Evolutionary Games and Ecosystems (11a)

Meaning of Knight & Peasants Game

There is nothing in this chapter which is technically demanding. But the content can be thought by some as irrevalent, repugnant, and socially distabilizing. So good boys and girls might want to skip this time.

Let's think over the implication of the results of "peasant and kight game". Our setting, as explained before, is that large number of people are brought in to be paired rondomely and play the game with his own preferred strategy, and he changes his strategy in some rare ocasion if he is not satisfied with his lot. So this is indeed a model of social division. Now, in order to play this game in this setting, one needs not to be really intelligent as human: He only need to compare his lot against others and change strategy. (Of course, he has to be smart enough to perform predatory behavior. ) Any social mammal such as dogs and cats qualify for this much of imtelligence.

As opposed to the stable income obtained by the "peasants", predatory life style of "kights" is based on rarer but larger yield in "one catch" of predation. The predatory behavior is very common in all sectors of life where there are abundance of lifes other than himself's. In a sence, it is one of a standard mode of life. What we have done in previous chapter is to construct a simplified model of this type of existence. Therefore, it is no wonder that it appears to be applicable to non-human ecosystems lacking human intelligence.

For the game with κ= 0, namely, in case every player adopts the play style to maximize his own immediate payoff, both individuals playing "peasants" and "kights", despite their different role, obtain the same average payoff. In fact, they both just survive with payoff zero. As pointed out before, in the analysis of prisoner's dilemma, "free competition" does not result in a uniform group, but a society with role division but with equal proffits, "an egalitalian class society" if we are allowed an oximoron.

The case of κ>０ do show that emergence of class disparity and overall wealth could indeed come hand in hand, as has been often suspected. The fact that the presence of the altruistic social onvention does cause disparity in happiness between different class is just the same as our previous "game theory research gulag". Social equilibrium with higher overall payoff is achieved by allowing certain mixture of "free-riders", or "predators" in this case. In such circumstances, the predatory behavior of "kights" is associted with two seemingly contradicting concepts of "evil" and "nobility", and that is what we experience in our daily life.

At the optimal point κ = 1/2, where the income per capita is highest, the "peasant" type (which is he only surviving type and there's no other type anymore) is half of its "natural" population. It is like a preemptive birth-control to the level of "optimally predated" case, through some social contract. Thus, the system avoids the extra cost of predation among themselves to achieve the "ideal rich democracy". An instructive strategic thought by mather nature that might have some further applications.