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using game theory to avoid overeating during the Holidays

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This post is taken from a post at mindyourdecisions.com. It has been adjusted to fit the upcoming Jewish Holidays.

Do you overeat on the Holidays?  I certainly do.  Usually by Yom Kippur I think to myself “okay Jon, you’ve overeaten two days, but on the other hand you’ve fasted two days as well.”  Now all that’s left is to control yourself over Sukkot.  And we all know how that goes…

But it isn’t all my fault.  As a Jewish man, I am expected to overeat at every Holiday meal.  Even if you don’t want to eat more, the Mother of the house will generously serve me more food. This was great when I was a kid. It’s not so great any more.

Somewhere the Jewish culture of generosity has morphed into a game where the host “wins” by getting you to overeat.  In general, my goal at a Yom Tov meal is to eat well but not stuff myself. I also want to be a good guest; this means I cannot waste food and I have to convince the host that I’ve eaten a lot.

I’ve gone through the game several times. I’ll explain how I used to fail but I now have a somewhat winning strategy.

A few years ago, I used to take a lot on my plate in the first serving. I was confident that I could talk my way out of more food. I would say that I was really full, and that I would not eat more. I would threaten that if the host put more on my plate, I would surely not eat the food. But then more food was put on my plate. Since it’s unacceptable to waste food, I was stuck stuffing myself. Jon 0, Host 1.

So started to change my strategy. I reduced my first serving to a medium-size. What I didn’t figure is that a real Jewish mother is always aware of how much each person ate. When she was servings seconds, I was given more to compensate for my smaller first serving. Again, I could not waste food so I had to stuff myself. Jon 0, Host 1.

After failing many times, I now use a different strategy. I first pile on a sampling of every food item so I can demonstrate I’m eating every thing. I’m active in voicing how much I enjoy the food (so I’m a good guest) and I explain that I’ll help myself to more food. I then serve myself a medium-sized second round, and the trick here is that I eat the food very slowly. Since I am still eating, the Jewish Mother cannot force more food on my plate without looking intrusive. The host is better off by doing nothing. And I finally get to eat a reasonable amount. Yes! Jon 1, Host 0.

What I described above can be graphically displayed in a game tree. Each node is a placeholder for a player to choose an action. Different actions correspond to different branches of the tree. The game ends at terminal nodes with payoffs for each player. In the game tree, my actions and payoffs are colored in blue and the host’s are in orange.

eating

I’ve also drawn in arrows to depict the equilibrium path for each of my first actions. For instance, if I choose “Self-serve lots of food,” the host will respond with “Serve more” and I will have to “Eat,” so I get a payoff of 0 and the host gets 1.

Notice that after a host chooses “Serve more,” I could choose “Waste Food” which gives me a -1 payoff since wasting food is bad. If I instead choose “Eat,” and stuff myself, I get a higher payoff of 0. What this means is once I’m served more food, I would definitely be better off choosing “Eat” over “Waste food.” Or saying it another way, my threat of “I’m not going to eat if you serve me” is non-credible. If I could convince the host I would choose “Waste Food” (say, if I were crazy), then my threat would become credible.

For now, I’m on the right-most path where I eat little and slowly, and the host responds with nothing, so I win the game.

Of course, the game tree has its limitations. In a real dinner setting, the host has many more options, as do I. Nevertheless, I find it useful to stylize the problem into a game tree to see the possible paths. From the tree, it’s obvious why I was failing before and succeeding now. And should the host introduce a new action, I can draw a new tree and hypothesize what might happen so I’m one step ahead of the game


2 Comments

  1. NG says:

    This is AWESOME.

  2. Stone says:

    In a Zero Sum game the -1,-1 result is better than the 0,1 result. At -1,-1 you are tied. At 0,1 you have increased your score by 1, but your opponent has increased their score by 2.

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