Consider a game in which player 1 moves first. The set of actions available to player 1 is A1={A,B,C}. After observing the choice of player 1, player 2 moves. The set of actions available to player 2 is A2={a,b,c,d}.
a) How many strategies does player 1 have?
b) How many strategies does player 2 have?
c) How many information sets does player 2 have?
My work:
For a) I said 3 because player one has 3 choices.
For b) I said 48 because player 2 has 4 choices times 4 choices times 4 choices which is 48.
For c) I am unsure of what to do? Player 2 is aware of player 1's move so would the answer be zero?
Let's Remember the definition of an information set: In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed.
Let's look at the problem. Player 1 takes a move. Player 2 has observed Player 1's move hence player 2 must differentiate their action based on Player 1 taking A, B or c (which they know since they observed it). Player 2 now has 3 different strategies for making decisions hence they have 3 information sets(Each containing One Game State).