Sarah and Claire are sisters. Their aunt gave 10 cookies to Sarah and asked her to share some with Claire. She could choose how many she would give her, but if Claire was not happy with her share, her aunt would take back all the cookies
a) How should Sarah decide how many cookies to give Claire if Claire prefers more cookies to fewer cookies? b) Will there be any change in her decision if she knows that Claire values fairness?
a) Sarah should decide how many cookies to give Claire using the technique of backward induction. Because Claire prefers more cookies to fewer cookies, she will always accept Sarah's offer. Given that Claire will always accept her offer, Sarah should offer the lowest possible number of cookies to Claire.
b) If Sarah knows that Claire values fairness, she will realize that Claire will not accept an unfair share of cookies. Because neither of them will get any cookies if Claire rejects the offer, Sarah will offer an equal share to Claire.
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