Our theme for the month of November is “firsts.”
I’ve had a busy month, so this post is serving a dual purpose. The first purpose is filling up 500-800 words for thepostcalvin.com on the theme of “firsts.” The second purpose is getting started on a research idea.[1] I hope it also gives insight into what economists do all day, what I do all day, and what I find interesting. If we’re extremely lucky, it’ll also be interesting to you.
Imagine you’re a gymnast in a gymnastics tournament.[2] You enter the final round in first place, and you’re asked to pick which routine you want to perform. Some routines are tougher than others. If you successfully pull off a routine, you get points: the tougher the routine, the more points you get. If you mess up the routine, you get no points — no matter how tough the routine was. Higher risk, higher potential reward. Everyone has to pick their routine before the final round starts. Your goal is to be in first place.[3] If so, you’ll win a million dollars or something.[4] Which routine do you pick? What would you pick if you were in second place? In last place?
How would an economist tackle this problem? Make a mathematical model of the situation and figure out the strategy that would maximize the expected payoff of each gymnast considering what all the other gymnasts will do.
Let’s try out the simplest interesting case: two gymnasts and two routines. The two gymnasts are Alex and Blair (which I’ll abbreviate as A and B), and going into the final round Alex is ahead of Blair by some number of points. The two routines are called Coinflip and Diceroll (which I’ll abbreviate as C and D). With Coinflip, the gymnast has a 1 out of 2 chance of succeeding, and a success is worth 2 points. With Diceroll, the gymnast has a 1 out of 6 chance of succeeding, and a success is worth 6 points.[5] So, if a gymnast could perform 100 times, the gymnast would expect 100 points from either performance. But, the gymnasts don’t get 100 performances; there’s only 1 performance left, so they need to make it count. What should Alex do?
For now, let’s say that Alex and Blair can’t do the same routine. So, the routine Alex doesn’t do is the routine Blair must do. I’ve got a table below with the results.[6]
When it’s close, Alex should pick the safer option so that Blair doesn’t get access to the highly likely small points it would take for Blair to get ahead. When Alex is further ahead, Alex should choose the riskier option to prevent Blair from getting the big points necessary to catch up. If Alex is ahead by more than 6, it doesn’t matter which routine is chosen.
Now let’s say that Blair gets to see which routine Alex picks and can pick either routine (probabilities and points stay the same). How does this change things?
In this case, the leader (Alex) almost always wants to choose the safer option and the one behind (Blair) almost always wants to choose the riskier option. The exceptions occur when they are really close (so Blair wants the safer option) or medium close (when the points for the safe option aren’t helpful for Alex, so the risky option is preferable).
There’s quite a bit of interesting stuff going on—even in this one example. This is fun.[7] However, I’m not going to dive further into this. Instead, I’m going to discuss why the heck an economist might be interested in this sort of thing.
One reason is that we can get insight into human behavior by comparing what people should do in this situation (if they want to maximize winning probability) to what they actually do. If I get some tournament data and find that people aren’t doing what I think is optimal, I have to figure out why not. Is it that they face different incentives than what I’ve assumed? Maybe gymnasts face social pressure to pick a particular routine—even if it doesn’t maximize the chance of winning. Or is it that people make mistakes when optimizing? Perhaps gymnasts are overconfident in their performing abilities so incorrectly estimate the probabilities of getting points. Each of these features will have implications for what we see in the data, so we can test them and learn about how and why people do what they do.
The other reason is more general. Maybe we don’t care about gymnastics per se. Maybe we don’t even care about literal tournaments of any kind. But, we probably care about things that are like tournaments. For instance, promotions might be given to the highest-performing employees. Elections are (usually) won by the candidate with the most votes. These are like tournaments because rank matters more than level of output—relative performance matters more than absolute performance. So, we might be able to make predictions with this model about those situations. As an example, suppose that self-promoting ads are low-risk/low-potential for political candidates, while attack ads are high-risk/high-potential. Using the second table above, we might predict that the leading candidate will use self-promoting ads if the race is extremely close or extremely far apart and would use attack ads if it’s in the middle. And, we’d predict that the trailing candidate would use self-promoting ads if the race is close and use attack ads otherwise. Now, these predictions may or may not actually be correct,[8] but they are demonstrative of the sorts of things we can do using these methods.
So that’s what’s been on my mind lately. Maybe it’ll be on your mind now, too.
[1] Shoutout to a fellow student for getting me thinking about this stuff.
[2] I know gymnastics tournaments don’t work like this. It’s an example. Relax.
[3] Get it? First place? Because the theme is “firsts.”
[4] For simplicity, I’ll say that if people tie for first, they randomly pick a winner.
[5] I’ll assume that the performances are independent of one another, so that the outcome of one doesn’t affect the outcome of the other.
[6] It’s fully possible I made some mistakes. The general ideas remain intact.
[7] Trust me.
[8] If they are correct, we could follow the idea a little further. People often complain about attack ads as a continuing degradation of political discourse. This may be the case, but it may also be a strategic response to changing margins in elections. What would change election margins? Demographic changes, redistricting, party platform changes, etc. We can answer these sorts of questions empirically and theoretically.
Tony graduated in 2012 with majors in mathematics and economics. He now lives in Chicago and is pursuing graduate study in economics. He also has a very good cultural trivia podcast called “Here’s My Number, So Call Me Ishmael” available on Libsyn, iTunes, and Google Play.
