Game Theory: converting extensive form to normal form

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SUMMARY

This discussion focuses on converting extensive form games to normal form in game theory, specifically addressing the complexities when player strategies vary. The example of transforming rock-paper-scissors illustrates the basic structure, where player 2's strategies are represented across the top and player 1's strategies along the side. The key takeaway is that when multiple strategies exist, the payoff matrix may contain repeated information to account for all possible outcomes, and the game can be solved using iterative elimination of dominant strategies.

PREREQUISITES
  • Understanding of game theory concepts, particularly extensive and normal forms.
  • Familiarity with payoff matrices and their construction.
  • Knowledge of iterative elimination of dominant strategies.
  • Basic grasp of strategic interactions between players.
NEXT STEPS
  • Study the construction of payoff matrices for complex games.
  • Explore the concept of sequential games in normal form.
  • Learn about iterative elimination of dominant strategies in various game scenarios.
  • Review advanced examples of converting extensive form games to normal form.
USEFUL FOR

Students and educators in game theory, researchers analyzing strategic decision-making, and anyone interested in understanding the conversion of extensive form games to normal form.

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.
 

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