Evolutionary Games and Ecosystems (11)

Advanced Sociology of Altruism : Knights & Peasants (Cont.d)

Both Parties Benefit Allowing Income Disparity for Now

As before, let's assume that a purely altruistic culture is introduced in the society. This could be trough law and punishment or monetary inducements. Everybody is forced to consider opponets payoff as his own. calculation shows that the system ends up in a state in which everybody's payoff is equally zero. How about mixing his own and opponents interests? Let's suppose that everybody play the game under the forced convention that one takes his own interest with probability κ and opponent's interest with probability (1-κ). The result is shown in the graphs in the right. The horizontal axis represents κ on which the left most point corresponds to the pure egoism and the right most, the pure altruism. Blue line is for peasants and the red for kights. The top graph shows the population of peasants and kights as functions of altruism parameter κ. The second graph shows the per-capita payoffs for each species. the bottom graph is the average per-capita payoff for whole system. When altruistic culture gradually sets in (by law or by financial incentive, for example) with increasing κ, more people will choose to play "peasant" because this is "easier" under the pressure of altruistic regime. The existence of "kights' are kept because of the lure of higher payoff.

... and Regime Change

When the value of κ exceeds certain value, the characteristics of the graph sudenly changes. This is because of the difficulty of kights maintaing their existence: Although their relative as well as absolute profit increases with increasing κ, the altyuistic social mores becomes more hostile to them and fewer of them survive. Eventually, there is a point when there is no room for them and their population vanishes. Everybody except "do-nothing"-folks play peasants. The total payoff of the whole society increases and attains a peak at κ = 1/2. An interesting fact is that, at this maximum payoff point, the number of "peasant" type individuals is given by b/(2a) which is the half of what would be the stable population for a game without kights b/a. Although the setting is different from the previous case of "maximum sustainable yied", the coincidence of the number is intriguing.