It’s over 20 years now since I took a “core elective” (yeah, the contradiction!) in IIT on “design and analysis of algorithms”. It was a stellar course, full of highly interesting assignments and quotable quotes. The highlight of the course was a “2 pm onwards” mid term examination, where we could take as much time as we wanted.
Anyway, the relevance of that course to this discussion is one of the problems in our first assignment. It was a puzzle .
It has to do with a large number of pirates who have chanced upon a number of gold coins. There is a strict rank ordering of pirates from most to least powerful (1 to N, with 1 being the most powerful). The problem is about how to distribute the coins among the pirates.
Pirate 1 proposes a split. If at least half the pirates (including himself) vote in favour of the split, the split is accepted and everyone goes home. If (strictly) more than half vote against the split, the pirate is thrown overboard and Pirate 2 proposes a split. This goes on until the split has been accepted. Assuming all the pirates are perfectly rational, how would you split the coins if you were Pirate 1? There is a Wikipedia page on it.
I won’t go into the logic here, but the winning play for Pirate 1 is to give 1 coin to each of the other odd numbered pirates, and keep the rest for himself. If he fails to do so and gets thrown overboard, the optimal solution for Pirate 2 is to give 1 coin to each of the other even numbered pirates, and keep the rest for himself.
So basically you see that this kind of a game structure implies that all odd numbered pirates form a coalition, and all the even numbered pirates form another. It’s like if you were to paint all pirates in one coalition black, you would get a perfectly striped structure.
Now, this kind of a “alternating coalition” can sometimes occur in corporate settings as well. Let us stick to just one path in the org chart, down to the lowest level of employee (so no “uncles” (in a tree sense) in the mix).
Let’s say you are having trouble with your boss and are unable to prevail upon her for some reason. Getting the support of your peers is futile in this effort. So what do you do? You go to your boss’s boss and try to get that person onside, and together you can take on your boss. This can occasionally be winning.
Similarly, let us say you seek to undermine (in the literal sense) one of your underlings who is being troublesome. What do you do? You ally with one of their underlings, to try and prevail upon your underling. Let’s say your boss and your underling have thought similarly to you – they will then ally to try and take you down.
Now see what this looks like – your boss’s boss, you and your underling’s underling are broadly allied. Your boss and your underling (and maybe your underling’s underling’s underling) are broadly allied. So it is like the pirate problem yet again, with people alternate in the hierarchy allying with each other!
Then again, in organisations, alliances and rivalries are never permanent. For each piece of work that you seek to achieve, you do what it takes and ally with the necessary people to finish it. And so, in the broad scheme of all alliances that happen, this “pirate structure” is pretty rare. And so it hasn’t been studied well enough.
PS: I was wondering recently why people don’t offer training programs in “corporate game theory”. The problem, I guess, is that no HR or L&D person will sponsor it – there is no point in having everyone in your org being trained in the same kind of game theory – they will nullify each other and the training will do down the drain.
I suppose this is why you have leadership coaches – who are hired by individual employees to navigate the corporate games.