This is a sequential game with two players A and B. In this game a dime...

This is a sequential game with two players A and B. In this game a dime is put on the table. A can take it or pass. If A takes a dime, the game ends; if A passes, then B can take 2 dimes or pass; if B takes 2 dimes, the game ends; if B passes, then A can take 3 dimes or pass; and so on until a choice of a dollar. This process is shown in the game tree below. The rollback equilibrium of this game is that B is sure to take the dollar at last round, so A should take 90¢ at the penultimate stage, and so on. Thus, A should take the first dime and end the game.

True

False

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Answer - True

Figure shows the tree for this game. Because of the appearence of the tree, this type of game is often called as Centipede game. Player B is sure to take the dollar at the last stage; so A should take the 99 cents at the penultimate stage, and so on. Thus, A should take the very first dime and end the game.

Note: A will get 99 cents at the penultimate stage, not 90 cents (mentioned in the question)

Rahul Sunny answered 1 year ago

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