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Let's just check. If my pair chooses Alpha,
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then my choosing Alpha yields 0, Beta -3:
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so Alpha would be better.
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But if my pair chooses Beta then Alpha yields -1,
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Beta yields 1: in this case Beta would be better.
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So Alpha in this case is better against Alpha,
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and Beta is better against Beta,
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but neither dominates each other.
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So here's a game where we just change the payoffs.
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We have the same basic structure, the same outcomes,
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but we imagine people cared about different things
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and we end up with a very different answer.