On the elements of parasitic management

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 1½ 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 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

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