int not null
     references games (game_id)
, participant_no smallint not null
,    constraint ... check (participant_no between 1 and 4)
,    primary key (player, game_id)
,    unique (game_id, participant_no) )

CREATE TABLE results 
( game_id int not null
, player char(8) not null
, score ... not null
,     foreign key (game_id, player)
      references player_games (game_id, player)


Example of queries that can easily be answered

Which games has a player participated in?

SELECT game_id 
FROM player_games
WHERE player = ?


JOIN with games if you need more info from each game

Which players participated in a game?

SELECT player 
FROM player_games
WHERE game_id = ?


JOIN with players if you need more info from each player

Order the players from game X according to there score:

SELECT player, score
FROM results
WHERE game_id = X
ORDER BY score