Each player must suggest three games to play, either all different, or with some duplication. Every game suggested must support the number of players who are playing Game Theory.
On paper, draw a grid with three columns and as many rows as there are players. Roll to see who goes first. In clockwise order, each player writes the name of a game they want to play in any remaining space on the grid. When the last space is filled, the last player in the turn order crosses out any row of her choice, and then players take turns counterclockwise with players alternating crossing out columns and rows until only two spaces are not crossed out. (Exception: when there are a large number of players, such as six or seven, anyone who would cross out the last column crosses out a row instead.) The game that will be played is chosen randomly from the last two games, for example, by flipping a coin.
TK: Draw example.