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Game Theory with Parents

When I was younger, I remember facing a dilemma more often than I would like.

If I have lost something, how long do I wait before telling my parents?

If I tell them immediately, I will probably be in trouble for not looking after my possessions. If I wait a while, there is a good chance that I will find it, therefore avoiding getting into trouble.

But occasionally, I would have left it somewhere that they found it and are holding onto it. They are waiting to see how long it takes before I notice that it is missing. In this case I would never find it and the longer I leave it, the more trouble I would be in.

I remember trying to work out, what the optimal time to admit defeat was, when would I minimise the trouble. I never did work out a good solution apart from not losing something in the first place1. As the quote from War Games goes:

the only winning move is not to play.

Notes

  1. easier said than done
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