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A Lesson In Game Theory And Incentives, Restaurant Edition…

September 6th, 2009 · 14 Comments
Incentives

“You might be an economist if you go to a Chinese restaurant and open the fortune cookie and add ‘at the margin’ at the end of it.” –The Stand-Up Economist

I was thinking about this quote because I feel that I should add “You might be an economist if you are at dinner with a friend and are more intrigued by how to split the bill than by what your companion is saying.” (I swear that my friends should not be offended by this. I just have issues.) In my defense, I don’t usually act on my impulses and usually just go along with whatever my friends suggest, though I will admit that there was that one time when I was at dinner with a group and the person who had consistently ordered the most expensive items on the menu suggested that everyone split the bill evenly. I made some sort of snide comment and the suggestion was quickly rejected, but I have a suspicion that now my friends know what I am thinking in such situations. :)

So what is the best thing to do when you go to dinner with friends and the bill comes? (Hint: the answer is NOT “pretend to go to the bathroom and escape via the window.” Yeah, you know who you are…) The efficient solution is the one that gives incentives that encourage neither overconsumption nor underconsumption. I did some brainstorming about the different ways that the bill sharing could work and took the liberty of evaluating them all in terms of efficiency and logistics. This is what I came up with…

Option 1: Each person looks at the itemized bill and pays for what he or she ordered. This is the most efficient option since each person is fully internalizing the cost of his or her choices. In other words, your choice of whether to another $1 of food results in you paying exactly another $1, so your desicion-making processes result in the “right” level of consumption. The downside here is that it’s somewhat cumbersome, it requires people to be able to add properly, and it can lead to awkward situations when there are shared items (eg. “Um, I only had 25% of the nachos, so…”). I mean, you don’t really want to end up like this guy:

Option 2: Split the bill evenly. This takes the cumbersome aspect partially (but not totally) out of the picture, but it introduces some misalignment of incentives. Why? Say you know that the bill is going to get split evenly, and assume that you are pondering whether to order that extra cocktail. Now, the extra cocktail is going to add, say, $10 to the overall bill, but because the bill is getting split down the middle you will only be paying $5 extra. Therefore, you are likely to order more than is actually optimal because you don’t have to internalize the full cost.

Option 3: Take turns paying the bill. This is probably the most logistically simple option, but it still suffers from incentive problems on the part of the non-paying party. It’s very tempting to order too much when you know that it’s not your turn to pay! The situation could get even worse if the non-paying friend tries to “get his money’s worth” by making up for the last time when the other guy ordered a lot and didn’t have to pay for it. Now you run the risk of being this guy…

Option 4: Flip a coin at the end of the meal. If the coin comes up heads, whoever flipped the coin pays. If it comes up tails, the other person pays. So now for each additional item you order you have a 50% chance of not paying anything for it and a 50% chance of paying for all of it. Therefore, on average (or in expectation, in mathematical terms) you’ll pay for half of every additional item that you order. This is different, however, from knowing in advance that you will be paying half of the bill. If a person is risk-averse, the 50% chance of having to pay for all of something looms larger than the sure knowledge that you will have to pay half. Therefore, the uncertainty serves to mitigate the incentive problem to a degree, but it could result in some lack of parity if the realization of the coin flips doesn’t match the 50/50 split perfectly. (Note here that it is important to flip a coin at the end of the meal rather than before!)

Option 5: Don’t talk about how to split the bill until dinner is over. If you go with this option, you know that you might be splitting or might be paying for what you ordered. In this case, risk-averse individuals are likely to order closer to their true preferences than in any of the sharing scenarios since there is some chance of having to pay for 100% of what they ordered. However, once dinner is ordered it becomes clear which sharing strategies are better for which people, and you could end up arguing about what to do. (See my introductory example above.)

Shortly after I started thinking about this, Russ Roberts voiced his opinion on the matter and also explained how this problem relates back to the moral hazard problem in insurance. Luckily, I think that, at least in the restaurant example, satiation and other factors (not wanting to be obese, etc.) play a role in mitigating the overconsumption problem. Furthermore, social pressures probably prevent people from being too opportunistic even when it is theoretically possible. One could argue that there are also factors that serve to mitigate the moral hazard in healthcare, if for no other reason than it’s not generally pleasant to go to the doctor!

In case you are curious, here is where the cartoons came from.

Tags: Incentives

14 responses so far ↓

  • 1 Surender // Sep 6, 2009 at 10:19 am

    Hey thanks……..It is very informative….Let me employ the option 5 when i go out with the friends next time………..i will definitely post my experience……..regards,

  • 2 hh // Sep 6, 2009 at 1:19 pm

    I’ve found that a combination between 1 and 2 work best in larger and mixed (i.e. employed/unemployed/underemployed) groups:

    Evenly split the shared items (appetizers), and everyone put in what you think you owe for your meal plus tip & tax (estimate 20%). Then, the “banker” adds it all up, and usually says “ok, we’re $10 short. So everyone (all 5 of us) put in another $2.” Those that know they underestimated usually throw in a bit more, and those that just want to move on throw in a bit more, and it all works out.

    Of course, after all of this you should then expect to get the person who wants credit card points, miles, dining credits, etc. offering to take the cash pot and put the bill on their card instead. (Yes, this makes the ordeal last even longer…) So, Econgirl, should the group make that person pay more since they are reaping their rewards benefits? Or maybe they should just be forced to spend their miles by taking the rest of the group on their next “free” trip…?

  • 3 Dan L // Sep 6, 2009 at 2:42 pm

    Random remarks:

    -Options 2, 3, and 4 all fail completely when the reason for disparity is systemic, which it often is. For example, if one person doesn’t drink alcohol or is a vegetarian or always orders steak, etc.

    -Isn’t Option 5 the default for most people who don’t regularly go out together as a group? What kind of strange people start talking about how to split the bill before ordering?

    -Nothing you say can convince me that Option 4 is not just plain absurd–an example of thinking out of the box for the sake of thinking out of the box.

    -Don’t forget that different people have different tipping standards.

    -If you have friends who would actually order an expensive dish just because they think or hope that their friends will end up subsidizing them, you need to find new friends.

    -The way you describe things, it makes one pine for the classic Chinese system of fighting for 15 minutes for the privilege of picking up the check.

    -Honestly, I can scarcely remember the last time I felt frustration in splitting a bill. Is that unusual?

  • 4 SteveO // Sep 6, 2009 at 4:11 pm

    I prefer the liberal option. I sound like the most compassionate person at the table by loudly and articulately explaining why the richest person at the table should pay-because he’s extracted so much from the rest of us in unfair business practices . Mr. Moneybags is forgotten, and I look like a hero.

  • 5 Bob Nease // Sep 6, 2009 at 7:06 pm

    Three thoughts:

    1. What’s quite remarkable is how well behaved people generally are in the “split the bill” scenario. There is a moral hazard, but human behavior tends to be better behaved than classical economics would suggest. Really poor behavior seems to be the exception rather than the rule.

    2. Gneezy et al studied different bill-paying methods using a randomized trial methodology in an actual restaurant setting. People eat more expensively when the bill is being split than when they are paying their own way. This, along with #1 above, suggests the possibility that we’re all misbehaving a little – and we’re unaware of it – when exposed to the split-the-bill arrangement.

    3. Dan Ariely has noted that because people really dislike losses (roughly twice as much as they like gains), a rotating bill-paying arrangement is psychologically attractive. This allows everyone but the person paying to feel no loss at any one dinner.

  • 6 econgirl // Sep 7, 2009 at 1:00 am

    @ Dan L: Nothing? I’ve actually seen Option 4 happen a decent amount in practice, probably because I hang around a lot of (no offense meant, I swear) wannabe hotshot banker types. Anyway, what they do is something called “credit card roulette”, where everybody throws in their cards (platinum of course) and somehow one is chosen and that person has to pay. Being bankers, they realize that this is roughly equivalent to splitting every time. Also, being bankers, they realize that they get to come off as ballers if they use this strategy.

  • 7 Tony // Sep 7, 2009 at 9:10 pm

    I like taking turns paying for the bill. It is less cumbersome. Of course, there’s the risk that people will overeat because it doesn’t cost them anything for that sitting at the table, but keep in mind that this is a repeated game.

    If Bill overeats, the group can have a rule (or social norm) that says, “everyone overeats when Bill pays.” He’ll be punished plenty well enough to not do it again. Or better yet, just stop being friends with Bill if he continues to exploit the system.

    On this strategy, Axelrod wrote a book called “The Evolution of Cooperation” that describes how Tit-for-Tat (you be nice, and so will I; you be mean, and I punish you) tends to be a successful strategy in repeated prisoner’s dilemma tournaments.

    Moreover, when everyone resorts to Tit-for-Tat, it looks like a lot of people are eating the right amount of food. And, very few people are stuffing themselves.

    Then again, I always appear to be stuffing myself. Maybe that’s why I don’t get invited to dinners.

  • 8 Dan L // Sep 8, 2009 at 4:25 pm

    @econgirl: I stand corrected. However, that doesn’t change my disdain for Option 4. In my defense, I don’t have any “hotshot banker” friends, wannabe or otherwise. (This is no small feat, considering where I went to school.) I would suspect that these banker-types are the same type of people who bid the $20 bill up to $40.

  • 9 Luke // Sep 8, 2009 at 8:03 pm

    Just a quick thought: The analysis of Option 4 (randomized bill splitting) mentions the interaction of risk-aversion with the incentives to order. Isn’t there also a more direct effect? If the diners are risk-averse, randomizing payment–and indeed any other form of “gambling”–results in a utility loss.

    Ahh… the tradeoff between “optimizing incentives” and “optimizing outcomes.”

    For what it’s worth, coin tossing may not also generalize well for larger groups. I have a friend who frequently dines out with the same companions. They shuffle credit cards under the table, and then randomly draw one or two with which to pay the bill.

  • 10 Modern manners: Paying the bill | Sentinel Weekly News // Sep 14, 2009 at 9:40 am

    [...] ourselves embroiled in a heated, yet determinedly ‘jovial’ argument on the arrival of the bill – “No, no, NO – let ME!” we screech through fixed grins, as we claw at the offending [...]

  • 11 econgirl // Sep 14, 2009 at 11:40 am

    Two things:

    1. Here is a good article that talks briefly about the economic experiments on this topic:

    http://www.ft.com/cms/s/2/75276c18-71a1-11de-a821-00144feabdc0.html

    2. I was told by one of my students (a banker-type, in case you were wondering) that the credit card roulette is usually carried out by having the waiter or waitress pick a card. Then he gave me some strategy tips on how to choose an ugly card so that it didn’t get picked. :)

  • 12 Modern manners: paying the bill | My Spirit DC // Sep 15, 2009 at 2:12 am

    [...] ourselves embroiled in a heated, yet determinedly ‘jovial’ argument on the arrival of the bill – “No, no, NO – let ME!” we screech through fixed grins, as we claw at the offending [...]

  • 13 Fred // Sep 21, 2009 at 2:48 am

    I usually use option number 1 and round up to the nearest $5.00. Then I split the tip. I guess my few months working in a restaurant years ago made me feel sorry for the servers.

  • 14 Ellyn Beacher // Nov 23, 2011 at 11:34 am

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