6. Nash Equilibrium, Evolution and Tradition

We began in Post 4 to discuss game theory, and it is traditional to place at the heart of game theory the concept of a Nash equilibrium. I will therefore explain what that means, then call into question whether the Nash equilibrium concept has any importance. Then I'll give my reason for thinking that Nash equilibrium is important after all, namely, that it's a simple placeholder for evolutionarily stable equilibrium, followed by a far-ranging romp through many illustrative examples. We'll learn a lot about history in the process, and gain some insight about the meaning, nature, and value of tradition.

First let me review what every trained economist or good undergraduate econ major knows about Nash equilibrium. (Begin review) John Nash is most famous for the concept of “Nash equilibrium,” in game theory. Nash equilibrium is defined as an outcome of a game, wherein all the players would choose to play the same strategy that they played, given what strategies everyone else played. Strategies can be “pure” or “mixed,” with mixed meaning probabilistic. Nash’s achievement was to prove that every game has a Nash equilibrium, if mixed strategies, in which the player randomizes and plays each available strategy with some probability, are allowed. Thus, the game Rock-- Paper-- Scissors has no pure strategy Nash equilibrium: whoever loses, wishes they played differently. But it has a mixed strategy equilibrium, namely, for each player to play Rock, Paper, or Scissors with ⅓ probability each. If player A plays this strategy, player B might as well play it too, and vice versa. If I roll the dice, play Rock, and lose, I might regret my bad luck, but not my strategy. And every game has such an equilibrium. (End review)

But does Nash equilibrium matter? Certain other concepts in game theory, such as the dominant strategy equilibrium, or the subgame perfect equilibrium of a sequential game, are clearly well-motivated, because it can be logically deduced that rational, self-interested players will play them. But not Nash equilibrium. Consider the following game:

Game 1. A Pure Strategy Nash Equilibrium that is Irrelevant

		PLAYER 2
		A	B	C
PLAYER 1	A	0, 100	100, 0	0, 0
	B	100, 0	0, 100	0, 0
	C	0, 0	0, 0	1, 1

Game 1 has only one pure strategy Nash equilibrium: C/C, highlighted in bold. (Throughout this post, I’ll use bold text to highlight Nash equilibria.) If Player 1 plays C, Player 2 wants to play C, and vice versa. Yet C/C is surely not the most likely outcome of the game! If Player 1 thinks there’s even a small chance that Player 2 will play A or B, he will play B or A, respectively, in the hopes of a payoff of 100 instead of 1. Likewise, if Player 2 thinks Player 1 might play A or B, he will try to do the same, to get a payoff of 100. Given that even a small probability of the other deviating will cause each player to deviate, it’s hard to see how the level of certainty required for the C/C outcome to become rational could be established or maintained.

Game 1 also has a “mixed strategy” Nash equilibrium, in which Players 1 and 2 both play A or B with 50% probability. That’s a far more plausible outcome. But never mind that for now. I’m more interested in establishing what exactly is wrong with C/C. To say that it's unlikely to occur must involve some judgment about the likely beliefs on the part of each player about the likely decision of the other player. Where could such beliefs come from? The obvious answer, indeed almost the only one available (unless we think it can somehow be deduced a priori) is “experience.” But experience of what? NOT, it turns out, experience of what THIS player does in similar situations, for that would make this a repeated game, and a repeated game is a different game. For Game 1 to be a correct description of an interaction, this has to be a one-off interaction. Experience, then, means experience of people generally.

If you were told to play this game with a stranger in a laboratory experiment, you would have to guess, based on your numerous but not very similar interactions with all manner of people in the course of your life, what this person is likely to do. Your inexperience with this game probably wouldn't make it hard for you to decide not to play C, but would make it hard to describe your reasons for not playing C. But it's more interesting to imagine Game 1 as representing a typical situation in some abstract world, since typical situations that occur again and again are generally more important than exceptional ones that occur once. In that case, Player 1 and Player 2 have played this game many times before, albeit not with each other, and have heard about many instances of the game secondhand, so they know what to expect. Two possibilities, then, can be distinguished:

1. In every instance, or almost every instance, of Game 1 they have experienced or heard of, everyone has played C.
2. They know of quite a few instances of deviation from C.

Now, in case (2), the players’ course is clear: don't play C. And by not playing C, they'll reinforce future players’ expectation that C isn't the only move that can occur. But even in case (1), though C seems by far the likeliest move for the other player to make, one player or the other or both might think it's just possible that the other player will deviate, and the payoff of 100 might be attainable. And they'll risk deviating. Then other players will see the deviation and adjust their expectations. Pretty soon, the population will shift to case (2), and the C/C outcome will disappear.

At this point, it's helpful to introduce a new term: evolutionarily stable equilibrium. That's what C/C fails to be, and that's why C/C is not very interesting. It is a Nash equilibrium, but it's not evolutionarily stable, so we should expect it, probably not to occur at all, certainly not to be lastingly dominant.

It turns out that, while not every Nash equilibrium is evolutionarily stable, every evolutionarily stable equilibrium is Nash. And I think that is why Nash equilibrium matters in the first place. The fact that each player would play the same way given that the other player plays as they do doesn't matter in itself, because in all the interesting cases (namely when play is simultaneous so that the players can't observe the other’s move before they move) the information about what the other player plays isn't available in time to be taken into account. So while Nash equilibrium vaguely seems connected to rationality, you can't really claim that Nash equilibrium play is specially rational unless you interpret the game as a frequently occurring social interaction and the Nash strategies as customary or instinctive behavior. Which is as much as to say that Nash equilibrium is irrelevant unless it is regarded as a placeholder for evolutionarily stable equilibrium.

One might ask, then, why settle for a placeholder? Why not just go straight to evolutionarily stable equilibrium and drop Nash from the curriculum? The reason is that Nash is much easier to define and apply. In fact, while I grasp the concept intuitively and can come up with plenty of examples, I couldn't give a logically precise definition of evolutionarily stable equilibrium. I'm not sure it's possible to define the concept with a clarity and exactitude comparable to that with which Nash equilibrium is defined. The concept has been around since John Maynard Smith in the 1970s, and I'm sure many attempts have been made, and in spite of my fierce manifesto in the first post that we must have zero tolerance for anyone who tries to take away our license to think by saying “you don't know the literature,” which I here reaffirm, in this case, I do wish I knew this literature, and could fairly assess how many attempts there have been to define evolutionarily stable equilibrium, how much the definitions differ, how well they work, whether there is any consensus, and so on. But I feel quite safe in saying that evolutionarily stable equilibrium can't be as simply defined and applied as Nash. And so for the remainder of this post, I'll write down a series of games, point out the Nash equilibria, interpret them as evolutionarily stable equilibria, and in the process shed a great deal of light on why the world in which we live is the way it is.

My first example, left-side vs. right-side driving, is of only minor importance, but is a good way to illustrate the concept because it is extremely lucid. Why do some countries drive on the left side, others on the right side of the road? For no reason at all, except that left-side and right-side driving are the evolutionarily stable outcomes of Game 2, the Driving Game, represented abstractly below:

Game 2. The Driving Game

		DRIVER 2
		Drive on left	Drive on right	Don’t drive
DRIVER 1	Drive on left	8, 8	-100, -100 (Crash!)	8, 0
	Drive on right	-100, -100 (Crash!)	10, 10	10, 0
	Don’t drive	0, 8	0, 10	0, 0

The Driving Game has two Nash equilibria: one where everyone drives on the right side of the road, and another where everyone drives on the left. Each Nash equilibrium in the Driving Game is evolutionarily stable, because once the practice of driving on the left or right side of the road is established, it's in everyone's interest to follow it. Such practices are, of course, required by law, and these laws are appropriate, because to deviate from the dominant local practice, to drive on the right side of the road in Britain or the left side in the US, is willfully to endanger the lives of others. Yet the laws probably don't matter much, because the “spontaneous order” of everyone doing what's in their own self-interest would almost certainly suffice to produce the same outcome.

“Spontaneous order” is a favorite concept of economists; Adam Smith’s phrase for it was “the invisible hand.” The market, as represented by the classic supply-and-demand curves, is the usual paradigm case. But left-side vs. right-side driving is an even clearer example, and in general, evolutionarily stable equilibria are not only instances of spontaneous order, but are, I suspect, the biggest reason why the concept of “spontaneous order,” or “the invisible hand,” appeals to or intuitions once it is introduced and understood.

Yet economists, far from identifying “spontaneous order” with tradition, tend, if anything, to see the two as opposed. Their habitual attitude is to want to set people few from the restraints of tradition, to pursue all the opportunities that market capitalism offers. And sometimes this is a good thing to do, for traditions may be obsolete or may have been corrupt from the beginning. But let left-side vs. right-side driving stand as a proof of concept for the principle that it can be highly destructive to liberate people from their traditions! Tradition, among other uses, enables people to interact with strangers, or even in a sense to render someone you have never met not a stranger because they are a member of your culture and share your traditions. As left-side driving permits Britons to avoid physical collisions, rules of politeness allow many people to avoid moral collisions which might be almost as disastrous.

The Driving Game differs from the classic supply-and-demand model in that there are multiple equilibria in the Driving Game, as a result of which history matters. There must be some historical explanation why Britain drives on the opposite side of the road from France and the US. Perhaps there were no norms at all in the Stone Age about which side of the road travelers should use, and almost certainly, there were times when nothing like a government had made anything like a law about it. That said, the logic of having everyone use the same side of the road makes sense without modern transportation, for pedestrians and people on horseback also want to avoid collisions. But it's far less IMPORTANT if everyone is walking, for collisions are less probable and dangerous. Automobiles make it a matter of life and death that everyone conform to the practice at all times, where in an age of pedestrians the consequences of deviation and difference would have been much less dire. And so it seems likely that at some point in the past, such practices were less widespread and rigidly mandatory than they are today, and that the arrival of the automobile caused whatever the prevailing local practice might have been to be far more rigidly observed by all. I have read that left-side traffic patterns originated in a dangerous age when travelers on foot, and carrying swords, wanted to have their swords ready to leap into their hands should trouble arise, and preferred to have their more dexterous right hands nearer to their potential enemies. I have read that right-side driving originated at a time when carriage drivers wanted to hold the reins in the middle of the carriage with their right hands, while watching the middle of the road. Such old rationales for left-side vs. right-side driving are long obsolete and largely forgotten, yet the practices they originated are highly stable, and favorable to the general welfare, long after the reasons for these traditions have vanished. Custom can seem very arbitrary and irrational, and yet be very useful, too.

Now, I drew the two Nash equilibria in the Driving Game as unequally desirable. I'm not sure whether driving on the left vs. the right affects road safety, but if nothing else, Britain’s left-side driving interferes with international trade in automobiles, since cars made for other places and having the steering wheel on the left side are somewhat unsafe on British roads. So it would probably be advantageous for Britain to switch to right-side driving. But the transition would be very difficult to manage! Unless it were extremely coordinated and sudden, it would involve a transition period during which some Britons drove on the left side and some on the right, probably resulting in many fatal car crashes.

Left-side driving happens to be a very clear example of a phenomenon that is usually harder to see because it is muddled up with other issues, namely, the value, stability, and possible suboptimality of all manner of norms, standards, conventions, fashions, protocols, traditions, practices, and habits. Americans and Europeans use different systems of measurement (metric vs., er, English? Is that what you call pounds and feel and miles, etc.? Also Celsius vs. Fahrenheit) and different types of voltages and plugs, to the annoyance of Americans traveling in Europe with appliances from home. Tipping practices differ from country to country. In some places, it's easy to find public restrooms for free, which is nice, whereas in other places you pay, which is annoying, but better than having no restroom at all, which also sometimes happens. In some places, hikers and hunters can walk on land that is private but undeveloped, in others they can't. And homeownership rates vary from place to place, even for a given level of GDP per capita, and marriage practices, and ideas about politeness, and people dress differently, and listen to different music. In some places, shoes can't be worn in the house, in other places they can. I am not saying that all these practices are as arbitrary and accidental as left-side and right-side driving, but one possible explanation, counterintuitive at first, but always available as a candidate explanation for during practice once the logic of it is understood, is that it's rational to do it when everyone else does it, so whatever accident might have set a society into one track has limitless staying power. Or in other words, differences in traditions and customs may have no reason at all except that there are multiple evolutionarily stable Nash equilibria.

Above all, people speak different languages. Languages have more or less the same communicative power, and while people may have preferences for the phonology of a language that rolls its r’s or has the th sound, or think a particular grammatical device, such as the to, chto construction in Russian, is especially nifty, or like some aspect of a language’s vocabulary, such as the four words for “love” in Greek (eros, philia, storge, and agape), ultimately any thought can be expressed in any language, and if anyone is hampered in their intellectual development by having one native language rather than another, that is because not all the world's books and blogs have been translated into that language, not because they couldn't be. Language matters for the economy, though not in the sense that speaking English is a necessary or sufficient condition for individuals and countries to flourish. Plenty of non-English speaking countries, Japan and Germany for example, are wealthy, while the widespread proficiency in English that India enjoys has not made it rich. But English is an economic asset to many people and countries, and there is a strong economic imperative for educated elites around the world to acquire it, and it's at least plausible that the Czech Republic, for example, would benefit by forgetting Czech and making English its national language. This scenario can be described, again, as the Nash equilibrium of a game:

Game 3. The Language Game

		SOCIETY
		Speak French	Speak English
INDIVIDUAL	Speak French	90, 90	0, 0
	Speak English	0, 0	100, 100

The Language Game looks almost the same as the Driving Game, except that I've labeled the players “individuals” and “society,” which complicates the interpretation. The Driving Game makes sense as a game between two drivers. Given that I expect the next driver I see to be on the right (left), I should drive on the right (left). It's because I live in a right-side driving society that I expect the next driver to be on the right, but beyond that, I don't need to bring society into it to make sense of the game. In the Language Game, though, I cannot speak English in a given encounter unless I have learned it, not be understood, unless my interlocutor has learned it, and if we both know French better, it's in both of our immediate interests to speak French, whatever the surrounding society does. The game makes sense only over the life cycle. Raised in France, a person becomes a French speaker, and it's in their interests to do so in order to talk to everyone around them, even though France might be better off if the whole society have up speaking French and learned English.

While some people are loyal to some languages over and above their practical usefulness, language isn't really a moral issue. But the logic of Nash-as-evolutionarily-stable equilibrium can shed light on issues of great moral importance indeed. Game 4 purports to describe religion in the same way as language, that is, an evolutionarily stable Nash equilibrium in a society-wide game, where it's in everyone's interest to conform to the prevailing religion.

Game 4. The Religion Game

		SOCIETY
		Be Catholic	Be Protestant
INDIVIDUAL	Be Catholic	90, 90	0, 0
	Be Protestant	0, 0	100, 100

Of course, this game is rather insulting to devout religious people, who would say that they worship as they do from genuine conviction, not simply because it's advantageous to conform to society. And history is obviously full of examples of religious people who first embraced and/or firmly adhered to a religious faith when it was very much not in their worldly interests to do so. The Christian martyrs in the pagan Roman empire are the outstanding example. Yet for every devout religious believer, there seem to be several religious slackers who can't be bothered to do basic religious duties like showing up to church, yet who still self-identify as belonging to some religion, and may gain a certain esteem, or avoid a certain social ostracism, and who may be able to marry people they otherwise couldn't, because they say they're Lutheran or Catholic or Mormon or whatever. Game 4 may be help explain why this kind of lukewarm, conformist religion persists.

Corruption is another area where different societies exhibit different equilibria, and Game 5 may shed light on the reasons why. According to this abstract representation, a citizen and official each choose honest or corrupt behavior. Corrupt behavior consists in the citizen offering, and the official receiving, a bribe to do something that is inconsistent with the law but in the citizen’s interest. The transaction benefits them both. However, if either of them decides to be honest and report the other’s corruption, the effect is disastrous for the one caught offering, or seeking, illegal bribes.

Game 5. The Bribery Game

		OFFICIAL
		Try to get a bribe	Be honest
CITIZEN	Try to bribe	10, 10	-100, 0
	Be honest	0, -100	0, 0

Now, law and policy can of course affect the payoff structure of the corruption game, and make it more likely that the bribe will occur, or not. But the striking thing about Game 5 is that it shows why there are multiple equilibria even if the payoff structure remains the same. What about evolutionary stability? Honesty is clearly stable, because deviation from it when it is the prevailing behavior is disastrous. Corruption is less stable, because if anyone suddenly turns honest, they're likely to spook others into honesty as well. The model suggests, then, that societies might flip from corrupt to honest equilibria, and I think this is actually what has historically happened in countries like Great Britain in the early 19th century. Be that as it may, the subtle and perhaps surprising point here is that national differences in corruption vs. honesty may be explained neither as reflecting differences in virtue, nor as differences in institutional design, but simply as a kind of accidental landing on different stable states in a game with multiple equilibria.

The topic of corruption might make this a good moment to mention that multiple equilibria can supply the basis for an argument for revolutionary change. “We're stuck in a bad equilibrium!” the revolutionist proclaims. “But there's a better equilibrium available! Let's overthrow the system and remake society!” Often the revolutionist is wrong, and the new society he envisions either isn't an evolutionarily stable equilibrium, or isn't better than the current one. Also, society may never attain the better equilibrium, or the damage done along the way may be greater than the benefit of the change achieved. But while revolution is usually a bad idea, history clearly shows that revolutions can occur, and can dramatically and swiftly change societies.

Indeed, when I look back over the landscape of modern revolutions, it seems to me that the perception that a society is stuck in a bad equilibrium, and the desire to jump to a better one, is indeed a major motive of revolutionaries. One might overthrow a king, in order to install another long, simply because the king is unjust or weak. That is usurpation, not revolution. But a revolutionist overthrows kingship, changes not just who wields power but how power is wielded, targets not so much the ruler as the constitution, and hopes to establish a new situation not just for the life of a new ruler or dynasty, but permanently. To have such ambitions, one needs a notion of an alternative system, and as far as I can tell, history’s revolutionaries have derived their notions from any or all of four sources: (a) ideology, (b) religion, (c) tradition or the memory of the past, and (d) foreign models. The last element on the list may seem surprising, yet if anything, I think it's the most important of all. Revolution has usually taken place in countries that were keenly and bitterly aware of being backward, that is, left behind by progress, and stubbornly inferior to the world's leading countries and usually, more particularly, to some neighbor or rival. Thus, France in 1789 was frustratingly inferior, in liberty, prosperity, and military and imperial success, to Great Britain, and its philosophes (figures like Voltaire and Diderot were not quite philosophers) had been noticing that for at least a generation. Again, Russia in 1917 was frustratingly inferior to western Europe and to Germany in particular, and keenly aware of the fact. Mexico in 1911 was uncomfortably aware of its inferiority to the United States. Perhaps the clearest case of a revolution inspired by foreign models is the Meiji Restoration, which attempted comprehensively and deliberately to transform Japan into a Western, European-style society, and was strikingly successful in the long run, albeit Japan got off track under the military regime in the 1930s, and is still culturally alien to an astonishing degree in spite of all its economic success. The French and Russian revolutions, by contrast, went through phases where they were trying to overcome national backwardness by emulating foreign models: in its early days, the French and Russian Revolutions seemed to be creating constitutional monarchies like Great Britain’s. Then the momentum of revolution carried them further, which makes sense in a way, for if you're going to go to all the trouble of revolution, why not aim, not just at the best institutions anyone has managed to implement, but at the best institutions ideology can conceive of? Unfortunately, the best institutions that ideology can conceive of might be infeasible because of the moral inadequacy of human nature, and my next example will provide a proof of concept for this. Lest the point be overlooked, however, let me add here that a bad but evolutionarily stable equilibrium can often be overcome by passing a law, or even through an organized campaign of moral suasion, and to attempt this is generally wiser than making revolutions. And for the past century or so, those aspiring to transform society seem to have been learning this lesson, and are increasingly likely to pursue social change through legislative action, lawsuits, or moral suasion, rather than through violent revolution. The feminist and gay rights movements are notable examples.

So far, I have studied cases where the optimal outcome is a Nash equilibrium. But in other cases, the Nash equilibrium outcome(s) is (are) clearly inferior to some other outcome which is available only if people do not act in a strictly self-interested fashion. To state my meaning precisely will require introducing a new term: Pareto-superior. To say that outcome A is superior to outcome B means that everyone without exception either prefers outcome A to outcome B, or is indifferent. Similarly, Pareto-improvement means a movement to a Pareto-superior state; and Pareto-efficient and Pareto-optimal describe a state than which no Pareto-superior outcome is feasible. Sometimes no evolutionarily stable Nash equilibrium is Pareto-efficient, for example in Game 6 below.

Game 6. The Bargaining Game

		BARGAINER 2
		Hard	Mixed (⅓ hard, ⅔ soft)	Soft
BARGAINER 1	Hard	0, 0	80/3, 20/3	50, 10
	Mixed (⅓ hard, ⅔ soft)	20/3, 80/3	80/3, 80/3	110/3, 80/3
	Soft	10, 50	80/3, 110/3	30, 30

In this version of the Bargaining Game, there is only one evolutionarily stable strategy, namely, a mixed strategy in which people play the hard bargainer ⅓ of the time and play the soft bargainer ⅔ of the time. Hard bargainers get most of the gains when they deal with soft bargainers, but nothing when dealing with each other. Soft bargainers share gains evenly when dealing with each other, and accept relatively bad, but still moderately profitable, deals when dealing with hard bargainers. Since 80/3 is less than 30, society is better off if everyone plays the soft bargainer all the time, but unfortunately, the more soft bargainers there are, the more is the incentive to be a hard bargainer and take advantage of everyone else’s meekness. In this case, revolution doesn't work: the soft-bargaining utopia can't be implemented, but will be shipwrecked on the rocks of people's self-interest. And yet a campaign of moral suasion just might induce everyone to be a soft bargainer, seeking to benefit the other party as much as themselves in any business deal! That would make the world of Game 6, and perhaps the real world too, a better place.

Evolutionarily stable equilibria are, by definition, broadly embedded in people's habits, but their foothold in human conduct may be either CULTURAL or GENETIC. Of course, they might be both. That is, habits may reflect cultural learning and imitation, or they may reflect older evolutionary adaptations to Stone Age environments, and be rooted, not only in our educations, but in our genes and our instincts, or they might have some instinctive basis but be reinforced and trained by culture. If the Bargaining Game above describes situations that occur only in relatively recent times, then it is reasonable to assume that our propensity for occasional hard bargaining is inculcated by culture alone, and not embedded in our instinct. If, by contrast, situations like that described by Game 6 regularly occurred in Stone Age times, biological evolution is likely to have endowed us with an instinct to be agreeable much of the time, but occasionally to drive a hard bargain.

But a clearer example of an evolutionarily stable equilibrium that is written into human genes and expressed in human instincts is hunter-gatherer specialization. I am no expert in the lifestyles of prehistoric mankind, but from what I understand, it is generally agreed that for tens of thousands of years before the dawn of agriculture, humans made their livings as hunter-gatherers, collecting fruits and nuts and roots and leaves from plants, and killing wild beasts for food. More specifically, the MEN hunted wild beasts, while the WOMEN gathered fruits, nuts, and other edible plant matter. This gender specialization gave prehistoric mankind a fairly balanced diet. Or perhaps it would be more accurate to say that we perceive an omnivorous diet with some meat and a wide variety of plant matter to be a balanced diet, because that's the diet our Stone Age ancestors ate, for a long enough period for human physiology to adapt to it and come to like it. However, there are doubtless nutritional benefits to this diet even relative to a more indeterminate human nature, which caused the hunter-gatherer lifestyle and the resulting omnivorous lifestyle to reward people who adopted it with greater evolutionary fitness and an expanding share of the gene pool, after which human appetites and instincts honed human nature to be a better and better fit for the hunter-gatherer way of life.

Game 7 elucidates the game-theoretic logic of hunter-gatherer gender specialization. I assume a monogamous, stable, husband-and-wife couple. (This assumption will be repealed in later posts.) That has evolutionary benefits for sexual and childrearing reasons, to which we'll return. Hunting tends, I believe, to be a less reliable producer of calories than gathering, so I gave a low payoff of 3 to the case where husband and wife both hunt. But meat also provides certain desirable nutrients that a gathering-only livelihood would make painfully scarce, so the case where both gather gets almost as low a score as the case where both hunt. If the wife hunts and the husband gathers, the household does better, but this is suboptimal because the wife will often be pregnant or nursing, which is a bad fit with a hunting lifestyle. It works much better for pregnant women and nursing mothers to do the gathering than the hunting. Also, hunting is dangerous, and if one spouse is to die, it had better be the husband, since unborn and nursing children may then survive. So the highest payoffs come when the husband hunts and the wife gathers.

Game 7. The Hunter-Gatherer Game

		WIFE
		Hunt	Gather
HUSBAND	Hunt	3, 3	10, 10
	Gather	8, 8	5, 5

Now, readers of my post on sociobiology will already know that this analysis of the economics of the hunter-gatherer lifestyle is relevant, not because I want to give advice to hunter-gatherers, but because we have good reason to think that the nature of modern humans is still adapted, at the level of genes and instincts, to hunter-gatherer gender specialization. And once you start reviewing human conduct for evidence for this theory, all sorts of hitherto inexplicable behavioral patterns leap up to present themselves as evidence. Hunting in the literal sense is no longer a livelihood for many people, but it is a pastime for many people, the vast majority of them men, who in spite of their modern gear are doing just what their Stone Age instincts demand. Gathering, meanwhile, has its modern equivalent, shopping; and just as the theory would predict, shopping is overwhelmingly a female pastime. Men have to shop sometimes in order to acquire needed goods, but if someone spends the whole day shopping just for the fun of it, that person is almost certainly a female, acting on the gathering instincts of her Stone Age ancestors. Men like to play sports, which resemble in some ways the Stone Age hunt: they are physically strenuous activities, requiring teamwork and skill, ending in well-defined success or failure. Women sometimes enjoy sports as well, of course, but not as much as men. War, too, resembles Stone Age hunting, not only in involving teamwork and skill, but also in its violence and the shedding of blood, and of course, war has been, throughout all history, an overwhelmingly male activity. When men aren’t actually fighting wars, they are much more likely to seek to enter imaginatively into the experience of war, through video games and action movies, than women are. Meanwhile, women, who in the Stone Age would typically have stayed nearer to the camp and disproportionately looked after it, seem generally to have more of an instinct for domestic cleanliness than men do.

By the way, while feminists tend to see all womankind before feminism as a vast victim class, women have arguably been happier in their lot, in that the life the typical woman has led since the birth of agriculture is probably more like the Stone Age gatherer-cum-mother lifestyle to which she is adapted. For men, by contrast, the birth of agriculture meant that their natural love of comradely adventure culminating in lethal violence, once innocent and useful, became wicked and destructive, and much more dangerous too. Hunting, once the general vocation of men, became by medieval times the privilege of the nobility, while peasant men had to spend their days digging in the dirt and weeding. A Stone Age hunter wearing blue jeans in suburbia has more impulses that must be overridden, lest they ruin him, than does a Stone Age gatherer in a skirt.

A final example of evolutionarily stable equilibrium is the breadwinner-homemaker gender specialization which, though it has gone somewhat out of fashion in the past few decades, seems to have been a widespread feature of the experience of civilized humanity all over the world, and has been especially characteristic of the fastest-growing economies of the West since the Industrial Revolution. It seems, moreover, to have much the same game-theoretic logic as does Stone Age hunter-gatherer gender specialization. A household’s work may be reasonably divided into two large functions, hunting and gathering in the Stone Age case, breadwinning and homemaking in the modern capitalist economy. Both tasks are done best by someone who is prepared for them well in advance. In youth, men and women don't know who they'll be paired with, but women know they'll be paired with men, and vice versa, so it's best to develop a skill set complementary to that which the other gender tends to have. So men, once trained for the hunt, are now groomed for jobs and careers, while women, formerly gatherers, were until lately encouraged to learn to cook and clean, marry and rear children, and make homes comfortable and pleasant. In the best case, specialization benefits both sexes, since all market work and no housework would leave people with messy houses, no home cooked meals, and an insoluble conundrum about how to take care of kids, while all housework and no income would leave households unable to meet basic material needs. Given specialization, it is advantageous to couple the pregnancy and childrearing that biology assigns to women with the homemaking function, and leave market earning, which is much less amenable to being combined with childrearing, to the men, who are more dispensable at home.

The big difference is that capitalism, and breadwinner-homemaker gender specialization in a capitalist economic framework, hasn't been around long enough for human nature to have adapted to it. In particular, no human is all that well adapted by nature to working a factory or an office job, since no one did that in the Stone Age. Hunting persists as a beloved pastime long after it has become superfluous to subsistence, but it's not likely that anyone will work on an assembly line or sit all day at a desk if the evolution of technology and the economy renders such activities needless for earning a living. Which, by the way, is one way to rebut the excessive optimism of many economists about modernity: yes, we live longer and have more stuff, but the revealed preference of the modern hobbyist shows, as sociobiology would predict, that people like doing the things by which they made their livings in the past, in a way that few of any of its naturally like the sorts of activities by which most of us have to make our livings today. Anyway, modern breadwinner-homemaker specialization isn't merely instinctive; it must be chosen through reason and/or inculcated by culture. Industrial societies have had to work hard educating men, in particular, to be very different, more docile and disciplined and conscientious, than their instincts want them to be. It then offered them, until recently, domestic felicity as a reward for being a gentleman.

Yet there may nonetheless be some instinctive basis for modern breadwinner-homemaker gender specialization, to the frustration of feminists who would like to erase it from the face of the earth, yet find that it is stubbornly persistent among much of the population, while the more gender-egalitarian lifestyles they would like to promote are less attractive and stable. I mentioned the female love of shopping already. What about men? Do the factory or the office provide at least some of the pleasures of the old Stone Age hunting ground? I suspect they do. If nothing else, commuting-- regularly going far from home and then returning, as part of making a living-- is a bit like what the Stone Age hunter would have done in search of prey. The assembly line is miserable drudgery, but some corporate management teams have the audacious and competitive spirit of Stone Age hunting bands. It has recently been famously argued by James Damore of Google that technology work is more natural to men than women, and that (and not discrimination) explains the predominance of men in tech. We'll see later some reasons to think it's pleasurable for a woman to see her husband work all day long for the maintenance of herself and her children, and for a man to have his wife safe and secure all day long in his house. Human instincts will never feel quite at home in industrial capitalism, but given that breadwinning in offices and factories, or homemaking and childrearing in suburbia, are the options, instincts would make men choose me breadwinning, while some or most women opt for homemaking.

I didn't bother to write down the payoffs to the modern breadwinner-homemaker game, because they would have been identical, in rank and strategic implications, to those of the Stone Age hunter-gatherer game. But since breadwinner-homemaker gender specialization seems to have been breaking down over the past generation or so, I thought it might be interesting to offer a game-theoretic model of why. I’ll start with three assumptions:

1. The natural preferences of men and women are somewhat favorable to breadwinner-homemaker gender specialization, which I model by giving husbands a +2 to their payoff for being breadwinners, and wives +2 for being homemakers.
2. Breadwinner-homemaker specialization confers a big advantage in that it supplies money income to purchase market goods, and also meets the household’s need for childcare and other domestic productive activities like cooking and cleaning. So there’s a +5 to both spouses’ payoffs if they pick different roles.
3. Certain recent changes, such as the decline in social capital, the cushier jobs that the modern economy offers to most workers, and society’s decision to give less social esteem to housewives than in the past, have made breadwinning relatively attractive compared to homemaking. So any breadwinner gets +3 added to their payoffs.

The payoff structure resulting from these assumptions is shown in Game 8.

Game 8. The Breadwinner-Homemaker Game

		WIFE
		Be breadwinner	Be homemaker
HUSBAND	Be breadwinner	5, 3	10, 7
	(Mixed: P(breadwinner) < 0.6)	5, ≥5	≤6, ≤5
	Be homemaker	5, 8	0, 2

In Game 8, classic breadwinner-homemaker gender specialization is still the only strict Nash equilibrium. If the husband works and the wife stays home to take care of the kids, they’ll both be glad they did, given their options. But there’s another “non-strict” Nash equilibrium, which we might call the Mr. Mom outcome, where some or all husbands choose homemaking, while wives choose breadwinning. By a “non-strict” Nash equilibrium, I mean that one or more players-- in the Mr. Mom case, it’s the husband-- does not strictly prefer the Nash outcome to available alternatives, but is merely indifferent. Given that his wife is a breadwinner, the husband isn’t particularly glad if he opted to be a homemaker, but he doesn’t quite regret it either. He’s indifferent. The advantages of extra money and status from breadwinning exactly balance the advantages of having someone-- unfortunately himself-- on hand full-time to take care of the kids. If a woman thinks there's a 0.6 probability or less that her husband will be a breadwinner, she becomes a breadwinner. And with the payoffs shown here, she actually slightly prefers the outcome where she's the breadwinner and her husband stays home. And if a man is certain that his wife will be a breadwinner, he might choose, without much conviction and a bit reluctantly, to stay home. Nonetheless, the Mr. Mom outcome doesn't look very evolutionarily stable, since even if a man is certain that his wife will work, he is no better than indifferent between Mr. Mom and working, and if he thinks there's a possibility that he'll marry a woman who stays home, then he'll definitely want to be a breadwinner.

We may be, this model suggests, in an unstable historical moment, where feminism, by stigmatizing traditional breadwinner-homemaker gender specialization as intolerably “patriarchal,” and thereby weakening men's commitment to full-time, lucrative, career-oriented work, has caused a massive rise in labor force participation by women, which is partly ideological, based on a belief that women should work, and partly defensive, since they feel they can't rely on men to be breadwinners, and that the Mr. Mom outcome is attainable, so they chase careers. Expect the next generation to learn a couple of lessons. First, men will realize that for them at least, a good career is the best way to flourish. There's really no reason for them to consider the Mr. Mom alternative. Second, women will see the downside of juggling a job and kids, and especially if they see more men stepping up and being good breadwinners, more of them will opt to be housewives, even if they'll still envy their husbands a little and regard the arrangement as a little bit unfair.

These predictions are meant only half-seriously, since this model is full of holes and is only meant as a suggestive placeholder for a richer analysis of the household in later posts. One feature of the model that will feel odd, however, is intentional and insightful. It is that husbands and wives make independent choices about breadwinning and homemaking. They do not coordinate or negotiate. Of course, in real marriages, husbands and wives do negotiate and coordinate, but there is an important sense in which breadwinning and homemaking are choices made before marriage, which are costly and awkward to revise later. On the breadwinning side, expensive education financed by student loans may bind a person to career path for years or decades. People get accustomed to lifestyles involving a certain level of income, and may neglect to acquire home repair or cooking skills that they would need in order to live on less money. People come to enjoy career activities and take pride in career milestones, and their professional networks become their social circles. On the homemaking side, people become attached to a different set of activities and friends, whom they would miss by working, and also, while one can enter the workforce at just about any time of (adult) life, you may have to start at the bottom, making far less than professionals at career peak, and not enough to contribute that much to a household budget. People could, of course, select marriage partners on the basis of economic complementarity, with breadwinners of each sex looking for homemakers of the other sex, but (a) as one gets older, one meets people more and more similar to oneself, and breadwinner types are less likely to meet homemaker types, and (b) it's a bit sad to marry for economic reasons. It's not only more romantic, but probably more realistic too, at least in contemporary societies, to treat falling in love as an exogenous factor that will determine who marries whom regardless of economic situations. So while husbands and wives sometimes can change course ex post to achieve complementarity, to do so is so costly that they probably can't regain much of the payoff that was lost because the work of making them economically complementary was not done in advance by socially prescribed differentiation of functions by gender. But again, all this is only half-serious.

This post has covered a lot of ground in a rather casual and unrigorous way, yet it would be unsatisfying and a bit disingenuous for me to conclude by apologizing and saying that, after all, I'm just illustrating the concept of evolutionarily sustainable Nash equilibrium with a series of examples, which may all be taken with a grain of salt. I care about my examples, and I think most readers will have learned something about language, and bargaining, and revolution, and perhaps-- especially if they started from a position of naive feminism-- even gender relations, which is worth remembering, and using to update their worldviews. I value rigor, but I think it's a bad principle, which unfortunately tends to be enforced by peer review and over-specialization, that one shouldn't theorize at all unless one can do it rigorously. An unrigorous formal theory that won't stand up well to critical scrutiny can still be a big improvement over no theory at all. For example, it is common nowadays, among people who should know better, to talk about the decline of breadwinner-homemaker gender specialization in an incredibly stupid way, as if housewives were completely useless, and the rise in female labor force participation in recent decades were an augmentation of the labor force at the expense of nothing but outmoded prejudices, with no opportunity cost at all. The clumsy, slapdash theory presented in Game 8 omits much, but it is a vast improvement over such silliness as that. In this process, I wanted to illustrate the sheer productivity and range of the concept of evolutionarily stable Nash equilibrium, and in the process I've learned about many other topics as well. But (and here's the point) I wasn't really “reinventing economics” in this post. Even if I were to refine such methods as I use here to the point where they constituted science rather than mere commentary, it wouldn't be continuous enough with the historic subject matter and methods of economics to deserve the name. I'll circle back to the core subject matter of economics a few posts from now. For now, I'm just warming up, providing context, and equipping us with a useful methodological "toolkit."

Finally, some may object to this post that it tends to promote gender “stereotypes.” The best definition I can offer for the word “stereotype” is a generalization at which someone chooses to take offense, and that definition will hint at my lack of sympathy for the contemporary crusade against stereotypes. Stereotype is a word we would be better off without, because it is indelibly stained with unjust connotations, and its use spreads the false view that anyone, in theory, or in practice an arbitrary list of protected categories of people, ought to be able to veto the use of any generalization applicable to themselves that they don't happen to like, regardless of its truth or usefulness. That said, while the reaction against stereotypes is excessive, it began as the remedy for a real injustice, namely, the too hasty and final imputation of traits, or assignment of roles, to individuals on the basis of their membership in various groups. People’s individuality is important, and while “statistical discrimination” is too useful to be abandoned altogether, it shouldn't be, if we can help it, an insurmountable barrier to individuals discovering their own talents, charting their own course, and pursuing excellence in their own way. I would be chagrined if my defense of breadwinner-homemaker gender specialization made some father go home and tell his daughters to abandon passionate aspirations to art or entrepreneurship.

There will probably be no more posts at this blog for about a month, as I need to catch up on some things. Come back in December!