0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

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).

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.