Hawk Dove Game and the Evolution of Property Rights
The First Property Rights Revolution
Background
In their paper, The First Property Rights Revolution, Samual Bowles and Jung-Kyoo Choi attempt to explain the emergence of individual property rights, which replaced the "collectivist and egalitarian social structures" common to mobile foraging bands. A key element in this investigation is why property rights only emerged about 11,000 years ago with the domestication of plants and animals, and how they were able to evolve without the aid of states which did not appear until many millenia later. From archaological evidence and recent behavioral experiments it is clear that sharing norms existed as early as 100,000 years ago, and that the lives of these mobile hunter-gatherers were regulated by social norms and collective punishment of violators of these norms. These norms most likely applied to certain items, like large game, which were available sporadically and in large quantities.
"In these ... communities, group sanction emerged as the most powerful instrument for regulation of individually assertive behaviors, particularly those which obviously disrupted cooperation or disturbed social equilibrium needed for group stability."
In addition, humans are not unique in having property rights. Many species of spiders and the male Hamadryas baboons respect prior possession of sites and objects by individuals of the same species. These facts are puzzling in the face of explainations which present property rights as a way to minimize the waste from conflict, but cannot explain why property rights did not develop nearly 100,000 years earlier.
Approximately 11,000 years ago there was a significant climate change which allowed the domestication of plants and animals to become a feasible strategy. The process of transition to agriculture was gradual, but eventually replaced the social orders of all but a few hunter-gatherer bands. The connection between domestication and the emergence of property rights is that the possesion of land and livestock is relatively straight forward. There is likely to be little confusion as to whose land and animals are whose, versus a large animal that many people work together in different manners to kill. Also, successful agriculture required these rights to be in place in ordered to develop.
The Model
The model propose by Bowles and Choi is very similar to the Hawk-Dove-Bourgeois Game that we have seen in class. In the model there are n members of a foraging band who divide a good of value v. Individuals may adopt one of three strategies: grabbing (Hawk), sharing (Dove), or punishing (Bourgeois). When a Grabber meets a sharer they take the good. When a Grabber meets a Grabber they fight. They either gain the good or bear the cost of defeat, c>v, with equal probability. When a Punisher meets a Grabber, all the Punishers try to punish the Grabber. If they win, the good is distributed amongst all Punishers, or bear the cost of defeat c. The probability of successfully punishing a Grabber is equal to the population frequency of punisher, ?. If ? is the population frequency of Sharers, the payoffs are as follows:
with expected payoffs for each strategy:
?s=(?+?)1/2v
?p=(?+?)1/2v+(1-?-?)(?v-(1-?)c)
?g=?v+?{(1-?)v-?c}+(1-?-?)1/2(v-c)
The cultural transmission process is based on the above payoffs according to a payoff monotonic updating process, where n is large enough that actual payoffs is approximate to expected payoffs. Thus:
d?/dt=?(?s-?av)
d?/dt=?(?p-?av)
where average payoff, ?av, is
?av=??s+??p+(1-?-?)?g
The vectors indicate the direction of movement in the regions defined by the loci along which ?,?, and ? are stationary. For this figure v/c=2/3.
Two of the stationary outcomes of this model are particularly interesting. Point b corresponds to the classic equilibrium found in the Hawk Dove game, and is asymptotically stable (cannot be invaded by punishers). The left side of the triangle corresponds to an all Sharer-Punisher composition. These points are stable (not invadable by grabbers), but not self-correcting (subject to drift). This second equilibrium appears to be what most of human history saw in terms of social arrangements, however, allowing for slight disruption (chance events) this equilibrium will not persist over time. In this equilibrium Sharers and Punishers recieve the same payoffs, so eventually Sharers will make up a large enough part of the population that Grabbers will be able to invade, falling back to the traditional Hawk Dove equilibrium. The Hawk-Dove does not appear to be what happened and several reasons could explain why the Sharer-Punisher equilibrium would be stable. If groups periodically encounter adversity from the environment or conflict with other groups, the groups with higher average returns have a better chance of survival. In addition, if there is conformist cultural transmission, this will work against drift and allow all Punishers to be a stable equilibrium, since when there are no Grabbers, Sharers and Punishers have the same payoffs. There might also have existed a second-order punishment which in addition to punishing Grabbers, punished Sharers as well, who free ride on the collective punishment of Grabbers. The all Punisher equilibrium would be stable even if the punisher incurred a cost and the cost to the Sharers of the second-order punishment was relatively small (temporary shunning, or slightly less of a shared resource).
