About game theory in kindergarten parties

Friday mornings are our guilty pleasures (for my wife and me). You see, in Israel, Friday is an off day, and the kids are in kindergarten and school, so for a few hours, we have quality time together. We find ourselves a coffee shop and then do weekend arrangements or shopping. It’s possible if the kids are in their kindergarten/school. Once the summer vacation is on – our Friday mornings are no longer free.

In recent years (as long as at least one of our children is/was in kindergarten), occasionally, our Fridays are interrupted by a “kindergarten party”, i.e., celebrating some kind of a holiday. Don’t get me wrong, I love seeing my children enjoying a good party, but why should it be instead of my quality time with my wife?

The kindergarten party is usually set to 9 o’clock for an hour and a half. The teacher usually says by the end of the party that she will be in the kindergarten until 12:30 if anyone wants to leave his child and return (12:30 is the regular pick-up time for Fridays). However, everyone picks up their children, and here goes our precious morning quality time- no one wants to be the parent who leaves his child alone with the teacher. It’s Catch22 – no child remains because all the children are being picked up.

A game theoretic perspective

So where is the game here? Surprisingly it’s an adult game, not a child’s game. It’s a cooperative game in which the parents can reach a coalition that will give them some more Friday morning time, and that’s the preferable strategy (assuming that most parents are like me and value their Friday morning with their significant other). However, it’s an unstable coalition since the moment some parents decide to pick up and not wait until 12:30 – all the children get picked up. The cost of a child remaining alone or with a tiny group of children, with the teacher, and feeling neglected, is too high to suffer for a parent, so we get a chain reaction.

A side note: game theoretic proof that you should believe in god

I’m an atheist, but I still remember reading a book as a math undergrad with Pascal’s wager about why we should believe in god. I don’t fall for it, but it’s a lovely paradox.

As a player, you can play one of two strategies: either believe in god and abide by his rules or be an atheist and do whatever you want.

If god exists and you do not abide by god’s rules, you can expect an infinite loss when you die (i.e., an eternity in hell). However, if you abide by god’s rules, you can expect an infinite gain (i.e., an eternity in heaven).
If god does not exist, being an atheist, you can expect a finite benefit (during your lifetime), and being a believer – a finite loss (of abiding by rules and constraints you don’t have to impose).

From an expected utility perspective (and assuming that there is a positive probability that god exists) – you should believe in god.

What can we gain from game theory?

A mathematical analysis based on sound game theoretic principles can at least be fun. Beyond that, it can be helpful – game theory is everywhere – in business (bids, markets with multiple actors such as competitors and clients, and negotiations). It’s also in politics (coalition, cooperation between coalition and opposition, etc.). Such an analysis helps us observe from the side and try to explain what the steps and preferable decisions are analytical.

Ran into interesting cases involving game theory and want to share them? Reach out! I would love to hear about them.

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