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So in our example, here's our sub-game.
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Here's our green sub-game.
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Here's the node it starts from.
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Here are all the nodes that are successors of that node:
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these are the children, and these are the grandchildren.
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If you have this grandparent node you have to have all of his children,
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and all of his grandchildren.
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So it comprises all the successors of that node.
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And finally--this is important--
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it does not break up any information sets.
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So a sub-game, informally,
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it's just a game within the game.