Are action set for each player identical at every information set in extensive-from game?

Question

I have an question regarding to sequential/extensive-form game. I am wondering if one player must have the same available action set at different node? Thanks very much!

Answer 1

No. In general, players can have different sets of actions at each node they take an action.

Take, for instance, the alternating offer bargaining game. Each player has different actions depending on whether it is an odd period or an even period.

Note that there need not even be any sort of pattern in the available actions at each node, as there is in the aforementioned game. However, typical games will have them, because completely general games are very difficult to solve.