# Conditions for Simultaneous move game & Sequential move games to lead to same equilibrium

Consider a game with two players with profit functions : $\pi_1 (p_1; p_2)$ and $\pi_2 (p_2; p_1)$, where $p_1$ and $p_2$ are the players' actions (say prices).

Is there any theorem that establishes conditions, when the pure strategy equilibrium will lead to the same prices, in the following two cases? :

1. If the prices are decided simultaneously
2. If the player 1 sets the price first and then player 2 observes the price of player 1 and then sets their own price

On the side, let me suggest that you add more context to your question. It seems you are implicitly assuming unique equilibria (how are we supposed to compare multiple equilibria?) and it is unclear whether $\pi_1$ and $\pi_2$ should be supposed to be symmetric.
• Thanks for your answer and the reference. To clarify on the points you asked, the game that is of interest to me is not symmetric ($\pi_1$ and $\pi_2$ are different), but has a unique equilibrium (in both simultaneous move and sequential move). – user917983 Aug 29 '17 at 13:22