I have posted one entry to this 'blog that made reference to Cournot-Nash equilibria, and I expect to write another soon. I'm going to use this entry to explain the concept of a Cournot-Nash equilibrium, without resorting to mathematical formulæ.

First, let me give my favorite example of the idea, the behavior of prairie dog mothers in at least some towns. Prairie dogs are omnivores; they are primarily herbivorous, but will also consume small animals such as insects. If a prairie dog mother stays away from her litter of pups, they are liable to be eaten by something, so she will prefer food that is close at-hand — such as the pups of another mother who is away from her burrow. In fact, in some towns, when pups are eaten, it is usually by mothers trying to get home before their own pups are eaten. If any one prairie dog were to stop eating pups while the others continued, then her own pups would more likely be eaten because she'd be away from home for longer or more frequent periods. They eat each other's babies because they eat each other's babies.

Some of you may be thinking of the Prisoners' Dilemma, which, under classic assumptions, results in a similar mess. It too is an example of a Cournot-Nash equilibrium.

The essence of a Cournot-Nash equilibrium is that each participant has no incentive to change behavior unless other players change behavior, so each — and thus every — participant sticks with his or her established behavior. Although the prairie dog example and the classic telling of the Prisoners' Dilemma are sub-optimal equilibria, it could be the case that an equilibrium were the best-possible equilibrium, and no one had an incentive to change his or her behavior so long as no one else changed his or her behavior; so it's important to distinguish optimal Cournot-Nash equilibria from sub-optimal Cournot-Nash equlibria.

The Nash to whom the name refers is John Forbes Nash jr, whose life and work were grossly misrepresented in the movie A Beautiful Mind (2001). Nash's most famous accomplishment was explicitly generalizing and formalizing the idea of a Cournot-Nash equilibrium, which some simply call a Nash equilibrium. But there were famous antecedent uses of the idea, the best-known of which was by Antoine Augustin Cournot, in an 1838 model of oligopolistic competition.[1]

A less-often recognized antecedent use was by Thomas Hobbes in Leviathan (1651). Hobbes famously proposes that, in the absence of a State, life will be nasty, brutish, and short. More specifically, he said

Hereby it is manifest that during the time men live without a common power to keep them all in awe, they are in that condition which is called war; and such a war as is of every man against every man. For war consisteth not in battle only, or the act of fighting, but in a tract of time, wherein the will to contend by battle is sufficiently known: and therefore the notion of time is to be considered in the nature of war, as it is in the nature of weather. For as the nature of foul weather lieth not in a shower or two of rain, but in an inclination thereto of many days together: so the nature of war consisteth not in actual fighting, but in the known disposition thereto during all the time there is no assurance to the contrary. All other time is peace.

Whatsoever therefore is consequent to a time of war, where every man is enemy to every man, the same consequent to the time wherein men live without other security than what their own strength and their own invention shall furnish them withal. In such condition there is no place for industry, because the fruit thereof is uncertain: and consequently no culture of the earth; no navigation, nor use of the commodities that may be imported by sea; no commodious building; no instruments of moving and removing such things as require much force; no knowledge of the face of the earth; no account of time; no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short.[2]

According to Hobbes, without the State, production is subject to predation, so potential producers have less incentive to produce and everyone has incentive to prey upon everyone else.

But Hobbes has also identified a special case of one solution to what would otherwise be a sub-optimal Cournot-Nash equilibrium. In Leviathan, men end the war amongst them by explicitly agreeing to the creätion of an institution (the State) which will change the equilibrium. More generally, agreements need not be explicit or conscious, and the transforming institution could be a code of conduct. For example, the classic statement of the Prisoners' Dilemma treats the game as played in a social vacuum of a sort. In real life, people build reputations, reward desired behaviors, and punish the behaviors to which they object. Commitment mechanisms don't necessarily free us from every possible sub-optimal Cournot-Nash equlibrium, but naïve game theory too often fails to consider their possibility. (There was some perverse gloating in A Beautiful Mind about how Nash had somehow refuted Adam Smith, but the liberal order of which Smith wrote is filled with commitment mechanisms. Private property itself is an example of such a mechanism.)

Perhaps, in time, even the prairie dogs will evolve a mechanism such that eating each other's pups is no longer an equilibrium.

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[1] Recherches sur les principes mathématiques de la théorie des richesses, Ch 7.

[2] Chapter XIII ¶ 8-9.

I've been pondering ideological taxonomy again.

As a classical liberal, I believe that there is a right-or-wrong prior to any actual human choice or action. A standard term for this preëxisting morality is natural law. Classical liberals typically test their notions of natural law by pondering how they would work in a state of nature — that is to say in a hypothetical environment when social institutions have been zeroed-out.

But what I've been pondering lately isn't classical liberalism per se, but conservatism — how it proceeds from a different foundational model, and how that that model affects (or effects) the politics of to-day.

Some conservatives have explained the essential difference between conservatism and liberalism (by which they may mean classical liberalism, or the social democratism that absconded with the name liberal in the 20th Century, or both) in that liberals did not believe in Original Sin. What one perhaps first sees here is a rejection of human perfectability; but there's something darker here.

There's a famous poem by Charles M. Province, It Is the Soldier, which declares that our freedoms and rights are not given to us by ministers, by reporters, by poets, by campus organizers, by lawyers, or by politicians, but by soldiers. The declaration is not merely that the front-line of defense of these rights is provided by the soldier, but that these rights are literally given to us by the soldier. In what sort of framework does the soldier give these rights to us?

Thomas Hobbes wrote of a state of nature in which rights as most of us now conceptuälize them did not exists. Hobbes indeed uses the word right, but it doesn't refer to anything that morally constrains others; rather, it is an obligation of some sort binding its possessor, and in this case binding him to follow a lex naturalis which is of every man for himself:

The right of nature, which writers commonly call jus naturale, is the liberty each man hath to use his own power as he will himself for the preservation of his own nature; that is to say, of his own life; and consequently, of doing anything which, in his own judgement and reason, he shall conceive to be the aptest means thereunto. By liberty is understood, according to the proper signification of the word, the absence of external impediments; which impediments may oft take away part of a man's power to do what he would, but cannot hinder him from using the power left him according as his judgement and reason shall dictate to him. A law of nature, lex naturalis, is a precept, or general rule, found out by reason, by which a man is forbidden to do that which is destructive of his life, or taketh away the means of preserving the same, and to omit that by which he thinketh it may be best preserved. For though they that speak of this subject use to confound jus and lex, right and law, yet they ought to be distinguished, because right consisteth in liberty to do, or to forbear; whereas law determineth and bindeth to one of them: so that law and right differ as much as obligation and liberty, which in one and the same matter are inconsistent.

And because the condition of man (as hath been declared in the precedent chapter) is a condition of war of every one against every one, in which case every one is governed by his own reason, and there is nothing he can make use of that may not be a help unto him in preserving his life against his enemies; it followeth that in such a condition every man has a right to every thing, even to one another's body. And therefore, as long as this natural right of every man to every thing endureth, there can be no security to any man, how strong or wise soever he be, of living out the time which nature ordinarily alloweth men to live. And consequently it is a precept, or general rule of reason: that every man ought to endeavour peace, as far as he has hope of obtaining it; and when he cannot obtain it, that he may seek and use all helps and advantages of war. The first branch of which rule containeth the first and fundamental law of nature, which is: to seek peace and follow it. The second, the sum of the right of nature, which is: by all means we can to defend ourselves.

Now, Hobbes would still be interesting if we discarded the famous stuff about life in a state of nature being nasty, brutish, and short — he'd got hold of the notion of sub-optimal Cournot-Nash equilibria being overcome by introduction of a commitment mechanism — but that business of life being thus wasn't simply grim speculation of how things would be, but an interpretation of how things had been; and, hence, on a deeper level, of how things were and always will be.

Consider the pre-feudal period in Western Europe, and feudalism in theory. Outside of the major cities, the central Roman state provided ever-weakening protection against raiders. (Indeed, to the extent that the state acted upon the country side, it was as itself a looter of a sort.) Those with sufficient resources and leadership abilities put together their own gangs (perhaps cobbled-together from the remains of the state). These gangs might themselves function as no more than local protection rackets, seizing tribute in exchange for protecting weaker people from nothing other than worse seizures by the gang itself, while protecting only themselves from other raiders. But in theory what the local gang did was to hold back those raiders, in exchange for goods or services from those who were subordinates of the leader of the gang.

As it evolved, the ideology of feudalism didn't present the gang simply as providing service-for-hire. Rather, the gang-leader was presented as himself the owner of the land and of what it produced. He granted use of this property, in exchange for stewardship.

Look at this model of the world. The community is under constant menace from external raiders. The warrior holds back those raiders; by virtue of this, he makes the community possible. All rights within the community are thus creäted by him, and any rights possessed by others have thus been granted by him — It is the Soldier.

Aside from ostensibly protecting the locals, the other engagement of the lord was in, well, raiding some other community. In fact, even when feudalism was operating according to theory, the immediate reason that each community needed a lord was that other communities had lords of their own. But, within this framework of rights being creäted by the soldier, there is nothing wrong with this — after all, the rights of the other community ostensibly were brought into existence by warriors to whom the raiders owe nothing! (And savages, who do not have a proper leader, are especially regarded as fair game, for they have no rights from anyone.)

Conservatisms emerge from and are informed by various things, including a respect for subtleties of social evolution. But I think that this model of civilization as carved-out of barbarism and always threatened by barbarism plays much the same rôle for most of them as do the thought-experiments of the classical liberals for them. The classical liberal begins with a perhaps romanticized model of the state of nature, to think about natural law, and adds barbarians (if at all) as a complication of the model; the conservative begins by imagining barbarism, and subsequently perhaps romanticizes the warriors who carve territories from it.

Even if I am wrong in this belief about conservatism, I think that a useful taxonomy could classify ideologies by what thought, if any, they gave to states of nature.

I have a conservative friend whose take on Dirty Harry was significantly different from my own. He saw men such as Callahan as dirty because such men must be, in order that there be civilization for the rest of us. In hindsight, I reälize that it was natural for my friend, qua conservative, to read things thus — it's a variation on the theme of barbarians (the Scorpio Killer) and of warriors (Callahan) who are required and thus empowered to do terrible things to stop them, though these warriors may be sickened by what they are doing.

(Though I have left him here unnamed, in justice I should draw attention to the point that my conservative friend indeed saw Callahan as dirty; my friend would by no means join and worship in a cult of the military. He speaks of soldiers wanting to be honored with parades every day, in what I take to be a metaphor for their propensity to mistake an essential contribution for a uniquely essential contribution.)

Almost every war-time Presidential Administration has tapped into the presumption that war suspends the ordinary rules. (That is, after all, why war is declared by these and by other administrations on things such as poverty.) But now-a-days, we've seen a resurgence, partly fostered by the present Administration, of a world-view in which barbarians are naturally and persistently at-the-gates, held back by warriors of various sorts (some apparently fighting in offices, armored in Loro Piana wool), who are the creätors and maintainers of civilization and thus (like Hobbes' Leviathan) not truly bound by the rules of civilization (though it is admitted that it is generally good policy for them to conform to those rules most of the time). And, within this ideology, it is not just in dealing directly with the barbarian (the enemy combatant) that the warrior is licensed — It is the Soldier, not the lawyer / Who has given us the right to a fair trial. The Soldier giveth, and the Soldier taketh away.

And, of course, as in the Middle Ages, those who have claimed the prerogatives that this ideology would grant to the warrior needn't actually have held back barbarians, or even tried to do so. They may, in fact, be more concerned to exploit the local population.

This mythology is also very much playing into the on-going Presidential election. The Republican nomination has been won by a man whose political career was founded upon military service, and who continues to be widely considered first-and-foremost as a soldier. Some conservatives have made it plain that they cannot abide by this man, but virtually all for reasons distinct from his performance as a soldier.