Race to the bottom


Imagine that you are participating in an open online contest. The rules are pretty simple.







                                                                                                                    Image - http://www.freedigitalphotos.net/


1.   All the participants are asked to pick a number in the range 0-100 (0 and 100 inclusive), such that... 
2.   The individual(s) who select the number closest to the 2/3 of the average of the numbers chosen, wins.


Now, I know that you are a busy person with absolutely no time for such petty games. But, do spare a moment, open the notepad, give it a thought and jot down a number. 

So, what would you choose? And, why?

Continue reading only after you’ve chosen your number. Else, it would be pointless. If it helps, imagine that you’ve paid a small entry fee to play the game and there is a prize money of 1000 USD at stake. Also, I’m very much interested to know what you choose and the reason behind it. I would encourage you to share your thoughts, but then again, it is left to you.

Done with your choice?

I conducted this game two times in the last fortnight. The first time, with four of my friends and the second, with my team of 25 at office. (Although, only 12 of them participated.) I sent across a group mail with the rules of the game, and asked them to reply only to me with their choice of number. Here’s what I got:

Friends

Sl No.
No. chosen


1
56
2
42
3
0
4
31


Total
129
Mean
32.25
2/3 of mean
21.5



Colleagues

Sl No.
No. chosen


1
50
2
21
3
22
4
7
5
11
6
56
7
34
8
11
9
33
10
11
11
20
12
9


Total
285
Mean
23.75
2/3 of mean
15.83



Intuitively, most sense that others would pick a random number in and around 50. In fact, as seen from the tables above, there is a certain percentage of the participants which go for 50 or 50+. Note that this is a very small sample to begin with.

So, your first instinct would be to guess the mean as 50 and choose 2/3 of mean as 33. This suggests the next stage of analysis. Can you assume everyone else is rational? If so, then all your opponents also may choose 33. Hence, your next choice would be to pick 22.

Well, we can make a similar argument as above. If your assumption is that everyone is rational and everyone assumes everyone is rational,  then it is clear that even others would choose 22.

If you continue with this logic, your choice would decline to 14, then to 10, and eventually at some point of time, to zero. Matter of fact, the case where everyone chooses zero would be the most rational and profitable explanation, wherein everybody wins! It requires that every single person assumes that everyone else assumes that everyone is rational.

Strictly speaking, there is a small flaw in the beginning. Logically, you wouldn’t start with 50. That is slightly biased thinking. You would actually start by eliminating all numbers above 66.66 as 2/3 of the mean, for obvious reasons. All numbers above 66.66 are weakly dominated strategies (game theory jargon), meaning that one cannot do worse and may do better by selecting a number outside this range. Then, your choice would trickle down to 44, 30…0 as explained previously.

In any case, do you think the winning choice would be zero?

It is unlikely that everyone would follow the chain of logic described above. Everyone maybe rational. Everyone may assume that everyone is rational. But, at some point, some people implicitly are going to stop the sequence. Apparently, most people nest these assumptions to four levels. 21.6 was the winning number in such a game with 19,196 participants organized by a Danish newspaper.

This game is used to explain another game theory concept. Race to the bottom.

Consider the tax competition between our state governments.

Each government may benefit from higher tax revenues by having a high tax on corporate profits. However, governments can benefit individually with a lower corporate tax rate relative to the other governments in order to attract businesses away from the jurisdictions of other governments. This action would hurt all governments except the one that undercut the others. In order to maintain the equilibrium, each of the other governments would have to lower their corporate tax rates to match the "defector" (the government that first lowered the tax rate). The end result is that each government adopts a lower corporate tax rate and, therefore, collects less revenue overall. – Wikipedia.

Another example would be retail pricing.

Have you noticed that major competitors like Coca Cola and Pepsi rate their soft drinks equally? Suppose Coca Cola reduces its prices, then it would definitely benefit in the short term as it would gain more consumers. But then, Pepsi would reduce it further to maintain the competition. If this chain continues, both companies will be at a loss. Hence, they come at a mutual understanding and settle at a common price to avoid this race to the bottom.

On reading these two theories by reputed economists, I couldn’t help but wonder if the same applied to our airlines as well.

Would it have been / Would it be better for our economy if all the airlines charge the same amount to the fliers? Perhaps, Kingfisher and Air India might not have ended up in the present tragic state if there was a healthy competition between the airline companies. I’m not suggesting that this is the reason for Mallya’s downfall. I’m just contemplating.

When Coca Cola and Pepsi have eliminated the competition in pricing and instead restricted it to the quality of their products, or to advertisements, maybe Indigo, Spicejet, Kingfisher could also charge equally and compete in other areas like comfort to passengers, service offered, time discipline and of course, air hostesses (Oh come on, admit it!). I’m intrigued to know the future effect by taking such an action.

Enough of this boring stuff, let us come back to the 2/3 of the mean game.
As I’ve said before, I’m always curious to dig inside people’s minds. I did conduct the game and receive the answers, but I wanted to know why they had chosen them. As I sent one more mail to my four friends asking them to share their reasoning and I waited for their replies, I pondered on my own to justify their selections.
Why would anyone think that the mean would be greater than 60, or even 80?! Is this some kind of reverse psychology?
Did he really go for the ideal answer (zero) ? I was slightly pleased that there was someone who would stick to rationality all the way, although it was impractical.
And, with respect to the last one; he must have stopped the logical sequence of thinking after just 2 levels.
I got their replies within a couple of minutes. Well, it wasn’t exactly what I had expected.

“I randomly picked that number. Didn’t give it much thought.”
“42 is the answer to life, the universe and everything.”
“Actually, I was simply trolling.”
“I just chose 31 as it is my birth date.”



That night, I slapped myself four times before going to bed.




Update:

This post was inspired by a free online course - Model Thinking at coursera.org. The "retail pricing" example was explained there. There are many other classes offered on coursera. I would suggest you to check it out once if you are interested to learn more and expand your knowledge.





8 comments:

  1. Replies
    1. That is way too much information for me to respond, Datta.

      Anyway, I know July 31st is still very far ahead, but advance birthday wishes. :)

      Delete
  2. Did you colleagues at least have a valid explanation ? Or were they trolling too ? :P

    ReplyDelete
    Replies
    1. No clue. I didn't bother to ask them.

      Once bitten, twice shy, you know. ;]

      Delete
  3. Interesting article. I raced to zero and then I tried to account for what other people would try to answer. That is where it all went haywire. Do we all have a lower expectation from everyone? I mean if I assume everyone is as smart as I am, I should have stuck to zero. :-P

    ReplyDelete
    Replies
    1. Aah, that comment almost made me cry.

      Well, I wouldn't say lower expectation from "everyone". Obviously, we cannot expect everyone to be smart. We don’t live in an ideal world. Intelligence is affected by many factors – genetics, race, language, social and economic conditions, peer group etc.

      So, that thought makes us to push our number up from zero.

      Let’s say, in a group of 100, 94 guys [including you] are smart [Very high aspirations, I know] and all of them raced down to zero, and 6 of them are, erm, not so smart. Consider the total as 300.

      Now, wouldn’t you want to win and change your choice to 2? And you know that the other 93 fellas would want to win as well and might choose 2. So, you might move higher now. But, where do you stop?

      What I’m trying to say is, high expectations from other people wouldn’t make your choice any easier. As you said, when you try to account for others’ choices, your thought process goes haywire. It is simply an awesome mind game! Anyway, did you finally choose any number?

      Spit it out, mate! :D

      P.S. - Read about "Prisoner's dilemma" when you get the time.

      Delete
    2. I forgot what I had picked. Must be 21 I think. Don't ask me why. I do not think anyone can answer that ... :-P

      Delete