ANARCHY AND GAME THEORY
For the past few days Molly has been serializing Doug Newdick's essay 'Anarchy and Game Theory'. In the last installment Newdick, drawing on the work of Michael Taylor, laid out why he thinks the Prisoners' Dilemma is not a realistic model of many social interactions. In particular he mentions the "game strategy" of TIT FOR TAT. In this section Newdick goes further into how cooperation can evolve in the situation where the "players" are assumed to be rational and self-interested. Molly wants to alert the reader that these assumptions do not always hold, and also refer the reader back to previous installments for terms that may seem obscure (see the January 2008 Archives if this page fails to hold Part One).
ANARCHY AND GAME THEORY, PART THREE...
6.3 ITERATED N-PERSONS PRISONERS' DILEMMA
A more realistic model of some social interactions, especially public goods interactions, is that of an N-person iterated prisoners' dilemma, that is an iterated prisoners' dilemma with more than two players (an indefinite number for purposes of analysis). The analysis is too complex to reproduce here (10), but the results of the analysis of the 2-person iterated prisoners' dilemma can be applied more or less straightforwardly to the N-person case. If cooperation is to arise at least some of the players must be conditional cooperators (ie utilizing something like B- Molly Note, a TIT FOR TAT "strategy"- and "it has been shown that under certain conditions the cooperation of some or all of the players could emerge in the supergame no matter how many players there are" (Taylor 1987:104).
6.4 CONDITIONS FOR CONDITIONAL COOPERATION
For mutual cooperation to arise a strategy similar to B needs to be used by individuals, and (B,B) needs to be an equilibrium. For the latter to be the case the discount parameter needs to be sufficiently high (Molly Note: an estimate of the value of "future games" which, of course, depends on the very likelihood of such "games") . For the former individuals need to be able to tell whether other individuals are cooperating or defecting (Molly Note- the problem of "information" is crucial in game theory) . The discount parameter is dependent upon the chance of the player having future interactions with the other player, and the frequent with which they have interactions. The greater the probable time between interactions, and the smaller the number of probable interactions, the lower the discount parameter and the lower the chance of getting mutual cooperation. There are a number of ways in which the discount parameter can be increased (Axelrod 1984:129-132): increasing territoriality (reducing population mobility), increasing specialization, concentrating interactions, so that an individual has more interactions with a smaller number of other individuals, decomposing interactions into more smaller interactions.
If more people are to employ a strategy such as B, they need to be able to monitor the behavior of other players. Thus it seems that mutual cooperation will be more likely in smaller societies than in larger ones. if the relations between individuals are direct and many-sided (ie they interact with others without any mediation, and they interact with them in a number of different ways) then monitoring behavior is much easier. this would translate into a less stringent size requirement. Such properties are to be found in societies that have the property of "community" (Taylor 1987: 105, 1982). (Molly Note: the critical reader may note that one of the properties of a society that promote cooperation is "specialization". It should also be noted that "complexity" is another promoting factor, as Newdick argues above. What this says is that the crude reductionism of the perversion of anarchism known as "primitivism" goes against at least this window into "human nature". In actual fact a "primitivist society" would be quite "cooperative" in the sense of being antagonistic to other "foreign societies" ie it would lead to a state of almost perpetual war. released from the need to fight the "other" such societies would be antagonistic within themselves, a state of pervasive paranoia and status struggle. Molly believe the anthropological record bears this out.
THE EVOLUTION OF TIT FOR TAT:
As TIT FOR TAT is the best strategy under certain conditions, we would expect that organisms that evolved in these conditions might well use this strategy as an adaption (with all the usual riders such as the variation might not have arisen, constraints of other structures might prevent this, etc.). This expectation is supported by a number of apparent examples of TIT FOR TAT behavior amongst certain certain organisms that do not live under iterated prisoners' dilemma conditions (Dawkins 1989: 229-233). If such human social interaction does take the form of a prisoners' dilemma (and we have seen that is this is the case then these will be mostly iterated), and if we assume that much of the evolutionary history of humans and their ancestors was spent in small groups (as evidence suggests) then we might expect that humans might have evolved such a behavioral strategy. One must be wary of drawing too strong a conclusion about humans and human behavior from evolutionary arguments. (Molly note.One must also beware of drawing too weak a conclusion because of loyalty to a leftist fashion that served the class interests of would-be managers of society ie a new ruling class) Human behavior is notoriously complex and very plastic, unlike much animal behavior. I do, however, think that this argument gives an additional reason for being optimistic about the possibility for mutual cooperation.
Molly Note: Here is another appropriate stopping place. Following the previous section Newdick will go on to argue further for his views in sections about altruism borrowed from the state of sociobiology at the time he wrote the essay. Today sociobiology is known as "evolutionary psychology" , and it is a vibrant and growing field of research. At the time when Newdick wrote his essay little had been elucidated beyond what he will mention later ie "kin selection" and what he does not mention, "reciprocal altruism" which, of course, is fully consistent with what he wrote about game theory.
Molly can remember when she first started to argue for the need to pay attention to sociobiology way back in the 1970s. It was, of course, met with predictable hostility, even from anarchists who should have known better. At the time the "left" was dominated by the Marxist religion, and paying attention to many facts, not just sociobiology, was considered blasphemy, and in the absence of any prospect of actually carrying out their fantasies of becoming commissars in the real world leftists loved to engage in campaigns of verbal aggression against suspected heretics. Molly was very much inured to this. As an ex-Marxist who had rejected pretty well all of the religion of Marxism she was well used to the fact that most leftists were assholes most of the time. Besides that she had an aggressive streak of her own and a skin of steel. As far as I can determine Newdick never came to the sort of conclusions that Molly did, and he retained far too much sympathy for his leftist professors and the social circles he found in University. Once leaving the "cloister" it was far easier to simply take up new interests. Hence his "disappearance". Nothing that I have read in Newdick's two internet essays says that he ever bothered to look beneath the surface of the rock of leftism. Crawly critters live there. When his efforts were met with the predictable hostility he simply "took a walk". This can often be the best way to handle many matters. Better to handle some sort of cognitive dissonance between the facts (such as Newdick laid out in his essays) and a social group such as "the left" by saying "bugger it all". Not the most creative solution I will grant. The outstanding example of an historical "leftist who hated the left and all its works" has been George Orwell, and Orwell's criticisms of the left of his day are amongst his best writings. But at least this is a theory as to why Newdick simply "disappeared" from lefty writing, as Molly remarked at the beginning of this serialization. Is it the "whole story" ? Obviously not ? In any case Newdick is still alive and prospering today, and Molly wishes him all the best and thanks him for what he contributed when he was younger.
Stay tuned for the conclusion of this serialization in the next few days here at the Molly Soap Opera Channel.