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Follow Up: A Lesson In Game Theory And Incentives, Restaurant Edition…

March 24th, 2010 · 4 Comments
Follow Ups · Game Theory · Incentives

(Subtitle: “Misalignment of incentives: There’s an app for that.”)

I wrote last year about the (sometimes perverse) incentives that splitting the check at a restaurant creates. Since I am not only an economist but also a techno geek, I couldn’t help but point out that there is now an iPhone app that allows you to split the check in various ways by bumping iPhones. (Economists do it with iPhones?)

Released earlier this week, the application helps PayPal and iPhone customers transfer money by simply bumping their phones together.

The “Split Check” feature factors in tip and tax, and then helps users divide and pay each other for the cost of a meal for up to 20 people.

While this doesn’t so much solve the incentive problem, it at least makes paying a bit more entertaining. I guess that then gives people an incentive to split the bill, which creates incentives for people to overorder…hmmm, I wonder if the development of this app was financed by the restaurant industry. 🙂

Hat tip to Nudge. The content of my original post is below.

“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: Follow Ups · Game Theory · Incentives

4 responses so far ↓

  • 1 CC // Mar 24, 2010 at 4:24 pm

    Option 6: Credit Card Roulette (aka Option 4 with more than 2 players)

    My friends and I sometimes play this game at the end of a night at the pub. We go to a diner, order our food and at the end of the night, everyone puts a credit card in and one is chosen at random. The rest of the players provide the tip. It keeps your ordering down because you want to minimize the potential costs to yourself and make people more likely to split appetizers than order their own (for the same reasoning).

    Who knew drinking could provide such wonderful economic insight?

  • 2 tim // Mar 24, 2010 at 5:05 pm

    its almost irritating when you go somewhere fairly nice and the wait staff, seeing 2 males, 2 females and 3 kids offers ‘one check?’

    clearly its more difficult, but come on–take the man and woman that are arguing, and the child that wont let go of the woman’s arm, and those are the families!

  • 3 tamara // Mar 24, 2010 at 10:09 pm

    Yeah, I went to dinner with my friends after reading something of this sort in a chapter of “armchair economist” that talks about the incentives to ordering dessert or not. So I was thinking about that, we all pay for our own stuff but somehow it comes short…. like someones is hiding. Because after the check arrives someone stars grabbing everyones money and there’s no official account (hey, if you start doing it they will probably wouldn’t go out with you anymore) so there’s an incentive for people to underpay….so when there’s not enough money in the pot (is that the word n_n ) you can just say “I already pay for mine, is all there, heyy who’s missing!”. Me, I always put more money because I know that someone is gonna play dumb.

  • 4 eh // Mar 29, 2010 at 9:05 pm

    If you look at it in the context of a repeated game, with a punishment strategy of the group refusing to eat with freeriders (or some other suitable punishment) then sharing or rotating starts to look more attractive… Hard to do this with people who aren’t really your friends though, as their discount factor is too close to zero for any reasonable punishment to work 🙂

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