# Strategy sets and SPNE

I need to find the startegy sets for the two players in this game. I understand that the game has only one subgame, that is, the entire game. I cannot seem to understand the strategy sets of the players. For player $$1$$, I believe the startegy set should be $$s_1={Ll, Lr, Rl, Rr}$$. Since the game is a simultaneous move game, I cannot understand why player $$2$$'s actions, given a singular information set, are different, i.e., $$U, D, P, Q$$, although I understand that this is a simultaneous move by players. Please help me understand the game and find SPNE for the same. Thanks!

• Where did you get this game? Unless there are typos, this game tree is simply invalid. As you rightly observe, the sets of actions available at different nodes of player 2's information set cannot be different. – Herr K. Feb 16 '19 at 22:47
• It was a question in one of the problem sets we were supposed to do. Thank you for your observation. I believe the question wanted us to trace the flaw. – S.Rana Feb 17 '19 at 5:15
• Also, as you mentioned, "unless there are typos"; if there are, how do we find the strategy sets? I cannot decipher how even 'rectifying the typos' could solve it. That said, how could I even rectify the typos for the game to be valid? – S.Rana Feb 17 '19 at 5:17
• "the sets of actions available at different nodes of player 2's information set cannot be different." So either change the set of actions to be identical or make it two different information sets. – Giskard Feb 17 '19 at 8:12
• Yes, denesp is right. Otherwhiles it would not be an informationset (does not make sense if you logically think about it). Also note that the set of strategies you provided for p2 in your questions includes strategies of p1. – shenflow Feb 17 '19 at 16:51