Game Theory: converting extensive form to normal form

In summary, converting an extensive form game to normal form can be done by creating a matrix with all possible strategies for each player and their corresponding payoffs. This includes leaving fields blank when there are repeated payoff information. The game can then be solved using iterative elimination of dominant strategies.
  • #1
elictricocean
1
0
Hi, I don't if this is place to asks this. I am teaching myself game theory and I am just confused on how to convert extensive form to normal form when there are different stategies for player 2' depending on the player 1's stretegie. I understand if you were turning rock paper scissors into normal form, on the top there would be Rock, Paper, and Scissorns for player 2, and Rock, Paper, Scissors, to the left for player 1. That is a really simple example with all of the same variables. What if there are more? Do you leaves fields of the matrix blank?

thanks,
elictricocean
 
Physics news on Phys.org
  • #2
Okay, i spent a really long time trying to figure out how to explain this without using the diagrams/matrices that can't be made in this forum reply box. So, instead, i'll send you to a link :
http://en.wikipedia.org/wiki/Normal-form_game#Sequential_games_in_normal_form

essentially, you just have the payoffs in multiple fields. the reason for this is later on you won't know where you are in the game, and you will need all of that information. but, essentially, you have a lot of repeated payoff information in order to capture every stategy of the players, even if they end up representing the same payoff information. then, you just solve the game as you normally would using iterative elimination of dominant stategies.
 

1. How do you convert an extensive form game to a normal form game?

To convert an extensive form game to a normal form game, you need to first list out all the possible strategies for each player in the game. Then, you need to create a matrix that represents the payoffs for each combination of strategies. Finally, you need to simplify the matrix by eliminating any dominated strategies and finding the Nash equilibrium.

2. What is the purpose of converting an extensive form game to a normal form game?

The purpose of converting an extensive form game to a normal form game is to simplify the game and make it easier to analyze. By converting the game to a matrix, it becomes easier to identify the Nash equilibrium and determine the optimal strategies for each player.

3. Is it always possible to convert an extensive form game to a normal form game?

Yes, it is always possible to convert an extensive form game to a normal form game. However, the resulting normal form game may not accurately represent the original extensive form game if there are imperfect information or sequential moves involved.

4. What are some limitations of converting an extensive form game to a normal form game?

One limitation of converting an extensive form game to a normal form game is that it may not accurately represent the original game if there are imperfect information or sequential moves involved. Additionally, the normal form game may not capture all the nuances and complexities of the extensive form game.

5. Can converting an extensive form game to a normal form game change the outcome of the game?

Yes, converting an extensive form game to a normal form game can change the outcome of the game. This is because the normal form game may not accurately represent all the strategies and payoffs of the original extensive form game, leading to different results. Additionally, the elimination of dominated strategies during the conversion process can also alter the outcome of the game.

Similar threads

  • Quantum Interpretations and Foundations
Replies
2
Views
734
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
951
  • Engineering and Comp Sci Homework Help
Replies
4
Views
995
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
7K
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
902
Replies
9
Views
952
  • Calculus and Beyond Homework Help
Replies
29
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
Back
Top