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Game Theory - Coggle Diagram
Game Theory
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Games and Problems
The ⅔ Game
In the 2/3 guessing game, players guess a number between 0 and 100, and the goal is to choose a number closest to 2/3 of the average of all guesses. The strategic approach is to continuously lower your guess considering that others are rational and will do the same, leading to a series of iterations that converge towards zero.
Monty Hall Problem
Setup
There are three doors: behind one door is a car (the prize), and behind the other two doors are goats.
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Gameplay
Monty Hall, who knows what’s behind each door, opens another door (let’s say Door C) that reveals a goat.
Now you have a choice: stick with your original choice (Door A) or switch to the unopened door (Door B).
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Hawk Dove
The Hawk-Dove game is a theoretical model used in game theory to analyze the behavior of individuals in a conflict situation where they can choose between aggressive (hawk) and peaceful (dove) strategies.
Hawks aggressively fight for resources, risking injury or cost.
Doves avoid conflict and share or retreat, incurring no injury but possibly gaining less.
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Form of games
Extensive Form
Represents games as a tree, showing how the game unfolds over time.
Each node represents a decision point, and branches represent possible actions.
Includes information about the sequence of moves, players’ possible actions at each decision point, and payoffs for all possible outcomes
Normal Form
Represents games as a matrix, summarizing the strategies and payoffs.
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Useful for identifying dominated strategies and Nash equilibria, but may lose some information compared to extensive form