Mathematics is no longer only for the young minds, as was a common belief held for centuries. Today, even a middle-aged corporate employee (perhaps unknowingly) applies mathematics in his day-to-day decisions. The focus of this article is on how applied mathematics (specifically Game Theory) governs the key politics of hierarchical interaction. I find it fit to dedicate this article to British mathematician (and politician), Dame Kathleen Mary Ollerenshaw, who turned 100 recently. Let us start with a thought experiment. Suppose you are among a given number of people simultaneously playing a game involving the following steps/rules that each individual knows.
1. You all get to choose a number between one and ten and write them on a piece of paper provided to each of you.
2. The (folded) pieces of the paper are collected by a game coordinator who calculates the average of all the numbers submitted.
3. The individual who submits a number closest to 1 times the average is declared the winner and gets a cash award of Rs.15,000.
4. If there is more than one winner, then each gets an equal fraction of the said reward amount.
To illustrate, suppose youre playing this game along with two other individuals who have chosen numbers one and two (you, of course, do not know this). Suppose also, that you have chosen the number three (and they do not know this). The game coordinator collects all the numbers to calculate the average (equal to two) which he multiplies by 1 to get three as the result the very number you had chosen. Congratulations! Youve just won yourself a sum of R15,000.
If youre already feeling happy about this, then let me remind you that it was just an illustration, and nowhere close to the outcome that should logically emerge, determining which needs some iterative reasoning. To start with, suppose that each of you had chosen the number one. The average would then be the number one itself, thereby making you all equally close to 1 times the same. The total reward amount will be equally split so that each gets R5,000.
Now, ask yourself if you couldve done better What if you chose two instead of one (given that the other individuals didnt change their minds) The average wouldve then been (roughly) equal to 1.3 which multiplied by 1 equals two so congratulations again. This time you solely get your hands on R15,000 so youve clearly made yourself better off by choosing a greater number.
Happy again Hold on a moment. The other two individuals can reason this just as well as you do each of you end up submitting the number two. Each of you will be a winner again and your individual earnings will fall back to R5,000. But what if you were smarter still and out-thought your rivals even at this stage You could simply choose the number three and have the entire reward to yourself yet again. Unfortunately, it is fairly reasonable to assume that the other two individuals would also try to out-think you in this series of reasoning.
We should just satisfy ourselves by agreeing that regardless of what others choose, any given individual can always make himself (possibly) better off (and definitely not worse off) by choosing a number greater than what he originally thinks. And with the same line of thinking for every individual, each goes on choosing greater and greater numbers till he can go no further. The logical outcome, therefore, of this simple game is that each of you chooses the number ten (the maximum allowed) and ends up with R5,000.
Now, if you are familiar with Game Theory, a variant of this game called guessing the average would immediately strike you. The outcome mentioned in the previous discussion is called a Nash Equilibrium. This simple game has a remarkable analogy with what many of you in the corporate sector face for reala parasitic manager. Hell tell you something like in your peer group of twenty individuals, only the top five performers will be promoted in the next appraisal period. What happens next Each of you twenty tries to outperform the others since one must be way more than just over average (the very nasty trick done by the choice of the multiple of 1 in our game). A direct signal of performance is, of course, the number of working hours one is willing to spend in office. Each individual therefore, ends up (rightly) reasoning that he must spend more (and more) number of hours than the others just like in our game where it was practical to choose only greater and greater numbers. Eventually, each of you is unhappy and the manager gets away with an explanation that each made his own decision about the number of hours devoted to the firm.
Do not fall into this trap. The parasite is only relying on your own intelligence to make you punish yourself with workload. He may just want to impress a client by promising him more than what he asks for which unfortunately, more often than not, happens to be irrelevant. Remember that you would do the work. If possible, let the higher authorities know, but do so strategicallyother employees in your peer group may have an incentive to gang up on you along with the parasite if youre the only one standing up against it. Being in a group has its advantages. Even then if nobody responds, for (say), the manager in question is very influential, may be you should move on but do not always lose yourself to what your work demands. After all, there is no merit in killing a parasite as long as you can carefully wash your hands off it. A life worth valuing is one with a reasonable balance of work and personal space.
This article is based on a talk the author was invited to deliver at the London Business School
The author is a research scholar (PhD Economics) at the Indian Statistical Institute, New Delhi. He is also member (with voting rights), Scottish Economic Society; committee member, American Statistical Association; and member, Royal Economic Society of England