Consider the game below played by three players. Player 1 chooses one of the rows (T vs B). Player 2 chooses one of the columns (L vs R). Player 3 chooses one of the three tables (A vs B vs C). Each payoffs cell gives payoffs to players 1, 2 and 3, respectively.
Why are the strategy profiles are (T, R, A), (B, L, A), (B, L, C) and (T, R, C)?
I am stuck in the fact that how do we start at choosing the equilibrium. So for example at A do I choose an equilibrium there and again at B and C. Or do you consider all three players simultaneously? For example, if Player 2 chooses L what's the player's 1 and 3 move?