I am in a game theory course and I need to come up with an example of a Matrix game with more than two players
I have consulted https://en.wikipedia.org/wiki/List_of_games_in_game_theory, but the ones that are more than two players cannot be posed as matrix games.
Note by matrix game I mean that there exists some matrices $A, B$ (for two players) that specifies the reward for the actions taken by player $1$ and player $2$. For more than two players, we need additional matrices.
Does there exists such a game?
Some thought experiment: for example, three players flip a coin simultaneously. If the coin lands on head, then player 1 wins. Tail, then player 2 wins. It doesn't seem that the third player has any role in it.
A simple solution to this is to imagine a 3-D matrix, with payoffs represented as a triplet.
But if you want to write it down, you can have two separate matrices.
For example, if Player 1 can choose [up, down], Player 2 can choose [left, right], Player 3 can choose [weak, strong], then we can first let Player 1 choose between [up, down].
Then, for each choice of up or down, we can make a 2x2 matrix for Players 2 and 3, and call them the "Up Matrix" and the "Down Matrix", both composing of choices that Players 2 and 3 can make, so the rows can consist of [left, right], and the columns consist of [weak, strong].
In practice, we do not make matrices for more than two players and rely on equations instead.