Game Theory: Why I Hate Dining With Large Groups

Some friends ask you to go out to dinner with them. It'll be fun, right? Well, if you're like me then it will unleash a living hell of anxiety in your brain.

These people don't understand the iceberg they are headed towards
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I've been to one or two large dinners in my life, and most of the time they are less than enjoyable experiences.

Why?

First off, there are some obvious logistical problems that arise when more than a couple of people sit down at a table. Large tables are usually harder to get at restaurants, which can mean a longer wait if the host wasn't proactive enough to get a reservation. But that's a small issue compared to the fact that as the number of people at a table gets larger, the ability for everyone to reasonably converse is impaired.

My rule of thumb is that for a rectangular table, 6-7 people is about the max that it can seat and hope to have everyone on the same page. Any larger and there will inevitably be multiple conversations that arise since there is not adequate line of sight and hearing between everyone at the table. Then you're stuck making small talk with whoever is across from you, which you'll be doing for a while since food usually takes longer to come out with a big table (another logistical problem).

A round table can potentially seat more people and hope to have decent conversation, but those are usually less common in restaurants. In any case, the conversation usually isn't as good since everyone is fighting to get a word in (not exactly the ideal scenario for introverted types such as myself).

Logistical issues aside, there is a much bigger problem that arises when dining with large parties, and that is the chore of splitting the check.

Now, living in 21st century America has its perks. We certainly have the technology to split the checks so that each person pays for what they ordered and no more. But that doesn't always happen. Oddly enough, it seems to be less likely to happen at fancier restaurants, where they seem to insist that either one person pays for the whole thing or they split the bill evenly amongst everyone. I mean, all restaurants probably have the ability to split bills fairly, but the waiter always gives you that look when you ask for it and they go off in a huff, leaving you to wonder if they are going to spit in your food. So, more times than not, the bill just gets divided evenly.

And this creates a nearly textbook prisoner's dilemma.

If you're unfamiliar with the prisoner's dilemma then I recommend you read my article about the basics of it before continuing...and then come back to this article please.

For the sake of a simple example, let's assume that you are dining with just one other person (but we'll get to how this problem is exacerbated with more people later), and the restaurant only has two items on the menu: a chicken dish that costs $15 and a steak dish that costs $25. Let's also assume that both you and the other diner enjoy steak more than you enjoy chicken, so the prices for each reflect what you are both willing to pay for them.

So you're sitting across from your friend, and you think, "the steak certainly sounds good, but I've been eating out a lot lately and I need to cut back on my expenses, so I'm just gonna order the chicken and save a bit of cash."

But then it dawns on you...you know that the bill isn't going to be split fairly at the end of the dinner, it will instead be split evenly, i.e. each diner will pay the average of the total meal cost.

This is where the seemingly harmless dinner becomes a prisoner's dilemma. If each of you orders chicken, then each of you will pay $15 for your meal. But if one of you orders chicken, and the other orders steak, then each person will pay $20 for the meal. This becomes a benefit for the person who defected and ordered steak, as they will pay $5 less than they should have, while the person who ordered chicken will pay $5 more. If both order steak, then they will both pay a fair $25 for their meal.

An astute observer (or someone familiar with the prisoner's dilemma) will realize that no matter what your friend orders, it will always be in your better interest to order the steak. If your friend orders chicken, then you save $5 on a $25 meal, and if they order steak then you just pay what the steak is worth ($25). This means that if both diners are acting logically, they will both order steak (the Nash equilibrium) even if both went to the dinner with the intention of saving money.

For a larger number of diners, the difference becomes more significant. Since there are a bunch of scenarios for more people, we'll assume just the simple cases. If, say, there are 6 people at the table and 5 order chicken, then everyone will pay $16.67 for the meal. This means that the person who ordered steak will get it at only slightly more than the price of chicken! Conversely, if all but one person order steak, then everyone will pay $23.33 for the meal, which means that the person who ordered chicken will have to pay nearly the same price as steak!

Real-Life Experience

Nearly this exact situation happened to me when dining with two friends at brunch one morning. All 3 of us were going to get one of the brunch entrees (all around the same price, about $20), but then the first guy who ordered decided to get a mimosa (about $10). When the other person ordered, he got a mimosa as well. When it was my turn to order, I originally wasn't planning on a mimosa, but made the game-time decision to get one (the correct choice from a game theory perspective).

As an aside, I don't normally like getting a drink (alcoholic or otherwise) with a meal. They are usually overpriced at restaurants and I don't feel like they are very value-added. Drinking one or two adult beverages with a meal probably isn't going to give me any sort of a buzz, and I don't really like the way most beers taste with food (with the exception of German beers with German food). If I'm going to order a drink, I'd prefer to do it after the meal and enjoy it over conversation (and as a way to justify sitting at a table at a bar or restaurant). Drinking with a meal seems just like a waste of money to me.

Back to my brunch scenario, I begrudgingly ordered a mimosa since everyone else did, and at the end of the meal we split the bill evenly and all paid about the right amount for what we ordered. Afterwards, one of my friends told me that he didn't really want to get a drink either, but once the first guy ordered one he knew that he would get shorted if he didn't, since he predicted that we would be splitting the bill evenly. Game theory in action!

Morality and Decision-Making

In the beginning of this article I asserted that the group dinner scenario was a nearly textbook prisoner's dilemma. It's not a perfectly textbook prisoner's dilemma because for it to be perfectly textbook each individual would have to have no loyalty or allegiance to the other individuals. This is not exactly the case in a dinner scenario, as people usually have some level of allegiance to people with whom they break bread.

This makes the decision of what to order even more nerve-wracking. Suppose that in the original example you are in the mood for steak and are perfectly willing to pay $25 for it. But you also know that everyone else at the table is trying to save money and will be ordering the chicken. If you are the only one to order steak, then it will make everyone else's meal more expensive, while making yours comparatively cheaper. You might be afraid that the other members of the party will think that you are trying to freeload off of them. In order to subvert this, you begrudgingly order the chicken. Now imagine how peeved you would be if everyone else turned and ordered the steak!

Morality can thus cause people to not order in the logically best way for fear of social judgement, which, as I have illustrated, can lead to problems of its own.

The thing is, moral decision making can break down as the group gets larger. For a small group, the price that each person pays will be noticeably affected if one or two people order something expensive. But as the group size gets large, the price will tend towards whatever the vast majority of people order. If you are at a table with 10 other people, and all 10 order chicken while you order steak, then your steak will only raise everyone's cost by 90 cents. This can motivate people to make less moral and more logical decisions, since they don't feel like their decision will affect the overall outcome very much. No single raindrop believes it is to blame for the flood. So if you have a large group of logical people, you can bet most of them will order steak, despite any fears of social judgement.

I F***ing Hate Tapas Restaurants

In case you are unfamiliar (lucky you), Tapas-style restaurants are Spanish-themed dining establishments (since tapas originated in Spain...or were popularized in Spain...I don't really care) that basically serve a bunch of appetizers (tapas) that are meant to be shared between the entire table.

I have many problems with this concept.

Firstly, the tapas are usually pretty small plates, i.e. like 5 shrimp, and while they are inexpensive by themselves, they are pretty pricey for the amount of food that you get. Because of this, you have to order a bunch of them to feed an entire table, and the bill can stack up without you realizing it.

The more troublesome part of tapas is that it complicates the game theory scenario by adding in the element of splitting not only the bill, but the food as well! Even if the waiter is more than happy to split a bill at a tapas restaurant, how in the hell would you even do that? Each person can pay for a dish, but what if 5 people order 8 dishes?? What if one person eats as much as everyone else combined?? There's no fair way to do it! This is why Spain is lagging behind the rest of Europe!

I'm glad the people at College Humor thought about this as well:

So if you're someone who isn't paying for the meal, doesn't want to eat a lot, and loves variety and ambiance over sustenance (*cough* girls), then tapas places are great! If you want to have a hearty meal on a single plate for a price that doesn't require a PhD in math to figure out who owes what on the bill, then you may wanna steer clear of tapas.

Conclusion

If I have sullied your enjoyment of large dinners after reading this article, then I apologize (not really). This is, to me, why I think the idea of dinner parties hosted at people's homes need to make a comeback. It's a far more intimate experience than a restaurant and allows you to make connections with people without having to worry about what to order (since it's already been decided by the host). Although I guess that scenario also creates a prisoner's dilemma if everyone takes turns hosting, since you can decide to cheap out on the meal when you host, but I guess that's regulated by the fact that if your meal really sucks then people might stop inviting you to their dinner parties, so maybe it works out? Maybe life is just easier if you don't have any friends...

I can't help but wonder if restaurant owners understand the game theory ramifications of evenly dividing bills and purposely don't allow fair division of checks because they know it will motivate people to order more expensive dishes. They say it's to make things easier for the wait staff, but when everyone pays with a credit card how much harder is it really? I urge you to boycott any restaurants that don't allow fair division of checks! We will not be divided against our own dinner party!

I'm sure glad that the everyone-pays-the-average model doesn't come up in bigger and more important expenses like insurance or government spending, that would be super bad! Oh wait...

 

2 thoughts on “Game Theory: Why I Hate Dining With Large Groups

  1. Summed it up beautifully. Also, I have a friend who manages a restaurant. He told me you should never have more than 6 people per table. There is no way for the kitchen to prepare more than 6 dishes at a time. If you order more than 6 then some will be held and getting cold while the others are prepared. Everyone always wants all of the dishes to come out at the same time.

  2. You should always pay for your date and tell server at the beginning you want separate checks when not with a date.
    A great example of a shared meal with little food was our meal at Star Noodle! Great article. We seem to end up at large group dinners too much.

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