Evolutionary Games and Ecosystems (8)

Why are there Bosses?

Mythical Origin of Russian Monarchy

You are surely familier with the story of King Rurik. In acient Russia, feuds among clans were rife, and chieftains finally agreed upon keeping peace by inviting a foreign king, in this case a Viking chief named Ruryk, and invest him with the power to punish the law breaking clans with his force of arms. His decendants took the title Knyad (prince) and nobody in russia doubted for 1000 years that ruler of Russia has to come from his line. One of the tragedy of Russia is in the lack of the primogeny among nobles, and as a result, Russia was full of pennyless princes by the end of 19th century. When you read about Prince Muishkin in Dostoyevsky's "Idiot", it sounds all odd, but in russian context, his existence did have lot of credibility. There are other lines of princes in Russia, one coming from Mongol overlords, the other Georgian, which give the matter some more complications.
So much for the princes, back to the main subject, there is a well-known rule called "alternating boldness principle" in the rulers of Russia. Looking at the recent example, Nikolas I was hairy, Alexander II was bold, Alexander III hairy, Nicolas II bold, Klensky hairy, Lenin bold, Stalin hairy, Khrushchev bold, Breznev hairy, Gobachev bold, Eltzin hairy, and currently, Putin is bold. So the tradition of Ruryk is well alive even after the demise of his line itself. Ruryk himself was repoted to be hairy.

"I Shall Give You the Law"

Now, really back to the main subject, we are running out of space, and we will just state the results. When there is a common predator (apex predator) lording over two competitive species, and this apex predator tweaks his aggression toward both preys independently to his own advantage, both competitors become better off refraining from atacking each other; Namely the "prisoner's dilemma" type game table in th previous chater turns into the one bellow

which is obviously of "collaborative game" type. This is because the stronger aggression of a competitor incurrs a severe punishment from the apex predator. For details, see our original paper (Phys. Rev. E, 2004).

So it appears that a commonly observed fact that there is always a single boss at the top in a group is a prely mathematical result. Leaders can be rest asured of their positions without in need of further justifying their dominance. But, of course, bosses should also be aware of the fate of Mr. Saddam nd other petty dictators who gets punished by even bigger boss.