ANARCHIST THEORY:

ANARCHY AND GAME THEORY by DOUG NEWDICK:

PART 4: THE CONCLUSION:

The essay of the above title has been serialized in three previous segments here at Molly's Blog (see our January 2008 Archives). In the remaining section Newdick delves into one explanation for why altruism is more common than might be predicted from standard game theory. This explanation is "kin selection", the first of several different ways in which cooperation can evolve to be investigated by evolutionary psychology. The basic idea dates back at far as J.B.S. Haldane(1) who remarked that he would "jump into the river to save two brothers or eight cousins". This was later given mathematical rigour by W.D. Hamilton(2,3) who formulated what has been called "Hamilton's Rule". This states that natural selection will favour altruistic acts if the donor and the recipient of such acts are closely related ie if the degree of their genetic similarity exceeds the cost/benefit ratio of the act of altruism. The idea of kin selection is also known as "inclusive fitness", a particularily apt name as the total fitness of the genes shared by the giver and the receiver is maximized by altruistic acts between them, even if the "donor" loses something by the act. For a more complete explnation of what inclusive fitness means see 'The Central Concepts of Inclusive Fitness' by Peter D. Taylor and Troy Day in the Oxford University Press 'Enclyclopedia of Evolution' (2002) (a pdf file-Molly).

The concept of "kin selection" is hardly the only mechanism whereby altruism becomes established and maintained in animal populations. Reciprocal altruism probably has a much more extensive influence on what Molly likes to call "pack animals" such as humans. The basic ideas of reciprocal altruism are as old as the hills, and were given an anarchist tinge by Kropotkin in his desacriptions of "mutual aid". Kropotkin's work, however, was largely descriptive and lacked any clear underlying mechanism. This is not surprising as genetics was in its infancy at the time when Kropotkin wrote 'Mutual Aid' (amongst other writings on the subject). Kropotkin, in fact, was a convinced Lamarkian, argueing through his life for the concept of the heritability of acquired characteristics. This was not so much from politically inspired blindness(though he tried to give an "anarchist tinge" to this opinion) as from the fact that Kropotkin had a life-long francophilia. France was basically the last major country to see the triumph of Darwinist views. Lamark was indeed French, and the scientific issues at stake were often greatly obscured by patriotic feelings.

It was 1971 before the concept of reciprocal altruism was given a firm mathematical basis by Robert Trivers in his 'The Evolution of Reciprocal Altruism' (4). This was later expanded upon by John Maynard Smith in his 'Evolution and the Theory of Games'(1982)(5).Trivers, by the way, has led an very interesting life, and Molly urges the reader to consult the above autobiographical essay. You might also want to see his conversation with Noam Chomsky on the subject of self-deception and politics (a video file-Molly). The Axelrod that Newdick cites in the essay wrote 'The Evolution of Cooperation' (6) in 1984. As Molly mentioned in her comments previously the game theoretical formulation of "tit-for-tat" has a "worm in the apple" because it has a tendency to degenerate into a frozen sequence of retaliation should one of the players defect. Other strategies such as "generous tit-for-tat" and "win-stay/lose-shift" have been shown to be better than tit-for-tat in establishing cooperation in a population and thereby increasing the fitness of the members of that population.

The present state of the field is very much wider than the two mechanisms mentioned above. For an interesting recent review see 'Five Rules for the Evolution of Cooperation' (Martin A. Nowak-2006)(7). Molly's notes follow below. After that I return to Newdick's essay and his notes.

MOLLY NOTES:

1)Haldane, J.B.S. (1955) Population Genetics. New Biology, 18, 34-51

2)Hamilton, W.D., (1964) The genetical evolution of social behavior I. Journal of Theoretical Biology , 7, 1-16

3)Hamilton, W.D.,(1964) The genetical evolution of social behavior II, Journal of Theoretical Biology, 7, 17-52

4)Trivers, Robert ,(1971) The Evolution of Reciprocal Altruism, Quarterly Review of Biology 46, 35-57

5)Smith, John Maynard (1982) Evolution and the Theory of Games ,Cambridge University Press, Cambridge

6)Axelrod, R., The Evolution of Cooperation, Basic Books, New York

7)Nowak, Martin A(2006), Five Rules for the Evolution of Cooperation, Science, 314, 1560-1563

Now back to our regular programming...Doug Newdick

7. Altruism

7.1 Altruism is not a rare phenomenon.

The purpose of the preceding section was to show that even if we grant the anti-anarchist her most pessimistic assumptions about humans (that they are rational egoists) and social interactions (that they have the preference structure of a prisoner's dilemma) mutual cooperation can still be achieved. I have already criticized the last assumption in S5, but the former assumption too is obviously flawed (footnote:this assumption is acceptable as an idealization when we have a specific explanatory or predictive purpose in mind-presuming it does not give us bad results), but in this justificatory role its inadequacies are central to the question at hand. People are not egoistic. If we think for more than afew moments we should be able to come up with a number of examples of pure altruism, examples where no beneifit whatsoever accrues to the performer of the action, not to mention examples of impure altruism. Donating blood is a good example of pure altruism; no measurable benefit accrues to someone who donates blood (without publicizing it), yet the benefits to others could be great, and there is a cost (even if it is not substantial). Then there are examples such as child-rearing. the cost of rearing a child is substantial, both in terms of monetary and other resources (eg time, missed opportunities,etc.), yet the benefit mainly accrues to the child, not the parent.

7.2 Kin Selection

An explanation for certain kinds of apprent altruism, and possibly for a greater than expected degree of reciprocal cooperation can be found in the theory of kin selection. Taking the gene's-eye-view proposed by Dawkins (1989)[11], imagine a gene for green beards. If this gene, besides causing green beards, causes the carrier of the gene to help other individuals with green beards, it has a greater than usual chance for spreading through a population.(Molly Note: the metaphor of the "green beard" is actually part of the question of how an individual can "recognize" either a relative or a reciprocator so that they can "play the game" with more confidence of cooperation) In a normal population an organism is more likely to share genes with its relations than with another member of the population. For any gene that is in your body there is a50% chance that it is in the body of your sibling. There is a 25% chance, for each of your cousins, that the gene is in their bodies. Thus, from the gene's perspective, if you sacrifice yourselves to save the lives of three of your siblings, then the gene has in fact gained because more copies of it were preserved than perished.

This is the mechanism of kin selection. the closer you are related to somebody the more it benefits the unit of selection (an entity which benefits from natural selection), in this case the gene,if you aid them, with the amount of aid directly proportional to the index of relatedness (Dawkins 1989:ch 6). In game theoretical terms, in any game the payoff to the gene is equal to the utility to the individual it is in plus the utility to the other individual times their index of relatedness.

The payoff in games between kin for player 1=z + xy, where x=index relatedness, y=player 2's utility and z=player 1's utility. The index of relatedness is the chance that a gene in X is present in their relation Y. For example, the value of x, if the two players are siblings, is 0.5. Thus the transformer prisoner's dilemma will looki like this...

...................................C..................D

C..........................4.5,4.5............3, 4.5

D.........................4.5, 3...............3,3

In this case we should expect mutual cooperation to be the outcome because it is an equilibrium and is preferred by both players. As we know from S6 the value of the discount parameter required for (B,B) to be an equilibrium decreases as the difference between the payoff for defecting while the other player cooperates and the payoof for mutual cooperation decreses. Thus mutual cooperation is easier to achieve when the mechanism of kin selection is operating.

It is also possible that such a mechanism might over generalize, that is, identify too many people as being related enough to alter behavior in prisoner's dilemma type situations. When you consider that in much of our recent evolutionary history humans have lived in small bands where the index of relatedness was fairly high (especially compared to today), such generalizations would have generated many false positives(12).

The mutual cooperation mengendered by kin selection can help the spread of reciprocal cooperation. It can create a large enough cluster of conditional cooperators to make conditional cooperation the best strategy in the population. If a cluster of conditional cooperators invades a population of unconditional defectors once the level of conditional cooperators reaches a certain level (dependant upon the discount parameter) the conditional cooperators earn more than the unconditional defectors by virtue of their interactions with each other (Axelrod 1984:ch 3).

8.SUMMARY

I have shown that premises 2 and 3 of the intuitive/Hobbesian argument are false. Therefore the conclusion that anarchies are non-viable and that the state is, in a sense, necessary do not follow. The analysis of the iterated prisoner's dilemma shows that even if we grant the opponent of anarchy their best case, their conclusions do not follow. Game theory shows us that even egoistic individuals will cooperate without coercion or coordination given certain conditions. Certain conditions which are practically possible. When added to Taylor's (1982) thesis that coercion can be utilized by an anarchic community to encourage cooperation(especially including "altruistic punishment"-Molly) the plausibility of an anarchy increases. I think that the analysis from game theory and kin selection should leave us optimistic about the possibility of cooperation without coercion, even under adverse circumstances. Thus the changes in human nature required for a viable anarchy are much less than the opponents of anarchy believe.

BIBLIOGRAPHY

Axelrod, 1984, 'The Evolution of Cooperation', Basic Books

Dawkins, 1989, 'The Selfish Gene', Oxford University Press, Oxford

Hardin 1982, 'Collective Action', John Hopkins University Press, Baltimore

Hobbes, 1968, 'Leviathan', ed C.B. MacPherson, Pelican Classics

Lewontin et al, 1984, 'Not in our Genes', Pantheon, New York

Lukes, 1974, 'Power:A Radical View', Macmillan Press

Mansbridge (ed), 1990, 'Beyond Self-Interest', University of Chicago Press, Chicago

Palfrey & Rosenthal, 1992, 'Repeated Play, Cooperation and Coordination"An Experimental Study', Social Sciences Working paper 785, California Institute of Technology, Pasadena

Taylor, 1982, 'Community, Anarchy & Liberty', Cambridge University Press, Cambridge

Taylor, 1987, 'The Possibility of Cooperation, cambridge University Press, Cambridge

Taylor (ed), 1988, 'Rationality and Revolution', Cambridge University Press, Cambridge

Wright et al, 1992, 'Reconstructing Marxism', Verso, London

FOOTNOTES

1)Much of this section is drawn from taylor 1987 and Axelrod 1984.

2)Taylor (1987:6) says that the free rider problems arise only when the collective good is non-excludable but not indivisible (that is when consumption of the good by an individual results in less of the good being available to others). I don't believe that this is the case. We are surely able to free ride on the public good of parklands, etc., by not payingt our taxes (point well stated-Molly).

3)This is really an example of an N-person prisoner's dilemma, rather than a normal prisoner's dilemma. See Taylor 1987: ch 4.

4)Taylor 1982 can be taken as an argument agfainst premise 4. I concur but will not go into the full argument hgere.

5)For a full presentation of the mathematical argument for this conclusion see Taylor 1987: 39-59.

6)In his book 'Amnarchy and Cooperation' . Taylor 1987 is a substantial revision of this book. Taylor (1987:70) points out that he had already proven what Axelrod proved with his tournaments (I don't know about that claim to priority-Molly). Axelrod's method, however was more interesting.

7)Note that unconditional defection (UD) is an equilibrium. any strategy that cooperates at any point with UD will score less than UD in that game.

8)B also has to do better than a strategy that alternates cooperation with defection, which occurs when w>0.5.

9)Strictlt speaking (B,B) being an equilibrium is a function of the relation between w and the value of the payoffs. Thus (B,B) is an equilibrium when w>(y-x)/(y-w) or w>(y-x)/(x-z). For the payoffs I am using this is the case if w > 0.5.

10)See Taylor 1987: ch4 for a detailed analysis of N-person iterated prisoner's dilemmas.

11)This is bad philosophy of biology, but it gets the point across easily.

12)Yet again this argument should not be taken too seriously, but merely adds additional reasons to be optimistic that humans are more inclined towards mutual cooperation than is predicted by the purely egoistic model.

MOLLY SUMS UP:

The reader breathes a sigh of relief. It is finally over. This essay serialized over the better part of a month is important for several different reasons. So, in the process of summing up as to what "anyone should give a shit" (a criticism that was once made of my similar efforts in the 1970s to introduce biological reality into anarchism) here are a few reasons:

A. As a general principle it is always better to tell the truth. The "left" is exiting a period when its dominant ideas were those of would-be new ruling classes, whether they were Leninist or social democratic. Even anarchists, unfortunately, trailed mindlessly behind the rhetoric of these would-be molders of human nature. No matter how dominant the idea of the "blank slate" was in leftist academia (and the would-be "saviours of the working class") common sense conceptions always knew that the leftist conception of human nature was wrong. Conservative commentators preyed on this tendency of the left to espouse nonsense by presenting what was really obvious to ordinary people as an argument against the left. Even before the utter and complete failure of communist dictatorship to "create the new socialist man" became glaringly apparent most people had great doubt about the blank slate theory held by leftism. If there is to be a new left that can reach out beyond the decay of academia it has to be reconciled with reality. It's very simple. If you lie people will see you as a liar.

B. Leading in from the above the theory of a "blank slate" is very obviously a theory that benefits certain social classes and those who aspire to be of such classes. Leninists, who wish to become a new ruling managerial class despite the overwhelming evidence of actual history that they are incapable of measuring up to the standards set by managerial elites in either corporations or social democratic states, have a vfery obvious vested interest in defending and propogating ideas of infinite human malleability. Their ideology-and therefore the justification for the sort of class rule that they propose- would fall apart without such a denial of reality.

C. If you don't pick up a weapon others will. Leaving aside the decaying remnants of Leninism and the much more important "social-welfare left" (who see further monies diverted to their attempt to mold people's behavior as the greatest of all causes), others use the realistic estimate of the human nature that the left denied to argue against any social progress (as the conservatives mentioned above do) or argue specifically against libertarian strategies. As an example of the latter the book 'The Rebel Sell' uses game theory to argue against libertarian tactics and for statist social democratic solutions. This book was recently reviewed in Linchpin, the Ontario platformist journal, but the reviewer missed a major point of the book. The authors use what is to me a very crude form of game theory to try and prove their points, as the good renegades that they are-trying to deny their "fashionable left" past. Their use of the theories is far more crude than Newdick espoused almost two decades ago, and I have made previous mention of how much the field has progressed since the time he wrote his essay. You can't counter their arguments by lies about the infinite malleability of humans. You can only counter them by showing just how crude their theories are and how little they accord with the present state of the field.

D. Finally and most importantly, exploration of human evolutionary psychology is important to the anarchist project-and not just as justification. If it were the latter, if anarchists were only to mine the theories for polemical purposes, the theories would be much less iumportant than they are. Newdick's essay is, to a large degree, an exercise in polemics. That is fine, but the important point is how acceptance of the realities of biology modifies anarchism rather than justifies it. What are the best conditions in which an anarchist polity can flourish ? What exactly has to be arranged so that the result is, if not the best of all possible worlds, at least one that is both worth living in and sustainable over the long term ? What does a realistic appraisal of human nature say about our present movement ? Big questions that people should think about.

That's it for now. Molly has blogged previously on subjects related to this question, and she will again in the future. Do a search of the tags on this blog for past comments if you want to read more. Check out the extra references that I have provided over the four part serialization of this essay. Also please excuse the typos (no doubt numerous) in my recent blogs. The spell check function of blogger has been down for some days. I have to proofread these entries myself, and there is a lot that I miss. Til then keep up cooperating for the sake of your fitness.

ANARCHIST THEORY:

ANARCHY AND GAME THEORY

PART THREE:

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.

BLOGGING

HERE AT MOLLY'S BLOG:

Things chug along at their usual slow speed here at Molly's Blog. I have begun the editing process ie the addition of Baron Mollydi's House of Zombies and the section for links in French (Liens en Francais), but there's still a lot of work to do on both. In terms of the Liens en Francais those that are listed in the general links section will be moved there, but those that are listed under some other categories such as 'Anarcho-Syndicalist Links", 'Platformist Links', etc. will be duplicated in both sections. Enlaces en Espanol will begin in the near future.

But now, I'd like to alert the reader to our growing texts section. Recent additions revolve around the extended reprint of Doug Newdick's 'Anarchy and Game Theory' on the main blog. I hope to complete this soon. The reprints are not just reposting but also contain info on other links that bear on this subject, so don't forget to look for them. The texts section now contains both this essay and Newdick's other essay 'Power and Consent'. There is also Jam Okra's 'Can Cooperation Ever Occur Without the State ?' and an interesting essay of the "tragedy of the commons" by Dennis Fox entitles 'Psychology, Ideology, Utopia and the Commons'. Molly found this while looking up things revolving around her comments about 'The Rebel Sell'. Molly read the latter book some time ago and planned to review it here, but , like many things it fell into the cracks in time. Maybe I should actually do it. But, speaking of Fox, look for an introduction to this man here at MB. His main site and blog have also been added to our links, and I have to say that he is well worth reading.

More later.

ANARCHIST THEORY:

ANARCHISM AND GAME THEORY:

PART TWO:

NEWDICK'S OBJECTIONS:


In Part One of Doug Newdick's essay presented the day before yesterday here at Molly's Blog the author outlined the basic format of what he calls the "anti-anarchist argument" of the prisoners' dilemma, as set out by Michael Taylor. The next part of this essay is devoted to Newdick's objections to this argument. It should be noted in passing that a rather simplistic form of the "Prisoner's Dilemma" is used by authors Joseph Health and Andrew Potter in their book 'The Rebel Sell'. The book is somewhat reminiscent of older generations of political recanters as they went from being communists to being neo-conservatives. The main point of the book is a criticism of fashionable counter-culture leftism, a stance that the authors apparently held in their youth (or before their present academic and journalistic careers anyways) and a stance that the authors take to be some sort of "anarchism". To say that whatever their earlier views were that they hardly resembled historical anarchism would be understating the case. The main point of their book is that so-called "culture-jamming" is both fruitless and ultimately hypocritical. That is largely true. The authors, however, don't go as far to the opposite extreme, from barbarism to barbarism, as ex-communist neo-cons do. They park themselves as basically right wing social democrats, a political viewpoint whose goals are at least as self-serving to people like them as "trendy leftism" is to others. Better than signing up with the Ahatollah Bush for Jihad I guess.




Whatever passed for "anarchism" in the rarified social circles that they travelled in when younger was, however, simply a crude "feeling", as is made plain by their discussions of it where they expose what only be termed "cosmic ingnorance" of what the word actually means. So, rather than going from barbarism to barbarism they have gone from crude to crude. Their presentation of the Prisoner's Dilemma, often under the alias of 'The Tragedy of the Commons", is crude in the extreme. It is as if everything that their professors threw at them in the economics classes where they "grew out" of their youthful naivity was taken from the state of game theory in the 1950s, without any regard to all the research that has been done since. Regular readers of Molly's Blog will know that I have a low estimate of the qualifications of many leftist academics. Reading Heath and Potter I came away with the "comforting "(???) feeling that the other side of the coin in academia is often just as lazy, thick and time-serving.




Heath and Potter's book has been reviewed in Issue Number One of the new Ontario platformist publication Linchpin (see earlier here at Molly's Blog) and also has been the subject of discussion of one of the forums over at LibCom. As might be expected such reviewers made much of the authors' criticism of subcultural politics and its futility, but they devoted little space to how distorted both the views of anarchism and the presentation of game theory were in the book.


All this is well and good, and it shows the other side of the coin, how game theory has become very much an in-topic outside of the leftist ghetto, even if some of its uses have all the airworthiness of lead bricks. If the reader is interested in this subject here's a further reference, 'Can Cooperation Ever Occur Without the State ?'. Also, the long time zinester and sceptical anarchist John Johson has recently written on anarchism and game theory in his zine "Imagine:Anarchism for the Real World', issue # 7. Sorry guys, no internet reference here, but you can get a copy for (I presume a small donation) at Imagine, Box 8145, Reno, NV 89507, USA. Now what a place to write about game theory from ! But now, on to the Newdick article...
5. PROVISION OF PUBLIC GOODS ISN'T ALWAYS A PRISONERS' DILEMMA.
"For a game to be a prisoners' dilemma it must fulfill certain conditions: "each player must (a) prefer non-cooperation if the other player does not cooperate, (b) prefer non-cooperation if the other player does cooperate. in other words: (a') neither individual finds it profitable to provide any of the public good by himself; and (b') the value to the player of the amount of the public good provided by the other player alone (ie. the value of being afree rider) exceeeds the value to him of the total amount of the public good provided by joint cooperation less his costs of cooperation" Toylor, 1987: 35).

5.1 CHICKEN GAMES.
For many public good situations either (a'), (b') or both fail to obtain. If condition (a') fails we can get what Taylor calls a Chicken Game, ie. if we get a situation where it pays a player to provide the public good even if the other player defects. But both players would prefer to let the other player provide the good, and we get this payoff matrix:
................................C.......D
C............................3,3......2,4
D............................4,2......1,1


Taylor (1987: 36) gives an example of two neighbouring farms maintaining an irrigation system where the result of mutual defection is so disasterous mthat either indididual would prefer to maintain the system herself. thus this game will model certain kinds of reciprocal arrangements that are not appropriately modelled by a prisoners' dilemma.


5.2 ASSURANCE GAMES.
if condition (b') fails to obtain we get what Taylor calls (1987:38) an Assurance Game, that is a situation where neither player can provide a sufficient amount of the good if they contribute alone. Thus for each player if the other defects then she should also defect, but if the other cooperates then she should prefer to cooperate as well. The payoff matrix looks like this:
........................C.......D
C....................4,4.....1,2
D....................2,1.....3,3
5.3 COOPERATION IN A CHICKEN OR ASSURANCE GAME.
There should be no problem with mutual cooperation in an Assurance Game (Taylor 1987: 39) because the preferred outcome for both players is that of mutual cooperation. With the one-off Chicken Game mutual cooperation is not assured. Mutual cooperation, however, is more likely than in an one-off Prisoners' Dilemma (5).
6. COOPERATION IS RATIONAL IN AN ITERATED PRISONERS' DILEMMA.
6.1 WHY ITERATION ?
Unequivocally there is no chance for mutual cooperation in a one-off Prisoners' Dilemma, but as has been pointed out, the one-off game is not a very realistic model of social interactions, especially public goods interactions (Taylor 1987: 60). Most social interactions involve repeated interactions, sometimes as a group (an N-person game) or between specific individuals (which might be modelled as a game between two players). The question then becomes: Is mutual cooperation more likely with iterated games ? (Specifically the iterated Prisoners' Dilemma). As one would expect, the fact that the games are repeated (with the same players) opens up the possibility of conditional cooperation, ie cooperation dependent upon the past performance of the other player.
6.2 ITERATED PRISONERS' DILEMMA.
There are two important assumptions to be made about iterated games. firstly, it is assumed (very plausibly) that the value of future games to a player is less than the value of the current game. The amount by which the value of future games are discounted is called thye discount value, the higher the discount value the less future games are worth (Taylor 1987:61). Secondly, it is assumed that the number of games to be played i8s idefinite. If the number of games is known to the players then the rational strategy will be to defect on the last game beacuse they cannot be punished for this by the other. Once this is assumed by both players the second to last game becomes in effect the last game and so on (Taylor 1987: 62).


Axelrod (1984) used an ingenious method to test what would be the best strategy for an iterated Prisoners' Dilemma. He held two round-robin computer tournaments where each different strategy (computer program) competed against each of its rivals a number of times. Suprisingly the simplest program, one called TIT FOR TAT, won both tournaments as well as all but one of a number of hypothetical tournaments. Axelrod's results confirmed what Taylor had proven in 1976 (6), TIT FOR TAT is the strategy of choosing C for the first game and thereafter choosing whatever the other player chose the last game (hereafter TIT FOR TAT will be designated stategy B, following taylor (1987).


An equiilibrium in an iterated game is defined as "a strategy vector such that no player can obtain a larger payoff using a different strategy while other players' strategy remains the same. An equillibrium then is such that, if each player expects it to be the outcome, he has no incentative to use a different strategy" (Taylor 1987: 63). Put informally, an equilibrium is a pair of strategies such that any move by a player awayfrom that strategy will not improve the player's payoff. Then mutual cooperation will arise if B is an equilibrium because no strategy will do better than B when played against B (7).


The payoff for a strategy in an indefinite iterated Prisoners' Dilemma is equal to the sum of an infinite series:
X/(1-w)
X= payoff
w= discount parameter (1-discount value)
UD playing with UD gets a payoff of two per game for mutual defection.If we set w=0.9, then UD's payoff is:
2/(1-0.9) = 20
(MOLLY NOTE: I retain the terminology "UD" as it appeared in the original essay, but I alert the reader that this probably should have been "AD" for "always defect" as it is usually referred to in game theory.)
B Playing with B gets a payoff of three per game for mutual cooperation. Thus with w = 0.9 B gets:
3/(1-0.9) = 30
(B,B) is an equilibrium when the payoff for B from (B,B) is higher than the payoff for UD from (UD,B):
B's payoff against B is
3/(1-w)
UD's payoff against B is
4 + 2w/(1-w)
Therefore UD cannot do better than B when:
(3/(1-w)))> (4 + 2w/(1-w))
= w > (4 -3)/(4 -2)
=w > 0.5
(Axelrod 1984: 208) (8) (9)


Can any other strategy fare better against B than B itself ? Informally we can see that this is not possible (assuming future interactions are not too heavily discounted). For any strategy to do better than B it must as some point defect. But is the strategy defects then B will punish this defection with a defection of its own which must result in the new strategy doing worse than it would have had it cooperated. Thus no strategy can do better playing with B than B itself. Now, if B is an equilibrium then the payoff matrix for the iterated game is:
........................B...........UD
B.....................4,4.........1,3
UD..................3,1.........2,2
Which is an assurance game. Thus if B is an equilibrium then we should expect mutual cooperation (Taylor 1987: 67). If, however, b isn't an equilibrium (ie the discount value is too high) then the payoffs resemble a Prisoners' Dilemma and thus mutual defection will be the result (Taylor 1987, 67).
This is a good place to stop until another day. The actual situation in game theory- and real life- is much more complex than what has been described above. In particular the game described above tends to drive towards iterated defection under a simple TIT FOR TAT strategy. Other refinements such as "forgiving tit for tat" are optimum in some situations, and the role of "spite" has been much further investigated in recent years. In the next section Newdick will describe "N-Persons" games. In such situations not just "spite" but also what has been called "altruistic punishment" comes into play. All this is to alert the reader that, while what will come in the next section is valuable, the present state of the theory is far more advanced than what will be presented here.

ANARCHIST THEORY:

ANARCHY AND GAME THEORY:

(OR "WHATEVER HAPPENED TO DOUG NEWDICK ?")

PART ONE:

What follows below is a reprint of a rather old essay that was first put on the internet, as far as I can determine, via Spunk Press in 1994. It was reprinted in a certain unnamed "anarchist" site without proper attribution, as per usual for said site. Molly reproduces it here because she thinks the matters discussed are important. Despite the obvious signposts in the "Anarchist Canon" such as the work of Kropotkin and his concept of an instinctual drive for "mutual aid", anarchism in the 20th century largely abandoned its earlier distinctive view of human nature and adopted the "blank slate" view of the Marxists and other ideologues of managerialism. Today this view of human nature lies in tatters and not just because of the obvious failings of communist tyrants to "create the new socialist man" by their propaganda and social engineering. While the blank slate is still popular amongst the leftist subculture it now has little credence elsewhere. To apply Marx to the Marxists, the financial interests of social welfare bureaucracies in maintaining the illusion that they can engineer the minds of the underclass and thereby, by some alchemy believed only by them, raise them up in class position is believable to few who don't make their money out of such efforts. They are supported by governments in general for reasons quite other than the illusions they have about themselves.

The author of this essay, Douglas Newdick, wrote this piece in the early 1990s, as can easily be seen from the dating of the references. The latest one dates to 1992. At the same time he published another essay, Power and Consent:Reductionism, Dialectics and Consent Theory, also available at the Spunk Press online library. Today Newdick is still resident in his native New Zealand, but he seems to have put his youthful anarchist phase far behind him. He presently works as a computer consultant. The essay that follows relies heavily on the early work of Michael John Taylor, author of numerous papers and books such as 'Anarchy and Cooperation' (1976), 'Community, Anarchy and Liberty' (1982) and 'The Possibility of Cooperation' (1987). All of these books, and many other papers use the language of "game theory" to argue that human society can be ordered so as to achieve cooperation without the cooercive hand of the state. Taylor was originally British, but since 1985 he has taught at the University of Washington in Seattle. While resident there he has published such papers as 'Rationality and Revolutionary Collective Action' (1988) and 'Cooperation, Norms and Moral Motivation' (1993). Taylor himself has published less and less in recent years.

For those unfamiliar with the whole concept of Game Theory, really a branch of applied mathematics, the Wikipedia online encyclopedia has an introduction. There is also an excellent portal to the whole matter at Game Theory.Net. Whether you see this as important or not depends upon whether you see the need for a properly grounded view of "human nature", one grounded in empirical fact and the theories that inform research devoted to governing such facts. Molly has referred to this matter earlier on this blog in her extended review of Tom Siegried's 'A Beautiful Math'. A properly scientific view of "human nature" is necessary not just for the polemical purpose of "proving anarchism realistic". It is even more necessary to inform anarchists about what paths may prove useful and which will prove futile. What would a functioning anarchist society look like ? Since Newdick wrote this essay game theory has continued to be used in a wide variety of fields in both the natural and social sciences. It has actually experienced an exponential growth in its development and applications. Thus some of the opinions expressed below may be "dated", but it is still a very useful starting point. Enough of the intro....

ANARCHY AND GAME THEORY:

BY DOUG NEWDICK

1:INTRODUCTION.

In any discussion of anarchism, or the conditions for a stateless society, sooner or later a claim like this surfaces; "people are too selfish for that to work". This, I believe, is based upon an assumption (or theory) about human nature that is taken to be evidently true rather than argued for. Often I hear a version of "I'm sorry but I just have a more pessimistic view of people than you do". the purpose of this essay is to show that even if we grant the assumptions of selfish rationality then cooperation without the state is still a possibility.

2.THE ANTI-ANARCHIST/HOBBESIAN ARGUMENT.

2.1. THE INTUITIVE ARGUMENT.

With tese sorts of objections to anarchism ("people are too selfish to cooperate without laws",etc) I think people tacitly appealing to an argument of the form:

1. People are selfish (rational egoists).

2. Selfish people won't cooperate if they aren;t forced to.

3. Anarchism involves the absense of force.

4. Therefore people won't cooperate in an anarchy.

The opponent of anarchism can then say either; as anarchy also rfequires cooperation, it involves a contradiction; or, a society without cooperation would be awful, therefore anarchy would be awful.

2.2 TAYLOR'S (1987) VERSION.

If we call the two options (strategies) available to the individual cooperation (C) and defection (D) (non-cooperation) then we can see the similarities between the inituative argument and Taylor's (1987) interpretation of Hobbes (1968) argument for the necessity for, or justification of, the state: (a) in the absence of any coercion, it is in each individual's interest to choose stategy D; the outcome of the game is therefore mutual defection; but every individual prefers the mutual cooperation outcome; (b) the only way to ensure that the preferred outcome is obtained is to establish a government with sufficient power to ensure that it is in every man's interest to choose C. Taylor 1987:17). we can see from this that the argument appears to be formalizable in terms of Game Theory, specifically in the form of a prisoners' dilemma game.

3. THE PRISONERS' DILEMMA.

3.1 THE PRISONERS' DILEMMA (1)

To say that an individual is rational, in this context, is to say that she maximizes her payoffs. If an individual is egoistic (ie selfish) then his payoff is solely in terms of his own utility. Thus the rational egoist will choose those outcomes which have the highest utility for herself. In the traditional llustration of the prisoners' dilemma two criminals have commited an heinious crime and have been captured by the police. The police know that the two individuals have commited this crime, but do not have enough evidence to convict them. the police, however, do have enough evidence to convict them of a lesser offense. the police (and perhaps a clever prosecuting attorney) seperate the two thugs and offer them each a deal. The criminals each have two options: to remain quiet or to squeal on their partner in crime. If they squeal on their companion and their companion remains quiet they will get off, if both squeal they will receive medium sentences, if they remain quiet and their companion squeals they will receive the heaviest sentence, and if neither squeals they will each receive light sentences. The two are unable to communicate with each other, and they must make their decisions in ignorance of the other's choice. There are four possible outcomes for each player in this game: getting off scot free, which we will say has an utility of four; getting a light sentence, which has an utility of 3; getting a medium sentence, which has an utility of 2; and getting a heavy sentence, which has an utility of 1. If we label the strategy of staying quiet "C" (for cooperation) and label the strategy of squealing "D" (for defection) then we get the following payoff matrix:

................................Player 2

................................C......... D

Player 1 C .............3,3....... 1,4

................D .............4,1....... 2,2

(where each pair of payoffs is ordered: Player 1, Player 2)

It is obvious from this that no matter which strategy the other player chooses each player is better off to defect, therefore the rational choice is to defect (In Game-Theory-Speak Defection is the dominant strategy). As this is the case for both players, the outcome of the game will be mutual defection. There is, howver, an outcome, mutual cooperation, which both players prefer, but because they are rational egoists they cannor obtain that outcome. This is the prisoners' dilemma.

More generally, a prisoners' dilemma is a game with a payoff matrix of the form

.........................C ............D

C...................... x,x .......x,y

D...................... y, z .....w,w

Where y>x>w>z . the convention is that the rows are chosen by player 1, the columns by player 2, and the payoffs are ordered "player 1, player 2" (Taylor 1987: 14)

Any situation where the players' preferences can be modelled by this matrix is a prisoners' dilemma.

3.2. RAMIFICATIONS OF THE PRISONERS' DILEMMA.

Many people have proposed that the prisoners' dilemma is a good analysis of the provision of public goods and/or collective action problems in general, they have taken the preferences of individuals in cooperative enterprises to be modelled by a prisoners' dilemma. Firstly, the prisoners' dilemma gives an interesting look at so-called "free-rider" problems in the provision of public goods. In public goods interactions, free rider problems emerge when a good is produced by a collectivity, and members of the collectivity cannot be prevented from consuming that good (in Taylor's terminology the good is non-excludable) (2). In this case a rational individual would prefer to reap the benefits of the good and to not contribute to its provision (ie defect), thus if others cooperate then the individual should defect, and if everyone else defects then the individual should defect (3). Secondly the prisoners' dilemma is taken to be a good model of the preferences of individuals in their daily interactions with other individuals, such as fulfilling (or not fulfilling) contractual obligations, repaying debts, and other reciprocal interactions.

3.3 MY VERSION OF THE ANTI-ANARCHIST ARGUMENT.

Given a game-theoretic interpretation of the claim in 1, and consequently a game-theoretic interpretation of the intuitive and Hobbesian arguments for the necessity of the state, we can reformulate them with the following argument

1. People are egoistic rational agents.

2. If people are egoistic rational agents then the provision of public goods is a prisoners' dilemma.

3. If the provision of public goods is a PD, then in the absence of coercion public goods won't be provided.

4. Such coercion can only be provided by the state, not by an anarchy.

5. Therefore public goods won't be provided in an anarchy.

6. Therefore then state is necessary for the provision of public goods.

7. The provision of public goods is necessary for a "good" society.

8. Therefore an anarchy won't be a "good" society.

9. Therefore the state is necessary for a "good" society.

4. OVERVIEW OF MY CRITICISMS/POSITION.

I think the game-theoretic model is the best (and most plausible) way of interpreting these sorts of arguments. I think, however, that premises 1 to 4 are false. Against premise 2, following Taylor (1987: ch 2), I argue that the prisoners' dilemma is not the only plausible preference ordering for collective action, and in some of these different games cooperation is more likely than in the prisoners' dilemma. The static model of the prisoners' dilemma game is unrealistic in that most social actions reoccur. Thus I argue that a more realistic model is that of an iterated prisoners' dilemma where cooperation (under certain circumstances) is in fact the optimal strategy (following Taylor 1987, and Axelrod 1984). Thus 3 is argued to be false. Finally, I argue that premise 1 is false, that indeed we do and should expect people to be (somewhat limited) altruists (4).

Molly will continue with this essay in the next few days. Stay tuned for more of Newdick's arguments. in the interim be sure to look up another argument in the same vein, Jam Okis' 'Can

Cooperation Ever Occur Without the State ?'. Til tomorrow then...By the way, sorry about the way I have to present matrices here. I've run into this problem before on blogger. Hopefully the form given here is comprehensible.

THE NEVER ENDING REVIEW: CHAPTER THREE OF 'A BEAUTIFUL MATH' : 'NASH'S EQUILIBRIUM':
Welcome back to this continuing review of Tom Siegried's 'A Beautiful Math', on the growth of game theory. I spend a goodly amount of time on this review because it is, in my opinion, important for a clear sighted view of social action- not because I agree with the author's often overinflated claims for the relevance of game theory. Even a sceptic of some of the grander claims can see just how important this matter is for a rational radicalism of the future. Anyways...
It's the third chapter of this book before the character of the title, John Nash, makes an appearance. Nash entered Princeton University as a graduate student in 1948. This was Von Neumann's stomping grounds. Morgenstein worked in the economics department and Von Neumann was at the Institute for Applied Studies a mile away.
To this point game theory had been restricted to the rather sparse world of "two player zero-sum" games. Nash rapidly broke into new fields of analysis, and his 1950 paper ('The Bargaining Problem, Econometrica 18(1950) pp 155-162) on which he was advised by both Morgenstein and Von Neumann, expanded the world of game theory into "cooperative games" in which the two sides work together to achieve a mutual benefit, and what he provided was a mathematical map for finding the optimal bargain that maximized the utilities of both players.
In the same year that he published the above paper he also presented his doctoral thesis- Non-Cooperative Games. This introduced the idea of an "equilibrium strategy" towards which a repeated round game will evolve. At this equilibrium Nash wrote in his thesis the situation is such that,
"...each player's mixed strategy maximizes his payoff if the strategies of the other players are held fixed."
What this idea did was to take game theory and make it possible to describe multi-player games, something that Von Neumann's ideas floundered on. Nash's proof depended upon something known as the fixed point theorem , an idea borrowed from topology. The ideas presented in this thesis were also published in the PNAC as 'Equilibrium Points in N-Person Games' in 1950 and in 1951 as 'Non-Cooperative Games' in the Annals of Mathematics.
As a side note "cooperative" and "non-cooperative" have a rather restricted meaning here. Cooperative refers to the coalition forming that Von Neumann and Morgenstein used to get around the fact that their theories couldn't deal with more than two players. Non-cooperative refers to Nash's expansion which can deal with any number of players who don't collaborate or communicate with each other. What Nash showed is that there is an "equilibrium strategy" that each player (at least one such but sometimes more than one) which maximizes their payoff no matter what the other players do assuming they also try to maximize their payoff.
This is, of course a simplified version of the real world where the "equilibrium states" of perfectly rational actors who try to maximize their self interest rarely exist. But armed with this general description the author goes on to describe specific "games" have analyzed, especially 'The Prisoner's Dilemma' (1), first described by Nash's Princeton professor Albert W. Tucker in 1950 (2) .
The game is set up as follows, two criminals, call them "Alice and Bob', are arrested. The police interrogate them separately. They have enough evidence to convict each of them on a minor charge, but they need confessions for convictions on more serious charges. If both refuse to confess they each get one year on the lesser charge. If one confesses and the other stays silent the squealer goes free and the other gets five years. If both confess they each get 3 years (two years off for "copping a plea". The payoff matrix is as below (once more excuse the limitations of blogger).

Alice

Keep Mum Rat

Bob: Keep Mum 1, 1 5,0

Rat 0,5 3,3

The above game is actually set up as something like a "routine procedure" by police interrogators, often with the predictable outcome (criminals are usually not heroes after all).

The 'Nash equilibrium' for the above is for both players to confess. from the point of view of either player the best choice is to rat no matter what the other player does. The outcome where both players squeal is "worse for the group" as 6 combined years is the maximum sentence, but is the best outcome for an individual acting in their own self interest. A real life example of this can be seen in continual news of "eco-terrorists" acting as squealers time after time in the USA. The ideology of those who promote such acts (while often remaining aloof from same) is insufficient to overcome the self interest of those who are caught in such acts (which they usually are), and their attempted "punishment" is as quite puny as compared to that of ordinary criminals. Hence the great incentive to confess on the part of people who are caught for such crimes. "Spite" may play a part in this as well, as those who have been caught may come to realize the self-interest of many who have "egged them on" while remaining out of danger themselves.

Another game mentioned, one closer to actual reality rather than anarchist cultism, is the 'Public Goods Game'. The question of this game revolves around the provision of public goods by voluntary donation- something closer to the heart of real anarchism rather than the posturing of certain American cults. In this case "defectors", otherwise known as "free riders" who don't voluntarily contribute can still reap the benefits of a "public good". It seems OK for the defectors, but if too many decide to "free ride" then the public good becomes unavailable and the defectors get no benefit.

One of the variants of the public goods game that Siegfried mentions is set up as follows. Four players are given monetary tokens and told that they could keep as many as they wanted or put them into a "public pot" where the amount would be doubled by the experimenter. There were a certain number of "rounds" in this game wherein each player would be told how much had been contributed to the pot, and they would be offered the chance to change their contribution; either decrease or increase it.

When the game was played repeatedly a stable pattern began to emerge. As Siegried says,

"Players fell into three identifiable groups:cooperation, defection (or free riders) and reciprocaters. Since all the players learned at some point how much had been contributed, they could adjust their behavior accordingly. Some players remained stingy (defectors), some continued to contribute generously (cooperators) and others contributed more if others in the group had donated significantly (reciprocaters).

Over time, the members of each group earned equal amounts of money, suggesting that something like a Nash Equilibrium had been achieved- they all won as much as they could, given the strategy of others. In other words,in this kind of game, the human race plays a mixed strategy- about 13% cooperators, 20% defectors (free riders) and 60 % reciprocaters in this particular experiment". (Molly Note: this emphasizes the importance of what is called "altruistic punishment" in evolutionary psychology. In a "game" where knowledge of an "opponent's" previous interactions with other players is given the percentage of "defectors" can be reduced by such punishment inflicted by players who were not part of the original rounds).

The author ends the chapter with an overview on 'Game Theory Today'. He notes that the field has been broadened considerably to cover "games where coalitions form, where information is incomplete, where players are less than perfectly rational". He also notes that there are arguments about whether game theory predicts behavior or "proscribes" what a rational person should do. He goes on to answer some of the criticisms of game theory's ability to "predict" in real world situations.

Siegried notes that game theory, like other scientific theories, is a model of reality, not reality itself. It makes reality comprehensible by simplifying it. As it is tested in experimental situations it is modified and grows just like any other scientific theory. The author quotes Colin Cameron in 'Behavioral Game Theory':

"The goal is not to disprove game theory...but it is to improve it"

Siegried goes on to describe the contributions of Thomas Schelling who won the 2005 Nobel Prize in economics. Schelling focused on games where there is more than one Nash equilibrium. he particularly analyzed conflict in international relations and the role of "bluff" in same. He also analyzed games where a "coordinated outcome" is better than any particular outcome. These are situations where, as Siegried says,

"...where it is better for everybody to be on the same page, regardless of what the page is."

The work of the other 2005 economics Nobel Prize winner, Robert Aumann, is also mentioned. Aumann analyzed the prisoner's dilemma game as a "repeated rounds" situation rather than a "one shot" affair and showed how cooperation could evolve in such situations (Much closer to everyday life:Molly Note). He identified situations where cooperation is less likely ie many players, limited communication or limited game time (fewer rounds). (Molly Note: The eventual "goal" of studying matters such as these is to identify what sort of conditions lead to "increased cooperation" in the presumed society that we want. Some things are obvious from the above. "Fewer players" means a decentralized society. "Full communication" means not just decentralization but also the elimination of "socialist managers" who mediate such communication and add "noise" to same).

Siegried finishes this chapter by naming multiple applications of game theory, not just in economics but also in medicine, politics,ecology and especially !!! evolutionary biology.

'THREATS OF WAR, CHANCES FOR PEACE'
The latest (March, 2007) edition of Scientific American has an interesting item by Earth Institute director Jeffrey D. Sachs with the title above. It basically a retelling of the Cuban missile crisis of 1962 and the lessons that can be drawn therefrom.
Now, the Earth Institute is certainly a worthy institution. Its mission statement says,
"The Earth Institute at Columbia University brings together talent from throughout the university to address complex issues facing the planet and its inhabitants, with particular focus on sustainable development and the needs of the world's poor. The Earth Institute is motivated by the belief that science and technological tools already exist, and could be expanded to greatly improve conditions for the world's poor while preserving the natural systems that support life on Earth."
The site is a wealth of information about research being undertaken in support of sustainable development. Jeffrey Sachs himself is an economist with special interests in development issues, and there's no doubt that he is "on the side of the angels". His telling of the tale, however, leaves little to the imagination about what his politics are. He's an American liberal who looks back to the Kennedy era as a sort of lost golden age. What is left out is as significant as what is included in his brief summary. The omitted fact that the USA started this whole game of brinkmanship by installing nuclear missiles in Turkey the year before is a convenient omission- one almost universally ignored in most popular western accounts of the crisis. For a fuller story of the Cuban missile crisis see the Wikipedia article on same. As a good liberal Sachs praises Kennedy- a praise that is hardly universally voiced- and ignores the good faith initiatives of the Soviets. Also, like a good liberal he ignores not just the crazies on the American side but also an equally detached set of hardliners in the Cuban ruling class. In the endgame the missiles in Turkey were removed albeit "secretly" without fanfare, and Sach's claim for the Kennedy administration that they "stressed the need to avoid humiliating one's adversary" really applies much more to the Soviet actions as opposed to the American ones. It was also the one, only and last time that the Soviet ruling class ever exposed their strategic nuclear forces in a position where they might escape from their immediate and total control (into the hands of Cuban ideologues in this case).
Anyways, whatever one may think of the moral rectitude of the various players in this game a point Sachs makes is that it was indeed a "game". He says,
"Today's game theorists would describe Kennedy's strategy as 'generous tit-for-tat(GTFT)' (The Soviet moves should also be so described- Molly). A player adopts a position of cooperation as long as the other side does too. If the second player begins to cheat, the first player stops cooperating as well, to show the cheater that there are adverse consequences to the collapse of this arrangement. The door remains forgivingly open to future cooperation, however, if the cheater reverts to form. And generously the first player might initiate renewed cooperation, with a view to enticing the former cheater to reciprocate. GTFT is so successful and robust that many evolutionary biologists suppose that the basic strategy is somewhat hardwired in human attitudes.".
Whatever one may think of Sach's assignment of blame and praise the essential point that he is trying to make is true. There are ways towards peace and security that are different from and more effective than the bluster of the present American administration and their equally ideologically driven Islamofascist opponents. The two sides actually mirror each other very well. Have a look at the essay for the full story. It will likely be posted on the net next month at the Scientific American website, which is usually one month behind the printed version.
It's also an example the application of game theory in real life, something that Molly will return to as she slowly posts her complete review of 'A Beautiful Math' on this site. The book is long finished, but reading is faster than writing about it.
Molly

GAME THEORY: SOME EXAMPLES:

Here are a few examples of what the author Siegfried uses to illustrate Von Neumann's game theory in his book 'A Beautiful Math'.
The first is from real life and has a trivial outcome ie a single best strategy fort each player no matter what the other player does.
During WW2 General George Kenney was in charge of the allied air forces in the southwest Pacific. During the battle of the Bismark Sea he knew that the Japanese would be sending a convoy of supply ships to New Guinea. The Allies wanted to bomb this convoy and could get in three days of possible bombing if the convoy too either of two possible routes, either north or south of New Britain. The complication was that the northern route would be stormy for one of these days, leaving only two clear days for bombing. Kenney could send his reconnaissance planes either north or south but not both (too few planes to cover both routes I guess). If they sighted the convoy the attack planes would follow. If not the attack force would head in the opposite direction the next day by a process of elimination.
I think you can see where the complications in this scenario lead, complications not mentioned by Siegfried and apparently not by the many textbooks that use this example. This first is why not send the attack planes in the opposite direction if the convoy is not sighted in due time ? The second is that one has to assume that reconnaissance is 100% effective. If the planes say that the Japanese are not there they are really and truly not there. this becomes particularly acute of day 1 is the rainy day. Can reconnaissance be 100% effective at the same time as bombing is 100% ineffective ?
But anyways Kenney made a decision by brute logic without the aid of game theory. The basis of his decision is best illustrated by the typical matrix used in game theory, outlined below(please excuse the limitations of the blogger format):
Japanese
-------------------------------------------------------------------
North South

-------------------------------------------------------------------

Allies North 2 2

South 1 3
-------------------------------------------------------------------

The game is "zero sum". Whatever the Allies gain the Japanese lose. The above matrix represents the days of bombing available given the choices of both the Japanese to go either north or south and the choice of Kenney to sent his reconnaissance planes either north or south. From the allied point of view sending the recon planes north would give two days of bombing in either case, and sending them south would give either one or three days depending upon what the Japanese did. Hard to choose from these possibilities. From the Japanese point of view, however, the choice is obvious. Going south results in a loss of either -2 or -3 (the Japanese "gains" are the obverse of the allied gains tabled above). Going north results in a loss of either -2 or -1. The best strategy is to go north no matter what the allies do. This indeed what happened in the real world. Both the convoy and the recon planes went north.
The secret of Von Neumann's proof is that it applied only to those cases where "the opponent plays as well as possible". It doesn't apply to an erratic opponent. Because of this there is a "minimax" strategy for the allies. Send the planes to the north because the Japanese are not fools. And maybe they aren't good at "bluff" either. Both "bluff" and "stupidity" are complications that often occur in real life.
Where Von Neumann's concept of "minimax" really becomes interesting is where the game is not, like the example cited above, a "one shot deal" but is repeated. Siegried uses an example modified from one given in Martin D Davis' book 'Game Theory:A Non-Technical Introduction' (Dover, Mineola NY 1983/1997). It goes as follows:
Two players, call them Alice and Bob are each dealt a single card. Black always beats red. Each player antes up "5" on each round so there is always "10" in the pot. Alice plays first, and she can either call or bet an additional "3". If she calls both players show their cards, and the black card wins the pot. If they both have black or they both have red they split the pot 50/50. Bob, on the other hand can, if Alice bets, either fold or match her "3". If he folds Alice takes the "13" in the pot. If he matches and calls the one with the black card wins the pot, and if both players have the same colour they once more split the pot 50/50.
The matrix for this game is considerably more complex than that given above. I'll spare you the attempt, but try it out if you are interested. Instead of the 4 possible entries in the matrix above there are 128 different possibilities because both Alice and Bob can follow 4 different strategies. From Alice's point of view she can either 1)always bet, 2)always call, 3)bet with red and pass with black or 4)bet with black and pass with red. The result with Bob's options is a 4X4 matrix with 8 entries in each cell because the different winnings have to be listed beside each other. This sort of game introduces the idea of "bluff", and it turns out that the best minimax strategy is a "mixed" one for both players. Alice's best strategy is to bet 60% of the time no matter what card she has (ie to "bluff" if she has black) and 40% of the time to bet only if she has black. Bob, on the other hand, should call Alice's bet 40% of the time no matter what card he has and 60% of the time call if he has black and fold if he has red. The choice of what to do should be totally random so that the percentages equal the above.
This game, by the way, is stacked in favour of Alice. She'll come away with a gain of about 30% if both players play their optimum strategies. So Von Neumann showed that there are minimax strategies that are "mixed strategies" where a given course of action is chosen randomly a certain percentage of the time.
Molly