Wednesday 20 August 2014

Lunchbox game theory

A practical lesson in game theory: the three-person game.

When helping the kids pack yoghurt for their lunch boxes, I found there was only strawberry yoghurt left in the fridge in the tear-off individual containers. Their preferred yoghurts, mango and vanilla, were finished.

So I asked Liam to grab new yoghurt from the garage fridge. He came back with two large containers (there were no tear-off packs left) which happened to be mango and vanilla. Since we could only open one of them, I asked Liam which one he wanted.

"Mango."

Liam then asked Michelle the same question, who replied, "Vanilla."

I said, "Sorry, we can only open one. So which one will we have?"

Same responses.

"Michelle.", I said, "We can only have one, so how about we have mango this week?"

"No!", she says, "I want vanilla!", as she starts to melt down.

"OK, Liam.", I said, "How about we have vanilla this week, since it seems to be important to Michelle?"

"No!", he says, "I want mango and I said it first!", as he also starts to melt down.

"OK.", I said, "Since you can't agree, I'm going to put them away and you can both have strawberry today."

"Noooooooo!"

OK that was traumatic. Unfortunately, in addition to the yoghurt wars, I see that tomorrow we will only have one bread roll left and one of the kids will have to have sliced bread...

2 comments:

  1. Ah, a practical lesson indeed.

    But you didn't note whether strawberry was a more preferred option than vanilla (for Liam) or mango (for Michelle). If it was the least preferred for both, then its like an asymmetric prisoners dilemma. But if its second choice for both, then you probably hit the optimal solution (though, game theory seems to lack an indicator for trauma inflicted in reaching optimal point)

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  2. Strawberry was their least preferred option so it really was like a prisoner's dilemma.

    My rule makes the optimal solution dependent on peaceful cooperation. Of course, as any kid in a supermarket knows, parents are players in the game as well and rules can be tested...

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