I am trying to find some literature on a variation of a Stackelberg game in which two players, P1 and P2, interact in the following order:

1. P1 plays
2. P2 plays
3. P1 plays

The best guess I have for the name of this sort of game, inspired by the "leader-follower" setting of a Stackelberg game, is "leader-follower-leader" but that's not giving me many useful results.

Question: Does anyone know if such a game has a name or has been studied?

• I think these types of game cover a lot of dynamic games. In fact I am not sure how this game would require a different set of assumptions or solution method from standard leader-follower games. You may want to assume perfect recall, but that is about it. – Giskard May 2 '20 at 16:11
• You do not need any such game to be studied in the past, you only need a precise definition of the type od game that you want to adjust. Then just implemnt your idea, but the Stackelberg is a leader follower game, which means that some player moves first by forcasting the strategy of her competitor if he makes a or some action and then he uses the backward induction to solve her initila problem... – Hunger Learn May 3 '20 at 9:00
• Contrarily, If the leader-follower-leader does not account in what you have to do, just stop thinking to use a specific type of game. Namely, create your type of stage game based on the best response problem and then you can see if this is a Stackelberg or maybe it is not,...So it is a game after all and it does not need to be some specific one! Remember, that you may need to use a fixed point theorem solution in some cases... – Hunger Learn May 3 '20 at 9:07
• @Giskard Thanks for the comment. By a similar solution method, do you mean that I can likely approach this game by looking at compositions of strategies similar to a standard Stackelberg setting? – jonem May 3 '20 at 20:12
• @jonem I mean backward induction. – Giskard May 3 '20 at 21:08