Neil and Derek are brothers who are very fond of watching television. They share a television but watch different shows. Every evening after coming home from school, they argue over who will watch television and for how long

Irritated with their fight, their parents asked Neil to decide for how long each of them would watch television. They also told him that if the brothers failed to reach an agreement, they would not let either of them watch it. a) How should Neil make his decision? b) What will be the outcome if Derek prefers fairness over watching television?

a) Neil should make his decision using the technique of backward induction. Because Derek is fond of watching television, he will prefer a few hours of watching to not watching it at all. Therefore, he will always accept Neil's offer. Given that Derek will always accept his offer, Neil should offer the minimum number of hours to Derek.
b) If Derek prefers fairness over watching television, he will not accept an unfair allotment of hours to him. In this case, neither of them will get to watch television. If Neil knows that Derek prefers fairness, then Neil has an incentive to offer a more equal time split.