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?

  • $\begingroup$ It is difficult to see how player 2 can have more than $3\times 4=12$ pure strategies $\endgroup$ – Henry Jul 16 '17 at 17:58

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 Players 1 move hence player 2 must differentiate his action based on Player 1 taking A, B or c(Which he knows since he observed it). Player 2 now has 3 different strategies for making decisions hence he has 3 information sets(Each containing One Game State).

  • $\begingroup$ Using this answer, you can check that 2 has $4$ actions for each of her 3 information sets, giving a total of $12$ pure strategies. (A strategy describes which action is played at each of the player's information sets.) $\endgroup$ – mlc Jul 17 '17 at 15:41

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