Discrete Actions and Inverted Incentives

I remember, about a year or so back, the US weekly non-farm payroll data had shown an uptick in unemployment. Intuitively, a higher unemployment rate indicates lower economic activity, since (among other things) the average purchasing power goes down and fewer things are getting produced (since fewer people are at work). So you would expect the stock market to react to this by going down.

The exact opposite happened. The higher unemployment was greeted with a big rise in the S&P 500. I remember tweeting about it but can’t find it now. But I can find some research someone has done about this:

But here’s the kicker: the S&P500 is inversely related to the unemployment rate, and thus the market actually goes up as a response to a release of a higher than expected unemployment rate. This may seem illogical conceptually, but historical analysis and statistics show that it is true.

In the last 3 years, the unemployment rate in the United States has been surprisingly higher than expected 11 times. The result? The S&P500 went up 80% of those times within a time-frame of 90 minutes (see Fig. 2, click to enlarge the image).

The basic issue (as I see it) is that higher unemployment means lesser likelihood that the US Federal Reserve will raise interest rates. Which means lower rates for the longer foreseeable future, which translates to higher stock prices.

The kicker here is the “discrete action” on part of the Fed. Because their decision (on whether to hike rates or not) is binary, news that decreases their odds of hiking rates, even if it (the news) is bad for the market, leads the market to go up.

You can see this in action elsewhere as well. Let’s say you are the number two at a manufacturing plant, and you are not happy with the way things have been run. However, you know that with the current level of production, the company management will not bother – they only see the numbers and see that the plant is being run well, and they won’t listen to you.

However, if the production drops below a certain level, the management is certain to review the operations, at which point you will be able to make your point to them and be heard, and you will be able to hopefully better influence how the plant is run.

Normally, your incentive is in keeping production as high as possible. But now, with this discrete action (management’s review of your operations) in the picture, your incentives get reversed. It suddenly becomes rational for you to not work so hard to increase production, since lower production means higher chance of a management review.

The problem with a lot of standard economics teaching is that it abstracts away the messiness of real world “step functions” and instead uses a deceptively simple continuously increasing or decreasing demand and supply curves. And so we are conditioned to think that incentives are linear as well.

However, given the step functions inherent in everyday business (which are only made worse (steps become steeper) with discrete actions), the incentives are not linear at all, and there are points in the curve where incentives are actually inverted! And this is everywhere.

I’m writing this on a lazy Sunday morning, having postponed this for over a week, so no enthu da to make pictures and explain my point. However, I guess I’ve explained sufficiently for you to catch my pOint.

Actually – since I have an iPad with a pencil, I did make a simple sketch. Limited by my drawing (and mentally adding curves) skillsBasically normal incentives is like the red line, but the discrete action (modelled here like a negative sigmoid) means that there is a region where the overall payoff is massively downward sloping. Which means your incentives are inverted.

The Personality Cult

So all business newspapers report that LK Advani had issued a “warning” to Yeddyurappa a while back that he was getting too corrupt. Nevertheless, several BJP “party workers” in Karnataka have been coming out in defence of Yeddy, saying he’s innocent and that he’s still their leader. Some of them have refused to accept the leadership of DV Sadananda Gowda. And some of the leaders themselves are quite silent on the issue, preferring to say that the “law will take its own course”.

This points to a larger problem that is afflicting Indian politics nowadays which is the “personality cult”. First of all, we have several parties (too many to name here) where the only ideology is “absolute loyalty to a certain party leader”. Even in parties that don’t fall under this definition (the BJP for instance), we seem to have several “local leaders” who carry significant weight, and local units of parties that are more loyal to their leaders than to the parties. In fact, if you were to objectively look at it, as a voter there seems to be no escape at all from this cult.

This has several disturbing consequences. One stems from the belief that “loyalty should be rewarded”. Given the loyalty that so many of our “leaders” get from “party workers” it is not surprising that the “leaders”, upon assuming power, accord to these workers plum rent-seeking posts, which will keep them happy. This can result in positive feedback – once a leader has shown that he  will “reward” loyalists, more people clamour to get close to him, and they too must get rewarded. And so it goes.

Another fallout of this personality cult is a dramatic increase in security, with not inconsiderable cost to the public. Given t he power that some of our “leaders” wield, the payoffs of bumping off an opposing leader are quite strong, both in terms of electoral politics and otherwise. Parties which have been built on “personal loyalty” as an “ideology”, upon losing their leaders, will suddenly have no “natural centre” and will tend to fragment. Hence, it is in the interest of all politicians to provide themselves “security”, which comes at the cost of the general public (cue traffic jams whenever there is “VIP movement” in some city, or the fact that our generally under-staffed police force has to spend so much of its effort in “VIP security” rather than other more important policing duties).

Then, we seem to be moving to a situation where parties are bereft of ideologies, and are simply collections of random leaders (who have lots of “followers”) thrown together. I’ll probably address this in detail in another post, but if you come to think of it there is very little to choose between different political parties now in terms of ideology. Yes, the BJP might have the nominal ideology of building a Ram Temple, but take that out and there is little to separate it from the Congress. The regional parties are even worse. The only difference you could probably see there is in terms of the dominant caste or lobby backing each party.

Again, it needs to be pointed out that multipolar politics in India is very young – it’s existed for little more than twenty years. Still, the future of Indian politics is worrisome, and I don’t know how we’ll get out of the rut we’re in.

When will my courier reach?

Earlier today, I had to urgently send a package to Mumbai. I was recommended that I use Bleudart since they guarantee next day delivery, and off I went to the Bluedart collection centre near my house. There, I learnt that there were 3 options.

For two hundred and eighty rupees (what I ultimately picked) I was guaranteed that the package would be delivered tomorrow. However, there were two premium offerings – promising 1030 am delivery, and 12 noon delivery. Given my payoffs I settled for the “normal” next day package. Now, I wonder when my package will reach.

What are the odds that the package would reach before noon? I would say the odds are very slim, for if my “normal” package were to reach before noon, there would be no reason for me in the future for me to pick the 1030 delivery or 12 delivery package. Even if the package would have reached close to the destination tomorrow morning (I expect that it’ll be sent on a late evening flight today or early morning flight tomorrow), the delivery person would be instructed to wait till after noon before delivering, I think.

What do you think? If you think it’ll reach before noon, you can bet on it. Leave a comment and we can discuss odds. I’ll give you the airwaybill number so we know when exactly it got delivered.


I win the non-existent bet.

Pickup Date 12 October 2011
From Bangalore
To Mumbai
Date of Delivery 13 October 2011
Time of Delivery 12:15

On Running a Consulting Firm

So most of the consulting firms are run as partnerships (as you might have already figured out). There was an experiment in the late 90s where a then leading firm was bought over by an IT company, and that saw stagnation for the next few years until the consultants did a “management buy out” in order to rid themselves of the IT company’s controls. By then, though, valuable time was lost, and last I heard this company was severely lagging its peers in terms of reputation, among other things.

As I had mentioned in the earlier post, the rut sets in once partners reach “steady state”, where they have an established set of relationships that they milk to get more business. And as I mentioned, it’s hard to get out of this rut, until employees start leaving protesting the poor quality of work, and lack of opportunities to make it big. And that starts sending the firm into a downward spiral. So what is it that the firms must do, in order to keep themselves dynamic, and not get into this kind of a rut?

The answer is something that is practiced by most leading consulting firms. Every few months or a year, these firms add to the partnership pool, mostly by promoting from within their ranks. Once thus promoted, it is the new partner’s responsibility to expand and generate new business for the firm, and he is not able to piggyback on the relationships established by the established partners. And thus, in his process to expand and get himself established, he has an incentive to take more risks. And take on projects with long-out-of-the-money option kind of payoffs.

Regular promotions to the partnership level means that there is always a bunch of partners who are thus taking risks, and that keeps the firm dynamic. I don’t know how well this works in practice, but in theory at least, this helps firms from getting into stagnation. That this is the model followed by most leading management consulting firms indicates that this is probably an appropriate approach.

So, if you think your consulting partnership is stagnating, get in more partners. Promote. Or make way. And keep the group dynamic and a great place to work.

Relationships and the Iterated Prisoner’s Dilemma

It was around this time last year that something snapped, and things have never been the same again. Until then, whenever she threw some tantrums, or we had some fight, I’d always give her the benefit of doubt, and unconditionally apologise, and make an effort to bring the relationship back on track. But since then, I don’t feel the same kind of sympathy for her. I don’t feel “paapa” for her like I used to , and have questioned myself several times as to why I even aoplogise, and not expect her to do that.

The optimal strategy for Iterated Prisoner’s Dilemma has been shown to be a strategy called “Tit for tat”. To explain the problem, you play a series of games against an “opponent”, and in each iteration, each of you choose to either “cooperate” or “defect”. For each combination of choices, there is a certain payoff. The payoff looks similar to this, though the exact numbers might be different. In this table, the first value refers to the first player’s payoff and the second represents the second player’s.

Player 1/ Player 2 Co-operate Defect
Co-operate 1 / 1 2 / 0
Defect 0 / 2 0.5/ 0.5

So you play this game several times, and your earnings are totalled. There was a tournament for computer programs playing this game sometime in the 1960s, where the winner was “tit for tat”. According to this strategy, you start by co-operating in the first iteration, and in every successive iteration you copy what your opponent did in the previous iteration. Notice that if both players choose this strategy, both will co-operate in perpetuity, and have identical payoffs.

Relationships can be modelled as an iterated prisoner’s dilemma. You can either choose to be nice to your partner (co-operate) for which you get a steady return, or you can choose to be nasty (defect), in which case you get a superior payoff if your partner continues to be nice. If both of you are nasty simultaneously both of you end up getting inferior payoffs (as shown by the Defect-Defect box in the above matrix).

Early on in the relationship, I was very keen to make things work and did my best to prevent it from falling into any abyss. I played the “Gandhi strategy”, where irrespective of her play, I simply co-operated. The idea there was that whenever she defected, she would feel sympathy for my co-operative position and switch back to co-operate.

So something snapped sometime around this time last year, which led me to change my strategy. I wasn’t going to be Gandhi anymore. I wasn’t going to unconditionally defect, either. I switched to playing tit-for-tat. You can see from the above table that when both players are playing tit-for-tat, you can get into a long (and extremely suboptimal) sequence of defect-defects. And that is what happened to us. We started getting into long sequences of suboptimality, when we would fight way more than what is required to sustain a relationship. Thankfully it never got so bad as to ruin the relationship.

Periodically, both of us would try to break the rut, and try to give the relationship a stimulus. We would play  the co-operate card, and given both of us were playing tit-for-tat we’d be back to normal (Co-operate – Co-operate). Soon we learnt that long defect-defect sequences are bad for both of us, so we would quickly break the strategy and co-operate and get things back on track. We weren’t playing pure tit-for-tat any more. There was a small randomness in our behaviour when we’d suddenly go crazy and defect. In the course of the year, we got formally engaged, and then we got married, and we’ve continued to play this randomized tit-for-tat strategy. And the payoffs have been a roller coaster.

Today I lost it. She randomly pulled out the defect card twice in the course of the day, and that made me go mad. While in earlier circumstances I’d wait a few iterations before I started to defect myself, something snapped today. I pulled out the defect card too. Maybe for the first time ever, I hung up on her. Do I regret it? Perhaps I do. I don’t want to get into a prolonged defect-defect sequence now.

And I hope one of us manages to give the relationship enough of a stimulus in the coming days to put us on a sustained co-operate co-operate path.

Diminishing Value of a Red Card

Often when we see players being sent off AND penalty kick being awarded in the event of an illegal stop of a goal-bound ball, Baada and I have thought that the punishment is too harsh. That for stopping one goal, the team effectively gives away the goal (conversion rate of penalties is high) and also loses a player (sometimes the goalie) for the rest of the game.

Now, after last night’s strategic hand ball by Luis Suarez, people are complaining that the punishment is not enough. Though it was a split-second instinctive decision by Suarez to handball, even if he were to replay the incident in his head and analyze the costs and benefits, I’m sure he would’ve done what he did. This clearly contradicts what I mentioned in the first paragraph.

The main issue here is with the value of a red card  at various stages of a game. The red card has intrinsic value – of being suspended for the next game. In addition to this, the red card leaves the team one short for the rest of the game, and so it is clear that the later a red card is given out, the lesser the disadvantage it causes the team because they’ve to play for lesser time with a man short.

What makes Suarez’s decision more logical is the time value of a one-goal lead. The lesser the time left in the game, the more the value of the one-goal lead since there is lesser time for which it needs to be protected. And in this case, the handball occurred on what might have been the last “kick” in the game, and so the value of the one-goal lead was really high.

The earlier this incident had occurred in the match, the less would’ve been Suarez’s incentive to handball – more time to win back the conceded goal and more time to play a man short if redcarded. At the time when it actually occurred, Suarez would’ve been a fool to NOT handball. The payoffs were heavily loaded in favour of handballing and he did it.

People on twitter are suggesting that rules be changed, that the goal should’ve been awarded anyway instead of the penalty and stuff, but considering that the same punishment costs much more if given out earlier in the game, I think the current punishment is appropriate. The excess of this punishment in earlier stages of the game is compensated by the punishment being too little in the latter stages, and on an average I think it is appropriate.

Let’s continue to keep football simple and not clutter it with Duckworth-Lewis kind of rules. And congrats to Suarez for taking the most logical decision at the moment. It is indeed as great a “sacrifice” as Ballack’s tactical yellow card against Korea in the 2002 semis.

And I feel sad for Asamoah Gyan. But then again, with Ghana being in the knockout stages solely on the merit of two Gyan penalties, it is only appropriate that they are going out nowon the demerit of Gyan’s missed penalty.

Gyaan From a Former All India Topper

CAT is less than a month away. Or more, depending on when you’re writing it. If any aspirants are reading this, I have just one piece of advice for you – which no one in any CAT Factory will give you. It’s about going for it. About batting like Sehwag. About reaching out far outside the off stump and playing every ball. I just want to assure you that percentages are in favour of this kind of a game.

In my zamaana, every correct answer in CAT gave you one mark, and every incorrect answer took away a third of a mark. Every question had four possible answers of which exactly one was correct. This negative marking had a completely psyching out effect on most takers, and people are afraid to go for it. And six years back, I liked it. For it made my own risk-taking strategy much easier – since I could now afford a larger number of errors.

The arithmetic is simple. Even if you have no clue about the question, and just put inky-pinky-ponky (or even better mark ‘C’, since years of research has proven that it’s the statistically most probable answer in CAT) you have one-fourth chance of getting it right – which gives a three-fourth probability of getting it wrong. And given the payoffs for correct and incorrect answers (1; -1/3) you can clearly see that the expected payoff of taking a completely random guess is ZERO!

So while this obviously rules out insane inky-pinky-ponkying, what it does tell you is that if you can eliminate at least one of the four choices, you are in the money! If you have to pick one of three possible answers, the expected payoff is 1/9 which is greater than zero. Yeah it doesn’t look very high but then the expected payoff is positive! So you need to go for it.

Back when I was in my 3rd year, there was some free mock CAT at IITM. And some of us 3rd years went just for the heck of it. I attemped 130 out of 150 questions, getting 90 right and 40 wrong. It still gave me a significantly higher score than any of my seniors (who were writing CAT that year) – most of whom attemped not more than seventy. Later that day a senior called me aside and told me that the art of CAT was about leaving questions. And that it was all about the questions that you left.

Leaving the ball makes sense in cricket where one mistake ends your innings. What if instead of ending your innings you were just deducted 2 runs everytime you got out? Would you still leave the balls outside off and play the waiting game? How on earth would you score runs if you were to leave every ball? It’s all about scoring, and you can score only if you attempt a shot.

I understand that CAT format has changed now and you have 5 possible correct answers for every question while the negatives are still at 1/3. Even then, if you can eliminate two out of the five answers (shouldn’t be too gouth), you have a positive payoff. And you must go for it. Keep in mind that you can’t score if you don’t play the ball.

I leave you with a video. The message is in the name of the song. Idu One Day Matchu Kano. This is a one day match dude. So you must go for every ball. And look to score.