# Nash equilibrium with three players

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?

• Hi, please see the faq on homework questions. Where exactly are you going wrong? have you attempted the question? We would really appreciate you showing some work, else you are very unlikely to get an answer and/or have the question closed in its current state. – Brennan Apr 28 at 21:40
• @Brennan Hi, I edited the question but I don't know if it goes against to the site's policies again – Ana Ellis Apr 28 at 23:31
• "For example, if Player 2 chooses L what's the player's 1 and 3 move?" Seems like you are having difficulties with the basic concepts. Do you understand bimatrix notation? Have you considered consulting with your lecturer/teacher's assistant? – Giskard Apr 29 at 7:02
• @Giskard I have no problem with games with two players, but I haven't dealt with three often. But I will discuss it with the TA for more clarity – Ana Ellis Apr 29 at 10:09