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, therefore, find it fit to dedicate this article to British mathematician (and politician), Dame Kathleen Mary Ollerenshaw, who turns 100 today. 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 1½ times the average is declared the winner and gets a cash award of R15,000.
4. If there is more than one ‘winner’, then each gets an equal fraction of the said reward amount.
To illustrate, suppose you’re 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 1½ to get three as the result … the very number you had chosen. Congratulations! You’ve just won yourself a sum of R15,000.
If you’re 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 1½ times the same. The total reward amount will be equally split so that each gets R5,000.
Now, ask yourself if you could’ve done better? What if you chose two instead of one (given that the other individuals didn’t change their minds)? The average would’ve then been (roughly) equal to 1.3 which multiplied by 1½ equals two … so congratulations again. This time you solely get your hands on R15,000 so