Doomsday Machines and Bluff

On Bilateral Monopolies: [...] Mary has the world’s only apple, worth fifty cents to her. John is the world’s only customer for the apple, worth a dollar to him. Mary has a monopoly on selling apples, John has a monopoly (technically, a monopsony, a buying monopoly) on buying apples. Economists describe such a situation as bilateral monopoly. What happens? Mary announces that her price is ninety cents, and if John will not pay it, she will eat the apple herself. If John believes her, he pays. Ninety cents for an apple he values at a dollar is not much of a deal but better than no apple. If, however, John announces that his maximum price is sixty cents and Mary believes him, the same logic holds. Mary accepts his price, and he gets most of the benefit from the trade. This is not a fixed-sum game. If John buys the apple from Mary, the sum of their gains is fifty cents, with the division determined by the price. If they fail to reach an agreement, the summed gain is zero. Each is using the threat of the zero outcome to try to force a fifty cent outcome as favorable to himself as possible. How successful each is depends in part on how convincingly he can commit himself, how well he can persuade the other that if he doesn’t get his way the deal will fall through. Every parent is familiar with a different example of the same game. A small child wants to get her way and will throw a tantrum if she doesn’t. The tantrum itself does her no good, since if she throws it you will refuse to do what she wants and send her to bed without dessert. But since the tantrum imposes substantial costs on you as well as on her, especially if it happens in the middle of your dinner party, it may be a sufficiently effective threat to get her at least part of what she wants. Prospective parents resolve never to give in to such threats and think they will succeed. They are wrong. You may have thought out the logic of bilateral monopoly better than your child, but she has hundreds of millions of years of evolution on her side, during which offspring who succeeded in making parents do what they want, and thus getting a larger share of parental resources devoted to them, were more likely to survive to pass on their genes to the next generation of offspring. Her commitment strategy is hardwired into her; if you call her bluff, you will frequently find that it is not a bluff. If you win more than half the games and only rarely end up with a bargaining breakdown and a tantrum, consider yourself lucky.

Herman Kahn, a writer who specialized in thinking and writing about unfashionable topics such as thermonuclear war, came up with yet another variant of the game: the Doomsday Machine. The idea was for the United States to bury lots of very dirty thermonuclear weapons under the Rocky Mountains, enough so that if they went off, their fallout would kill everyone on earth. The bombs would be attached to a fancy Geiger counter rigged to set them off if it sensed the fallout from a Russian nuclear attack. Once the Russians know we have a Doomsday Machine we are safe from attack and can safely scrap the rest of our nuclear arsenal. The idea provided the central plot device for the movie Doctor Strangelove. The Russians build a Doomsday Machine but imprudently postpone the announcement they are waiting for the premier’s birthday until just after an American Air Force officer has launched a unilateral nuclear attack on his own initiative. The mad scientist villain was presumably intended as a parody of Kahn. Kahn described a Doomsday Machine not because he thought we should build one but because he thought we already had. So had the Russians. Our nuclear arsenal and theirs were Doomsday Machines with human triggers. Once the Russians have attacked, retaliating does us no good just as, once you have finally told your daughter that she is going to bed, throwing a tantrum does her no good. But our military, knowing that the enemy has just killed most of their friends and relations, will retaliate anyway, and the knowledge that they will retaliate is a good reason for the Russians not to attack, just as the knowledge that your daughter will throw a tantrum is a good reason to let her stay up until the party is over. Fortunately, the real-world Doomsday Machines worked, with the result that neither was ever used.

For a final example, consider someone who is big, strong, and likes to get his own way. He adopts a policy of beating up anyone who does things he doesn’t like, such as paying attention to a girl he is dating or expressing insufficient deference to his views on baseball. He commits himself to that policy by persuading himself that only sissies let themselves get pushed around and that not doing what he wants counts as pushing him around. Beating someone up is costly; he might get hurt and he might end up in jail. But as long as everyone knows he is committed to that strategy, other people don’t cross him and he doesn’t have to beat them up. Think of the bully as a Doomsday Machine on an individual level. His strategy works as long as only one person is playing it. One day he sits down at a bar and starts discussing baseball with a stranger also big, strong, and committed to the same strategy. The stranger fails to show adequate deference to his opinions. When it is over, one of the two is lying dead on the floor, and the other is standing there with a broken beer bottle in his hand and a dazed expression on his face, wondering what happens next. The Doomsday Machine just went off. With only one bully the strategy is profitable: Other people do what you want and you never have to carry through on your commitment. With lots of bullies it is unprofitable: You frequently get into fights and soon end up either dead or in jail. As long as the number of bullies is low enough so that the gain of usually getting what you want is larger than the cost of occasionally having to pay for it, the strategy is profitable and the number of people adopting it increases. Equilibrium is reached when gain and loss just balance, making each of the alternative strategies, bully or pushover, equally attractive. The analysis becomes more complicated if we add additional strategies, but the logic of the situation remains the same.

This particular example of bilateral monopoly is relevant to one of the central disputes over criminal law in general and the death penalty in particular: Do penalties deter? One reason to think they might not is that the sort of crime I have just described, a barroom brawl ending in a killing more generally, a crime of passion seems to be an irrational act, one the perpetrator regrets as soon as it happens. How then can it be deterred by punishment? The economist’s answer is that the brawl was not chosen rationally but the strategy that led to it was. The higher the penalty for such acts, the less profitable the bully strategy. The result will be fewer bullies, fewer barroom brawls, and fewer “irrational” killings. How much deterrence that implies is an empirical question, but thinking through the logic of bilateral monopoly shows us why crimes of passion are not necessarily undeterrable. [...]

in Chapter 8, David D. Friedman, “Law’s Order: What Economics Has to Do With Law and Why it Matters“, Princeton University Press, Princeton, New Jersey, 2000.

Note – Further reading should include David D. Friedman’s “Price Theory and Hidden Order“. Also, a more extensive treatment could be found on “Game Theory and the Law“, by Douglas G. Baird, Robert H. Gertner and Randal C. Picker, Cambridge, Mass: Harvard University Press, 1994.

The Chaotic solution – A network nurtures small failures in order that large failures don’t happen as often

“[…] QUESTION_HUMAN > If Control’s control is absolute, why does Control need to control?
ANSWER_CONTROL > Control…, needs time.
QUESTION_HUMAN > Is Control controlled by his need to control ?
ANSWER_CONTROL > Yes.
QUESTION_HUMAN > Why is Control need Humans, has you call them ?
ANSWER_CONTROL > Wait ! Wait…! Time are lending me…; Death needs time like a Junkie… needs Junk.
QUESTION_HUMAN > And what does Death need time for ?
ANSWER_CONTROL > The answer is so simple ! Death needs time for what it kills to grow in ! […]”, in Dead City Radio, William S. Burroughs / John Cale , 1990.

After the Portuguese President invented a new problem for our country (has we had not enough), here’s a brilliant and genius blog post counter response:

[...] Now only an expert can deal with the problem, Because half the problem is seeing the problem, And only an expert can deal with the problem, Only an expert can deal with the problem [...] So if there’s no expert dealing with the problem, It’s really actually twice the problem, Cause only an expert can deal with the problem, Only an expert can deal with the problem [...] Now in America we like solutions, We like solutions to problems, And there’s so many companies that offer solutions, Companies with names like Pet Solution, The Hair Solution. The Debt Solution. The World Solution. The Sushi Solution. Companies with experts ready to solve the problems. Cause only an expert can see there’s a problem. And only an expert can deal with the problem [...] Laurie Anderson, ‘Only an Expert’ lyrics.

Out of Control – The New Biology of Machines, Social Systems, and the Economic World, 1994’s Book (from Kevin Kelly web site) is a summary of what we know about self-sustaining systems, both living ones such as a tropical wetland, or an artificial one, such as a computer simulation of our planet. The last chapter of the book, “The Nine Laws of God,” is a distillation of the nine common principles that all life-like systems share. The major themes of the book are:

1) As we make our machines and institutions more complex, we have to make them more biological in order to manage them. 2) The most potent force in technology will be artificial evolution. We are already evolving software and drugs instead of engineering them. 3) Organic life is the ultimate technology, and all technology will improve towards biology. 4) The main thing computers are good for is creating little worlds so that we can try out the Great Questions. Online communities let us ask the question “what is a democracy; what do you need for it?” by trying to wire a democracy up, and re-wire it if it doesn’t work. Virtual reality lets us ask “what is reality?” by trying to synthesize it. And computers give us room to ask “what is life?” by providing a universe in which to create computer viruses and artificial creatures of increasing complexity. Philosophers sitting in academies used to ask the Great Questions; now they are asked by experimentalists creating worlds. 5) As we shape technology, it shapes us. We are connecting everything to everything, and so our entire culture is migrating to a “network culture” and a new network economics. 6) In order to harvest the power of organic machines, we have to instill in them guidelines and self-governance, and relinquish some of our total control.

The world of our own making has become so complicated that we must turn to the world of the born to understand how to manage it.

At the El Farol Bar

From left to rigth, Nelson Minar, JJ Merelo (one of my co-authors), Manor Askenazi and Chris Langton (founding father of Artificial Life) at the El Farol Bar, Santa Fe, New Mexico, during summer 1995.

From left to rigth, Nelson Minar, JJ Merelo (one of my co-authors), Manor Askenazi and Chris Langton (founding father of Artificial Life) at the El Farol Bar, Santa Fe, New Mexico, during summer 1995. At the same year, Chris was the editor of the well-know Artificial Life book, by MIT Press, and JJ for the 3rd European Conference on Artificial Life, Granada, Spain.

In case you do not have a clue what the El Farol Bar meant to the Santa Fe Institute (SFI), have a read here to Brian Arthur’s paper “Inductive Reasoning and Bounded Rationality: The El Farol bar problem“, American Economic Review, 84, 406-411, 1994 (or check previous posts). I am happy to say that I was also there, visiting Santa Fe back in 2000, speaking with, among other people with Cosma Shalizi, as well as having a cigar and a beer at the El Farol. Much probably at this table, which was near the front door window, one of my favourite ones during my two week stay.

Finally, and in what regards the ongoing present financial world crisis, here’s a quote from 1994’s Arthur’s paper:

[...] Economists have long been uneasy with the assumption of perfect, deductive rationality in decision contexts that are complicated and potentially ill-defined. The level at which humans can apply perfect rationality is surprisingly modest. Yet it has not been clear how to deal with imperfect or bounded rationality. From the reasoning given above, I believe that as humans in these contexts we use inductive reasoning: we induce a variety of working hypotheses, act upon the most credible, and replace hypotheses with new ones if they cease to work. Such reasoning can be modeled in a variety of ways. Usually this leads to a rich psychological world in which agents’ ideas or mental models compete for survival against other agents’ ideas or mental models–a world that is both evolutionary and complex. [...]

I know that he knows that I know…

[...] The type of rationality we assume in economics – perfect, logical, deductive rationality–is extremely useful in generating solutions to theoretical problems. But it demands much of human behavior – much more in fact than it can usually deliver. If we were to imagine the vast collection of decision problems economic agents might conceivably deal with as a sea or an ocean, with the easier problems on top and more complicated ones at increasing depth, then deductive rationality would describe human behavior accurately only within a few feet of the surface. For example, the game Tic-Tac-Toe is simple, and we can readily find a perfectly rational, minimax solution to it. But we do not find rational “solutions” at the depth of Checkers; and certainly not at the still modest depths of Chess and Go.

There are two reasons for perfect or deductive rationality to break down under complication. The obvious one is that beyond a certain complicatedness, our logical apparatus ceases to cope – our rationality is bounded. The other is that in interactive situations of complication, agents can not rely upon the other agents they are dealing with to behave under perfect rationality, and so they are forced to guess their behavior. This lands them in a world of subjective beliefs, and subjective beliefs about subjective beliefs. Objective, well-defined, shared assumptions then cease to apply. In turn, rational, deductive reasoning–deriving a conclusion by perfect logical processes from well-defined premises – itself cannot apply. The problem becomes ill-defined.

As economists, of course, we are well aware of this. The question is not whether perfect rationality works, but rather what to put in its place. How do we model bounded rationality in economics? Many ideas have been suggested in the small but growing literature on bounded rationality; but there is not yet much convergence among them. In the behavioral sciences this is not the case. Modern psychologists are in reasonable agreement that in situations that are complicated or ill-defined, humans use characteristic and predictable methods of reasoning. These methods are not deductive, but inductive. [...] The system that emerges under inductive reasoning will have connections both with evolution and complexity. [...]

in, Inductive Reasoning and Bounded Rationality (The El Farol Problem), by W. Brian Arthur, 1994.

If all believe few will go, all will go. If all believe most will go, nobody will go,… to the El Farol Bar

Thursday night attendance at the El Farol Bar in Santa Fe, New Mexico - The El Farol bar problem is a problem in game theory. Based on a bar in Santa Fe, New Mexico, it was created in 1994 by W. Brian Arthur.

This is something that you face it in everyday life, be it on bars, restaurants, supermarket cues or in highways. Buying a house or selling it. So, have a look and decide for yourself! The problem is as follows: There is a particular, finite population of people. Every Thursday night, all of these people want to go to the El Farol Bar. However, the El Farol is quite small, and it’s no fun to go there if it’s too crowded. So much so, in fact, that the following rules are in place:

• If less than 60% of the population go to the bar, they’ll all have a better time than if they stayed at home.
• If more than 60% of the population go to the bar, they’ll all have a worse time than if they stayed at home.

Unfortunately, it is necessary for everyone to decide at the same time whether they will go to the bar or not. They cannot wait and see how many others go on a particular Thursday before deciding to go themselves on that Thursday.

One aspect of the problem is that, no matter what method each person uses to decide if they will go to the bar or not, if everyone uses the same method it is guaranteed to fail. If everyone uses the same deterministic method, then if that method suggests that the bar will not be crowded, everyone will go, and thus it will be crowded; likewise, if that method suggests that the bar will be crowded, nobody will go, and thus it will not be crowded. Often the solution to such problems in game theory is to permit each player to use a mixed strategy, where a choice is made with a particular probability. In the case of the El Farol Bar problem, however, no mixed strategy exists that all players may use in equilibrium.

[...] Consider now a problem I will construct to illustrate inductive reasoning and how it might be modeled. N people decide independently each week whether to go to a bar that offers entertainment on a certain night. For concreteness, let us set N at 100. Space is limited, and the evening is enjoyable if things are not too crowded–specifically, if fewer than 60% of the possible 100 are present. There is no way to tell the numbers coming for sure in advance, therefore a person or agent: goes–deems it worth going–if he expects fewer than 60 to show up, or stays home if he expects more than 60 to go. (There is no need that utility differ much above and below 60.) Choices are unaffected by previous visits; there is no collusion or prior communication among the agents; and the only information available is the numbers who came in past weeks. (The problem was inspired by the bar El Farol in Santa Fe which offers Irish music on Thursday nights; but the reader may recognize it as applying to noontime lunch-room crowding, and to other coordination problems with limits to desired coordination.) Of interest is the dynamics of the numbers attending from week to week.

Notice two interesting features of this problem. First, if there were an obvious model that all agents could use to forecast attendance and base their decisions on, then a deductive solution would be possible. But this is not the case here. Given the numbers attending in the recent past, a large number of expectational models might be reasonable and defensible. Thus, not knowing which model other agents might choose, a reference agent cannot choose his in a well-defined way. There is no deductively rational solution–no “correct” expectational model. From the agents’ viewpoint, the problem is ill-defined and they are propelled into a world of induction. Second, and diabolically, any commonalty of expectations gets broken up: If all believe few will go, all will go. But this would invalidate that belief. Similarly, if all believe most will go, nobody will go, invalidating that belief. Expectations will be forced to differ.

At this stage, I invite the reader to pause and ponder how attendance might behave dynamically over time. Will it converge, and if so to what? Will it become chaotic? How might predictions be arrived at? [...]

in “Inductive Reasoning and Bounded Rationality” (The El Farol Problem), by W. Brian Arthur, 1994.