Game Theory: converting extensive form to normal form

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Converting extensive form to normal form in game theory involves representing multiple strategies for players within a payoff matrix. When player 2's strategies depend on player 1's choices, the matrix will contain repeated payoff information to account for all possible scenarios. It is important not to leave fields blank, as this could lead to missing critical information about the game's structure. The process allows for a comprehensive understanding of the game, enabling the use of iterative elimination of dominant strategies for solving. Understanding these concepts is essential for effectively analyzing complex games.
elictricocean
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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
 
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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.
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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