Secret Santa and Risk Aversion

Part of the Christmas Spirit is the Secret Santa game, or known as the “Secret Friend” in other places (such as Venezuela, where I grew up). I guess all of you know how it works, but just for those who don’t here is the main idea: a group of people decide to play the game, and randomly (or pseudo-randomly to be more correct) each individual receives a small piece of paper (or maybe an email if the recruiting is done virtually) with the name of another individual. Now, each person has to give at least one gift to the person that was assigned to him. The only thing that has to be taken care of by the organizers at the first stage is to make sure that no one received his own name.

This whole process is secret, meaning that if I received Juancito’s name in my little paper, then Juancito won’t know that I am his “Secret Santa” until I give him the final gift on a day that is agreed among all of the participants. There can be two ways to play this:

• The game lasts for a couple of weeks, in which people are expected to give “small gifts” constantly, until the last day of the game in which people give the “final gift”, and at that moment they reveal themselves to the “receiver” as their Secret Santa.

• The first stage of the game with the “small gifts” can be skipped, and people only buy one “final gift” revealing their identities as well in that very same moment of handing out their gifts.

Why is this in my blog? Well, first because it is a blog about nothing, so why shouldn’t it be on it? But, second, because this creates an interesting situation in which each individual has to decide how much to spend in the gifts they are buying. So, let’s assume for the simplicity of this post that everybody loves everybody else in the group equal ways, so that you decision on how much to spend is not a function of how close you are to the person you are giving to or how happy will make you give a cooler gift to an specific person. In economic language, let’s assume that everybody has the same utility from receiving the same gift, and everybody has the same utility from giving the same gift to any person in the group. These assumptions don’t change the main results of my post (economists love to say this about their models).

Now the big question is how much will you spend. As we have seen during all these posts, you as a rational consumer will think in the following way: you have to spend some money to buy a gift, and you are going to receive a gift back. Now, we assumed that there is a fixed utility from playing in the game (see previous paragraph), so now what is left is another computation: you will spend as much money in buying a gift for other person such that the utility that you will get from receiving the gift that they are going to buy you is equal or higher than what you could have bought for yourself with the money you are spending. That was long, let me rephrase it. Say that you know with certainty that you will receive a collection car that will raise your utility by 100 units (utility units have no meaning and it is just for the sake of the example). So, the money you will spend will be equal or less than what you need to consume something else that will raise your utility by 100 units or less. Meaning that if you decide to spend $20 dollars, it is because those $20 when you consume them in any other thing (restaurants, movies, etc) it will raise your utility by 100 units or less. Otherwise, you will spend less than $20 in your Secret Santa gift.

This formula becomes more complicated if you don’t know with certainty what the gift you will receive is - which is usually the case – because you don’t know who is buying it. So at this point, you will have to see the distribution across the members of your group, and only then your decision will be based in the expected value of the gift you are going to receive.
How can you know then what is the expected value? Well, if you know the persons you are playing with, then you can think about how wealthy or not they are or how much “givers” they are. If they usually invite you for a drink, or even for lunch once in a while, this means that the expected value of the gift you may receive goes up. If people are not like that, then you will lower the quantity you are willing to spend.

So this scenario involves risk. By buying a gift you are taking the risk that at the end your utility will remain at least at the level it was before entering the game. A very risk averse person will always buy cheap gifts (even below the expected value of the gift he may received), because he prefers to cover his back and not spend too much money since he might get the bad gift. A risk lover person will be happy to play Secret Santa. The interesting issue is that this games appears to be consistent with individuals that show Decreasing Absolute Risk Aversion (DARA) – the wealthier you are, the more you can run the risk of buying a more expensive gift without your utility being hurt so much (if you have a lot of money and you received a bad gift, you can go afterwards to the mall and buy anything else to compensate for that).

So, this situation appears to show a “market” with failures. As any other markets, there have been “regulations” trying to solve the incompleteness of the information:

• One possible regulation is the “small gifts” and “final gift” mode of the game. By making people give small gifts during a couple of weeks before you decide how much to spend in the final gift you may get more information about the expected value of the final gift. However, this system is problematic. Your expected value is being affected by the person who is giving you the small gifts. If, for instance, you are receiving crappy gifts (if any) and you decide to buy a bad final gift you may be punishing a person who gave good gifts along the way. This is not fair. Again, if the game is composed by risk averse individuals, all gifts will be bad.

• A second one is to establish a spending range or limit for the “final gift”. This is clearly an expected value. Is an average in terms of price of what is going to be the gift you are going to receive. Clearly, this helps a lot, but if it is not mandatory it still leaves some space to uncertainty.

As a final takeaway, if you want to play Secret Santa, do it only with Risk Lover persons!

Happy Holidays!

Why don't you recycle?

Let's be honest. Many of us don't do all what is in our hands to help the environment. Why? It is just another 5 minutes? We just need to separate paper and glass from the trash and put it in different containers, and then take the trash to the trash disposal, and the recyclable items downstairs to the entrance of the building... pffff... that sounds like a lot of work if you are in a hurry...

The building I live in asks its residents to recycle. However, we have trash disposals in every floor in the building... but look at the message that its written there:

Ok, so where should I take my recyclabels? Then here is the map of the complex:

Mmmh... alright. So, actually recycling involves some work and some time. But of course, it is worth of doing so, since we will save the environment for us, and the next generations.

But... if everybody is recycling but me, nothing bad is going to happen... My actions, either if I recycle or I don't, are not going to change anything. Well, that is exactly what I believe is the cause of this equilibrium of the majority of the world not recycling. Allow me to explain myself. The marginal contribution of one individual to the environment when he/she do environmental activities such as recycling tends to zero. We can save the environment if ALL of us work together, and the aggregate contribution is quite large.

So, if you are clear that if you recycle you could save the world, maybe you'll do it... but maybe not. Why not? Well, again, this will take you an extra 10 minutes of your day, maybe in average. You'll have to take down the recyclables, and maybe deviate from your routine walk from the elevator to your car or to the exit of the building. But maybe if you are in a hurry one day you won't do it... why? Because your time is valuable!

So let's put together all the components of the equation. First, your marginal contribution - as an individual - from recycling is zero (or almost zero) because you by yourself are not contributing. Moreover, the marginal utility you gain from recycling is almost zero, because the fruits of your work will be enjoyed by the future generations, and probably not by you, so unless you care too much for the future generations (which is not a bad assumption sometimes) you don't have any direct gains from recycling. But even if you care, in some countries you have uncertainty that even if you bring all your recyclables to the right place, they are not going to be recycled, so you just lost your efforts.

On the other hand, the cost of recycling is not zero, you have to invest some time in it, which has costs involved.

Consumer theory explains that you will keep consuming one good every time that the marginal utility from consuming it will be higher than the price that you are paying for it. So if recycling is not bringing you any utility, then there is no sense in recycling, and put your efforts in doing this.

Ok, at this point you are thinking that I am a inhumane person, that don't care about the environment. Not true. I care. The bottom line of my post is not that you don't recycle, but is that there are ways that could increase the rate of recycling among people. How? Incentives!

What can be done so that people will recycle more? Two things: either you increase their marginal utility from recycling, or you reduce the price of recycling. Both can be done.

• The goal of publicity and concientization campaigns are intended to make you understand two things: (1) that your marginal contribution to the environment is more than zero, and (2) that you can have marginal utility from recycling. They argue that things can be done now, and that you will enjoy from a better Earth if you recycle, or put it in another way: you won't suffer from a deteriorated Planet Earth in 30 years time. This is what Al Gore is doing.
• The other posibility is to reduce the cost of recycling. For example, putting in every floor recycle bins, and not ask people to go behind their buildings with 3 bags in the morning when they are in a hurry because they are late for work. Reclycling has to be MORE comfortable than non-recycling. The incentives has to be in place so that people will choose to recycle because is more convenient for them. Otherwise they will waste time.
  

So, for all of you out there, seriously, things are pretty tough, so start recycling!

Happy holidays!

Online Dating and Search Costs

So, what is it about online dating that is sometimes controversial or awkward? Well, I don't know. But sometimes one thinks about online dating as something associated with people for whom is difficult to find a partner through "conventional" methods. And this is sometimes associated with people who is ugly or non-friendly or any combination of both. I will try in this post to convince you that this perception of online dating can be explained through economic theory.

The economic concept of "search costs" relates to the cost of transaction for buying a good. From my loyal source Wikipedia we have that "Rational consumers will continue to search for a better product or service until the marginal cost of searching exceeds the marginal benefit".

Well, dating - or looking for a partner - has an associated search costs with it. You may think about it as the time you have to invest in going to places where there are people you could date, or investing the energy in thinking in strategies to approach the other person, or even you could think about the drinks and food you'll have to pay in dating until you find the person that you are looking for. All this involves time and money. These are "search costs".

However, we should think in this case - as opposed of the search cost associated with the "good" you want to consume - as a cost that it is associated to the consumer: the person that is looking for a partner. We could assume that search costs are the same for each individual (independently on which girl/boy he or she is searching for), but search costs are not the same across individuals. For instance, Pablito (a fictitious name) always has a hard time trying to invite a girl out - independently of which girl - he is very shy and he is not that handsome. So his search costs are constant. He has to ask 20 girls to go out with 1. He has high search costs. However, Juancito, is very handsome. He doesn't even need to ask a girl out - because they come after him. His search costs are very low.

So the assumption for my "model" is that search costs are a function of your characteristics that are relevant for dating (how good looking and friendly you are, how funny you are, etc).

At this point, let me bring another ingredient. Online shopping (not dating!). What is the good thing about online shopping? Well, it decreases the search costs for each good. If you wanted to buy a computer in the early 90s, you had to go to 5 stores, and spend some time in each one, probably buy some magazines, in order to decide which is the best computer for you. The time and money you spent in doing all this - before you buy the computer - are search costs. So now, Google shopping and Amazon.com do all this for you. Also, online product reviews from buyers also help you with all this. You can fairly do all the 2-weeks research you would have done in the 90s for buying a computer in roughly one day through the internet. Search costs has been reduced sharply.

So, online dating is the same concept. What online dating is doing is that is reducing at some extent the search costs of people who want to date. Why? Well, you go into a website in which everybody else is looking the same as you, and you have all the "options" so that you can "see what suits you better" in only one place. You don't have to go to 10 parties, and 5 social events in two weeks to see if you find one single person that is willing to date you. The search costs has been reduced.

So now, what is left is to understand who has the incentive then to do online dating. Clearly, people who want to reduce their search costs. It can be people who are less likely to find someone to date in their day to day life at the moment. But here I will add other components that affect the outcome of your search costs. Before I only included phisical characteristics and how friendly and nice you are. But there is information involved as well. People who lack of information on where to find other single people with the same interests also have search costs, either because they are new in town, or they are no longer in an enviroment where it is likely to meet new people every day (such as in college or graduate school). These are the people that are likely to join online dating.

People who have already low search cost don't have too much of an incentive to join such a network. Going back to the definition at the top of the post, their marginal cost (the membership fee) exceeds the marginal benefit that they can get from online dating. But it doesn't mean that "pretty" people will not join. Maybe "pretty" people are having a hard time looking for an specific kind of person that they are not able to find in their local environment.

So it might be that in the future, as almost everybody in developed countries have bought at least something over the internet, maybe more and more people will say that they have dated at least one person thanks to the internet. We'll see...

Miami's I-95 Highway

Some of the readers of my previous post about tolls efficiency have commented about a new policy in the I-95 Highway in Miami area that have more or less some similarities with my ideas about efficiency in tolls.

My loyal reader with the nickname "Anonymous" (I still don't know if he choose that nickname or he just lack of nicknames), have commented about this. I publish his comments:

Your main point, if I understand correctly, is that there should be programs that permit people to pay MORE and get through traffic quicker. There are, however, programs that allow people to pay LESS...and get through traffic quicker. E-Z Pass (in NY, NJ, PA)..Sunpass in Florida, among others. There is a time incentive and an economic incentive (not to mention an environmental incentive since)

Another new program, recently implemented in Florida, does precisely what you describe. The 95 Express Program provides 2 lanes over a 7 mile, highly congested are of the freeway, where motorists are guaranteed an average speed of at least 50 MPH. To use these lanes, drivers can either pay a toll (which varies depending on traffic), buy and register a hybrid vehicle, or register a 3+ person carpool. While the details of this program are worth discussing (there are certain incentives to cheat) in general this does what you describe...while also encouraging people to carpool more or buy more eco-friendly cars.

So, first of all, thank you Anonymous for your comments and for your being such a loyal reader. I actually looked at some of the details of this project right at the 95 Express Website and it certainly looks interesting. However, there are some important questions to raise. For instance, the policy guarantees for those who get into the 95 express lanes that their average speed will be at least 50 MPH, and that those who are exempt of paying after registering: hybrids and 3+ car pools (motorcycles and public transportation are exempt from paying but don't have to register), should take out their Sunpass (so that they won't be charged automatically) and they should have a sticker given by the authorities to identify their car as "exempted from pay". However, as soon as they enter the 95 Express the system won't detect the Sunpass and will send an alert to the police or - as they describe in the website: "Drivers without transponders will have their license plates photographed and receive an Unpaid Toll Notice (UTN) for failing to pay a toll. Failure to resolve the UTN will result in a Uniform Traffic Citation (UTC)".

So the question that arises is, is the police able to see every car that didn't pay if (1) they have a sticker? and (2) if they are hybrid and/or they are a carpool of 3+ individuals? All these at 50 MPH. It sounds a bit difficult, doesn't it? If they stop every car that goes by without paying, and it happens that everything is OK with that car, so he wasted 5 or 10 minutes of his time because of this. It doesn't sound terrible. But how many policemen you need in the roads? Or maybe they will stop cars randomly and do an aleatory check?

So, my question is, why instead of using those cameras that they describe in the website to picture the plates, they don't use the cameras to photograph the plate of every car and use another technology to determine how many people are in the car (maybe x-rays or another camera), and then send them the bill by mail. Through the plate they can now if the car was registered as a car pool, if it is hybrid or otherwise he will have to pay the toll... and forget about the Sunpass for this 95 Express Lane.

Thank you Anonymous for your insights!