You are currently browsing the tag archive for the ‘Game Theory’ tag.
Fig. – A Symbolical Head (phrenological chart) illustrating the natural language of the faculties. At the Society pages / Economic Sociology web page.
You have much probably noticed by now how Scoop.it is emerging as a powerful platform for those collecting interesting research papers. There are several good examples, but let me stress one entitled “Bounded Rationality and Beyond” (scoop.it web page) curated by Alessandro Cerboni (blog). On a difficult research theme, Alessandro is doing a great job collecting nice essays and wonderful articles, whenever he founds them. One of those articles I really appreciated was John Conlisk‘s “Why Bounded Rationality?“, delivering into the field several important clues, for those who (like me) work in the area. What follows, is an excerpt from the article as well as part of his introductory section. The full (PDF) paper could be retrieved here:
In this survey, four reasons are given for incorporating bounded rationality in economic models. First, there is abundant empirical evidence that it is important. Second, models of bounded rationality have proved themselves in a wide range of impressive work. Third, the standard justifications for assuming unbounded rationality are unconvincing; their logic cuts both ways. Fourth, deliberation about an economic decision is a costly activity, and good economics requires that we entertain all costs. These four reasons, or categories of reasons, are developed in the following four sections. Deliberation cost will be a recurring theme.
Why bounded rationality? In four words (one for each section above): evidence, success, methodology, and scarcity. In more words: Psychology and economics provide wide-ranging evidence that bounded rationality is important (Section I). Economists who include bounds on rationality in their models have excellent success in describing economic behavior beyond the coverage of standard theory (Section II). The traditional appeals to economic methodology cut both ways; the conditions of a particular context may favor either bounded or unbounded rationality (Section III). Models of bounded rationality adhere to a fundamental tenet of economics, respect for scarcity. Human cognition, as a scarce resource, should be treated as such (Section IV). The survey stresses throughout that an appropriate rationality assumption is not something to decide once for all contexts. In principle, we might suppose there is an encompassing single theory which takes various forms of bounded and unbounded rationality as special. cases. As with other model ingredients, however, we in practice want to work directly with the most convenient special case which does justice to the context. The evidence and models surveyed suggest that a sensible rationality assumption will vary by context, depending on such conditions as deliberation cost, complexity, incentives, experience, and market discipline. Beyond the four reasons given, there is one more reason for studying bounded rationality. It is simply a fascinating thing to do. We can mix some Puck with our Hamlet.
[…] Nash: See if I derive an equilibrium (link) where prevalence is a non-singular event where nobody loses, can you imagine the effect that would have on conflict scenarios, arm negotiations… (…) currency exchange? […], in Memorable quotes for “A Beautiful Mind” (2001), movie directed by Ron Howard, starring Russell Crowe, along with Ed Harris.
” […] What I refused to see is what the prisoner’s dilemma teaches: anyone who plays the “All Cooperate” strategy is a sucker, and incents the other to defect on every move. I now believe that the lesson of the prisoner’s dilemma is that a robust ethic succeeds where a weak one fails. Be fair, be strong, reward cooperation and punish defection, and you will have nothing to regret. […] “, in An Ethic Based on the Prisoner’s Dilemma, The Ethical Spectacle, September, 1995.
[…] Martin Nowak is known for his many influential papers on cooperation and in theoretical biology. This book is a popular writing on his scientific adventures, personal motivations and collaborations. Given his work it is remarkable is that this book does contain nor mathematical equations neither graphical illustrations. Nowak is currently a professor of mathematics and biology at Harvard University. Moreover, he directs since 2003 his own research program on Evolutionary Dynamics. This program has been made possible by a 30 million pledge by Wall Street tycoon Jeffrey Epstein. This is just one ingredient of the remarkable story of Nowak scientific life. The book starts with laying out the puzzle of cooperation illustrated by the prisoner’s dilemma. If both players are selfish and rational they will defect. Why do we see so much cooperation in human societies and other domains of the biological world? This puzzle was introduced to Nowak by Karl Sigmund, a professor in mathematics from the University of Vienna, while Nowak was a student in biochemistry. Sigmund talked about the famous Axelrod tournament and Nowak got hooked. The tournament of Axelrod assumed that the strategies did not make errors. What if there are errors? Will Tit for Tat still be a good strategy? His analysis showed that a more promising strategy is a more Win Stay, Loose Shift. This strategy leads to cooperation if both agents do the same, and defect if not. Hence agents can forgive.
The analysis of strategies that do well in direct reciprocity is one of the five chapters in which Nowak discuss five ways in which the prisoner’s dilemma can be solved. The second chapter is on indirect reciprocity. In a landmark paper with Karl Sigmund Nowak showed that when agents derive information on their reputation (image score) cooperation can evolve in one-shot prisoner’s dilemma. The third chapter is on spatial games and features another landmark paper on spatial chaos. This paper, written with Lord Robert May, shows that cooperation can evolve if agents interact with neighbours and imitate the best strategy of their neighbours. The forth chapter is on group selection. This controversial approach is now better known as multi-level selection. Finally, the fifth chapter is on kin-selection, the first theory on cooperation based on genetic relatedness. The discussion on the five ways to overcome the prisoner’s dilemma is especially interesting due to the discussion on the scientific process. How long hikes with Sigmund let to inspirations that let Nowak drop all other activities he was working on. How chance meetings let to new ideas. How he got, to Oxford, Princeton and finally Harvard.
In the second part of the book discusses cooperation in biology. It covers his applications to the origins of life, the study of cancer and the dominance of ant colonies. This work might be less familiar to the readers of JASSS. Especially the work on cancer, defectors in our own biology, can lead to practical applications. The final part of the book focuses on human societies. Humans are called supercooperators since they are the only organism that uses all five ways to solve social dilemmas. First the evolution of language is discussed. Nowak made important contributions to the study of language by simulating agents benefiting from mutual understanding in language games. According to Nowak, the emergence of language is the most important development in life since 600 million years. It resulted to new types of cooperation. Especially in the context of indirect reciprocity it is key to have language. We need gossip and other types of information transmission to derive reliable estimates on the reputation of strangers.
Then Nowak discusses public goods and the use of costly punishment to derive cooperation. This is the only part of the book where he discusses empirical research. With two graduate students he performed experiments which showed that punishment is not something special, but in line with earlier work on reciprocity and tit for tat. Then Nowak continues with his recent work on network theory and set theory. The book closes with a reflection on the consequences of his work. Cooperation is a crucial ingredient to evolution, but there always will be cycles. The question is how to re-establish cooperation after it has been collapsed. This book provides a nice overview of the findings of Nowak’s work. Note however, that Nowak has substantial work in other areas of research not discussed in the book such as infectious diseases. Together with science writer Roger Highfield, Nowak provides an inspirational story on science in practice. This covers the importance of his mentors in his early years, and his current role of a mentor to his students at Harvard. In conclusion, this is a marvellous book. Although I may not always agree with the findings of Nowak’s research, it is a motivating account on the messy practice of science. I highly recommend this book for students and faculty in social simulation and science in general. […], Reviewed by Marco A. Janssen
(Arizona State University) on JASSS 2011 [Nowak, Martin, Supercooperators: Altruism, Evolution, and Why We Need Each Other to Succeed, ISBN 9781439100189 (pb), Free Press (The): New York, NY, 2011].
Picture – The European Conference on Complex Systems (ECCS’11 – link) at one of the main Austrian newspapers Der Standard: “Die ganze Welt als Computersimulation” (link), Klaus Taschwer, Der Standard, 14 September [click to enlarge – photo taken at the conference on Sept. 15, Vienna 2011].
“Take Darwin, for example: would Caltech have hired Darwin? Probably not. He had only vague ideas about some of the mechanisms underlying biological Evolution. He had no way of knowing about genetics, and he lived before the discovery of mutations. Nevertheless, he did work out, from the top down, the notion of natural selection and the magnificent idea of the relationship of all living things.” Murray Gell-Mann in “Plectics“, excerpted from The Third Culture: Beyond the Scientific Revolution by John Brockman (Simon & Schuster, 1995).
To be honest, I didn’t enjoy this title, but all of us had a fair share with journalists, now and then by now. After all, 99% of us don’t do computer simulation. We are all after the main principles, and their direct applications.
During 5 days (12-16 Sept.), with around 700 attendees the Vienna 2011 conference evolved around main important themes as Complexity & Networks (XNet), Current Trends in Game Theory, Complexity in Energy Infrastructures, Emergent Properties in Natural and Artificial Complex Systems (EPNACS), Complexity and the Future of Transportation Systems, Econophysics, Cultural and Opinion Dynamics, Dynamics on and of Complex Networks, Frontiers in the Theory of Evolution, and – among many others – Dynamics of Human Interactions.
For those who know me (will definitely understand), I was mainly attending those sessions underlined above, the last one (Frontiers in Evolution) being one of my favorites, among all these ECCS years. All in all, the conference had highly quality works (daily, we had about 3-4 works I definitely think should be followed in the future) and to those, more attention should be deserved (my main critics to the conference organization goes in here). Naturally, the newspaper article also reflects on the FuturICT, being historically one of the major scientific European projects ever done (along, probably, with the Geneva LHC), which teams spread across Europe, including Portugal with a representative team of 7 members present on the conference, led by Jorge Louçã, the former editor and organizer on the previous ECCS’10 last year in Lisbon.
Video – “… they forgot to say: in principle!“. Ricard Solé addressing the topic of a Morphospace for Biological Computation at ECCS’11 (European Conference on Complex Systems), while keeping is good humor on.
Let me draw anyway your attention to 4 outstanding lectures: Peter Schuster (link) on the first day, dissected on the source of Complexity in Evolution, battling among – as he puts it – two paradoxes: (1) Evolution is an enormously complex process, and (2) biological evolution on Earth proceeds from lower towards higher complexity. Earlier on that morning – opening the conference -, Murray Gell-Mann (link) who co-founded the Santa Fe Institute in 1984, gave a wonderful lecture on Generalized Entropies. Besides his age, the 1969 Nobel Prize in physics for his work on the theory of elementary particles, gladly turned his interest in the 1990s to the theory of Complex Adaptive Systems (CAS). Next, Albert-László Barabási (link), tamed Complexity on Controlling Networks. Finally, at the last day, closing the conference in pure gold, Ricard Solé (link) addressed the topic of a Morphospace for Biological Computation, an amazing lecture with a powerful topic to which – nevertheless – I felt he had little time (20 minutes), for such a rich endeavor. However – by no means -, he have lost his good humor during the talk (check my video above). Next year, the conference will be held in Brussels, and by just judging at the poster design, it promises. Go ants, go … !
Picture – The European Conference on Complex Systems (ECCS’12 – link) poster design for next year in Brussels.
Figure – Poker final hand rankings. Poker is a typical example of bounded rationality in our daily lives. Without having all the information available, you still have to make a decision. In one of his works, Herbert Simon states: “boundedly rational agents experience limits in formulating and solving complex problems and in processing (receiving, storing, retrieving, transmitting) information“.
[…] Bounded rationality is the idea that in decision making, rationality of individuals is limited by the information they have, the cognitive limitations of their minds, and the finite amount of time they have to make decisions. It was proposed by Herbert Simon as an alternative basis for the mathematical modelling of decision making, as used in economics and related disciplines; it complements rationality as optimization, which views decision making as a fully rational process of finding an optimal choice given the information available. Another way to look at bounded rationality is that, because decision-makers lack the ability and resources to arrive at the optimal solution, they instead apply their rationality only after having greatly simplified the choices available. Thus the decision-maker is a satisfier, one seeking a satisfactory solution rather than the optimal one. Simon used the analogy of a pair of scissors, where one blade is the “cognitive limitations” of actual humans and the other the “structures of the environment”; minds with limited cognitive resources can thus be successful by exploiting pre-existing structure and regularity in the environment. Some models of human behaviour in the social sciences assume that humans can be reasonably approximated or described as “rational” entities (see for example rational choice theory). Many economics models assume that people are on average rational, and can in large enough quantities be approximated to act according to their preferences. The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice due to the finite computational resources available for making them. […] In Wikipedia, (link).
Book cover – Herbert A. Simon. Models of Bounded Rationality, Volume 1, Economic Analysis and Public Policy, MIT Press 1984. The Nobel Prize in Economics was awarded to Herbert Simon in 1978. At Carnegie-Mellon University he holds the title of Professor of Computer Science and Psychology. These two facts together delineate the range and uniqueness of his contributions in creating meaningful interactions among fields that developed in isolation but that are all concerned with human decision-making and problem-solving processes. In particular, Simon has brought the insights of decision theory, organization theory (especially as it applies to the business firm), behavior modeling, cognitive psychology, and the study of artificial intelligence to bear on economic questions. This has led not only to new conceptual dimensions for theoretical constructions, but also to a new humanizing realism in economics, a way of taking into account and dealing with human behavior and interactions that lie at the root of all economic activity. The sixty papers and essays contained in these two volumes are grouped under eight sections, each with a brief introductory essay. These are: Some Questions of Public Policy, Dynamic Programming Under Uncertainty; Technological Change; The Structure of Economic Systems; The Business Firm as an Organization; The Economics of Information Processing; Economics and Psychology; and Substantive and Procedural Reality. Most of Simon’s papers on classical and neoclassical economic theory are contained in volume one. The second volume collects his papers on behavioral theory, with some overlap between the two volumes. (from MIT).
Video lecture by Ken Long (at the Statistics Problem Solvers blog) on Nassim Taleb‘s 4th Quadrant problems [1,2], i.e. a region where statistics not only don’t work but in which statistics are downright dangerous, because they lead you to make predictions as well as control systems that are unprepared for the kinds of systems shocks awaiting you.
“Statistical and applied probabilistic knowledge is the core of knowledge; statistics is what tells you if something is true, false, or merely anecdotal; it is the “logic of science”; it is the instrument of risk-taking; it is the applied tools of epistemology; you can’t be a modern intellectual and not think probabilistically—but… let’s not be suckers. The problem is much more complicated than it seems to the casual, mechanistic user who picked it up in graduate school. Statistics can fool you. In fact it is fooling your government right now. It can even bankrupt the system (let’s face it: use of probabilistic methods for the estimation of risks did just blow up the banking system).”, Nassim Taleb, in [1].
[1] Nassim Nicholas Taleb, “The Fourth Quadrant: A Map of the Limits of Statistics“, An Edge Original Essay, Set., 2008. (link)
[2] Nassim Nicholas Taleb,”Convexity, Robustness, and Model Error inside the Fourth Quadrant“, Oxford Lecture (Draft version), Oxford, July 2010. [PDF paper]
Fig. – Christ having some problems on passing the right message. Comic strip from Zach Weiner (Saturday Morning Breakfast Cereal blog – smbc-comics.com ).
Social psychologists, sociologists, and economists have all proposed theories of norm emergence. In general, they views norm emergence as depending on three factors: (i) actors’ preferences regarding their own behaviour (inclinations); (ii) actors’ preferences regarding the behaviour of others (regulatory interests); and (iii) measures for enforcing norms (enforcement resources), such as access to sanctions and information. Whereas most studies of norm emergence have focused on inclinations or enforcement resources, this article analyses the role of regulatory interests in norm emergence. Specifically, it analyses systems of collective sanctions in which, when and individual violates or complies with a rule, not merely the individual but other members of that person’s group as well are collectively punished of rewarded by an external agent. These collective sanctions give individuals an incentive to regulate one another’s behaviour. This paper demonstrates that when a group is subjected to collective sanctions, a variety of responses may be rational: the group may either create a secondary sanctioning system to enforce the agent’s dictates, or it may revolt against the agent to destroy its sanctioning capacity. According to the proposed theoretic model. the optimal response depends quite sensitively on the group’s size, internal cohesion, and related factors. Abstract: D.D. Heckathorn, “Collective sanctions and the creation of prisoner’s dilemma norms“, American Journal of Sociology (1988), Volume: 94, Issue: 3, Publisher: University of Chicago Press, Pages: 535-562.
…
Video – […] see, in this world, there are two kinds of people, … my friend, … those with ‘loaded guns’ and those who dig. You dig. […] Last 8 minutes finale of The Good, the Bad and the Ugly (Il buono, il brutto, il cattivo), a 1966 Italian epic spaghetti western film directed by Sergio Leone, starring Lee Van Cleef, Eli Wallach and Clint Eastwood in the title roles, playing a kind of 3-agent Prisoner’s dilemma game. Now, one of them, the Good (Clint Eastwood) is the only who knows he is in fact just playing a 2-agent PD game. And that, besides the inner non-linearity complexity of the ‘game’, makes all the difference…
Book – Karl Sigmund, The Calculus of Selfishness, Princeton Series on Theoretical and Computational Biology, Princeton University Press, ISBN: 978-1-4008-3225-5, 192 pp., 2009.
[…] Cooperation means that a donor pays a cost, c, for a recipient to get a benefit, b. In evolutionary biology, cost and benefit are measured in terms of fitness. While mutation and selection represent the main forces of evolutionary dynamics, cooperation is a fundamental principle that is required for every level of biological organization. Individual cells rely on cooperation among their components. Multicellular organisms exist because of cooperation among their cells. Social insects are masters of cooperation. Most aspects of human society are based on mechanisms that promote cooperation. Whenever evolution constructs something entirely new (such as multicellularity or human language), cooperation is needed. Evolutionary construction is based on cooperation. The five rules for cooperation which we examine in this chapter are: kin selection, direct reciprocity, indirect reciprocity, graph selection, and group selection. Each of these can promote cooperation if specific conditions are fulfilled. […], Martin A. Nowak, Karl Sigmund, How populations cohere: five rules for cooperation, in R. M. May and A. McLean (eds.) Theoretical Ecology: Principles and Applications, Oxford UP, Oxford (2007), 7-16. [PDF]
How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the “invisible hand” that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation. Focusing on some of the best-known social and economic experiments, including games such as the Prisoner’s Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions. Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps, The Calculus of Selfishness analyses to what extent one key facet of human nature–selfishness–can lead to cooperation. (from Princeton Press). [Karl Sigmund, The Calculus of Selfishness, Princeton Series on Theoretical and Computational Biology, Princeton University Press, ISBN: 978-1-4008-3225-5, 192 pp., 2009.]
What follows comes partly from chapter 1, available here:
THE SOCIAL ANIMAL: Aristotle classified humans as social animals, along with other species, such as ants and bees. Since then, countless authors have compared cities or states with bee hives and ant hills: for instance, Bernard de Mandeville, who published his The Fable of the Bees more than three hundred years ago. Today, we know that the parallels between human communities and insect states do not reach very far. The amazing degree of cooperation found among social insects is essentially due to the strong family ties within ant hills or bee hives. Humans, by contrast, often collaborate with non-related partners. Cooperation among close relatives is explained by kin selection. Genes for helping offspring are obviously favouring their own transmission. Genes for helping brothers and sisters can also favour their own transmission, not through direct descendants, but indirectly, through the siblings’ descendants: indeed, close relatives are highly likely to also carry these genes. In a bee hive, all workers are sisters and the queen is their mother. It may happen that the queen had several mates, and then the average relatedness is reduced; the theory of kin selection has its share of complex and controversial issues. But family ties go a long way to explain collaboration. The bee-hive can be viewed as a watered-down version of a multicellular organism. All the body cells of such an organism carry the same genes, but the body cells do not reproduce directly, any more than the sterile worker-bees do. The body cells collaborate to transmit copies of their genes through the germ cells – the eggs and sperm of their organism. Viewing human societies as multi-cellular organisms working to one purpose is misleading. Most humans tend to reproduce themselves. Plenty of collaboration takes place between non-relatives. And while we certainly have been selected for living in groups (our ancestors may have done so for thirty million years), our actions are not as coordinated as those of liver cells, nor as hard-wired as those of social insects. Human cooperation is frequently based on individual decisions guided by personal interests. Our communities are no super-organisms. Former Prime Minister Margaret Thatcher pithily claimed that “there is no such thing as society“. This can serve as the rallying cry of methodological individualism – a research program aiming to explain collective phenomena bottom-up, by the interactions of the individuals involved. The mathematical tool for this program is game theory. All “players” have their own aims. The resulting outcome can be vastly different from any of these aims, of course.
THE INVISIBLE HAND: If the end result depends on the decisions of several, possibly many individuals having distinct, possibly opposite interests, then all seems set to produce a cacophony of conflicts. In his Leviathan from 1651, Hobbes claimed that selfish urgings lead to “such a war as is every man against every man“. In the absence of a central authority suppressing these conflicts, human life is “solitary, poor, nasty, brutish, and short“. His French contemporary Pascal held an equally pessimistic view: : “We are born unfair; for everyone inclines towards himself…. The tendency towards oneself is the origin of every disorder in war, polity, economy etc“. Selfishness was depicted as the root of all evil. But one century later, Adam Smith offered another view.An invisible hand harmonizes the selfish efforts of individuals: by striving to maximize their own revenue, they maximize the total good. The selfish person works inadvertently for the public benefit. “By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it“. Greed promotes behaviour beneficial to others. “It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own self-interest. We address ourselves, not to their humanity but to their self-love, and never talk to them of our own necessities but of their advantages“. A similar view had been expressed, well before Adam Smith, by Voltaire in his Lettres philosophiques: “Assuredly, God could have created beings uniquely interested in the welfare of others. In that case, traders would have been to India by charity, and the mason would saw stones to please his neighbour. But God designed things otherwise….It is through our mutual needs that we are useful to the human species; this is the grounding of every trade; it is the eternal link between men“. Adam Smith (who knew Voltaire well) was not blind to the fact that the invisible hand is not always at work. He merely claimed that it frequently promotes the interest of the society, not that it always does. Today, we know that there are many situations – so-called social dilemmas – where the invisible hand fails to turn self-interest to everyone’s advantage.
“If you want to be incrementally better: Be competitive. If you want to be exponentially better: Be cooperative“. ~ Anonymous
Two hunters decide to spent their week-end together. But soon, a dilemma emerges between them. They could choose for hunting a deer stag together or either -individually- hunt a rabbit on their own. Chasing a deer, as we know, is something quite demanding, requiring absolute cooperation between them. In fact, both friends need to be focused for a long time and in position, while not being distracted and tempted by some arbitrary passing rabbits. On the other hand, stag hunt is increasingly more beneficiary for both, but that benefice comes with a cost: it requires a high level of trust between them. Somehow at some point, each hunter concerns that his partner may diverts while facing a tempting jumping rabbit, thus jeopardizing the possibility of hunting together the biggest prey.
The original story comes from Jean Jacques Rousseau, French philosopher (above). While, the dilemma is known in game theory has the “Stag Hunt Game” (Stag = adult deer). The dilemma could then take different quantifiable variations, assuming different values for R (Reward for cooperation), T (Temptation to defect), S (Sucker’s payoff) and P (Punishment for defection). However, in order to be at the right strategic Stag Hunt Game scenario we should assume R>T>P>S. A possible pay-off table matrix taking in account two choices C or D (C = Cooperation; D = Defection), would be:
Choice — C ——- D ——
C (R=3, R=3) (S=0, T=2)
D (T=2, S=0) (P=1, P=1)
Depending on how fitness is calculated, stag hunt games could also be part of a real Prisoner’s dilemma, or even Ultimatum games. As clear from above, highest pay-off comes from when both hunters decide to cooperate (CC). Over this case (first column – first row), both receive a reward of 3 points, that is, they both really focused on hunting a big deer while forgetting everything else, namely rabbits. However – and here is where exactly the dilemma appears -, both CC or DD are Nash equilibrium! That is, at this strategic landscape point no player has anything to gain by changing only his own strategy unilaterally. The dilemma appears recurrently in biology, animal-animal interaction, human behaviour, social cooperation, over Co-Evolution, in society in general, and so on. Philosopher David Hume provided also a series of examples that are stag hunts, from two individuals who must row a boat together up to two neighbours who wish to drain a meadow. Other stories exist with very interesting variations and outcomes. Who does not knows them?!
The day before last school classes, two kids decided to do something “cool”, while conjuring on appearing before their friends on the last school day period, both with mad and strange haircuts. Although, despite their team purpose, a long, anguish and stressful night full of indecisiveness followed for both of them…
“It is not the strongest of the species that survives, nor the most intelligent that survives. It is the one that is the most adaptable to change“. Charles Darwin (On the Origin of Species, Nov. 1859)
During the Victorian era where high prudery and morality were constant, it would be hard to imagine seeing Charles Darwin wearing a Scottish-kilt. In fact, men’s formal clothing was less colourful than it was in the previous century, while women’s tight-fitting jersey dresses of the 1880s covered the body, leaving little to the imagination (source). There is however, one beautiful – as in strict sense of delighting the senses for exciting intellectual or emotional admiration – reason, I think he should have done it (!), regardless the obvious bearing consequences of a severe Victorian society. Surprisingly, some how, that reason is linked to cheetahs chasing gazelles, among many other things…
As the image of Charles Darwin wearing a kilt, you will probably find these awkward too, but when a cheetah chases a gazelle, banded tartan Scottish-kilt woven textile like patterns soon start to pop-up everywhere. Not at the ground terrain level, of course. Instead, they appear as a phenotype-like map between your present and the past. You may think that this banded tartans will have no significance for your life, but do mind this: crying babies do it all the time with their mommy’s and fathers, companies do it with other companies in their regular business, people commuting in large cities do it over large highways, human language, literature and culture does it, friends do it, PC virus and anti-virus software do it, birds singing do it also, … and even full countries at war do it.
One extreme example is the Cold War, where for the first time on our Human history, co-evolutionary arms-race raised to unprecedented levels. Co-Evolution is indeed the right common key-word for all these phenomena, while large white banded strips punctuated by tiny black ones (bottom-left woven kilt above), would be the perfect correspondent tartan pattern for the case of the Cold War example mentioned. But among these, there is of course, much more Scottish-kilt like patterns we could find. Ideas, like over this TV ad above, co-evolve too. Here, the marketeer decided to co-evolve with a previous popular famous meme image: Sharon Stone crossing his legs at the 1992 ‘Basic Instinct‘ movie. In fact, there is an authentic plethora of different possible behavioural patterns. Like a fingerprint (associated with different Gaelic clans), each of these patterns correspond to a lineage of current versus ancestral strategies, trying to solve a specific problem, or achieving one precise goal. But as the strategic landscape is dynamically changing all the time, a good question is, how can we visualize it. And, above all, what vital information and knowledge could we retrieve from this evolutionary Scottish-kilts maps.
Fig. – The frontispiece drawing to the English edition of Ernst Haeckel‘s Evolution of Man (trans. 1903) presents a skull labelled “Australian Negro” as an intervening evolutionary stage between the “Mediterranean” skull and those of the lower primates (from the 1891 ed. of the Anthropogenie).
In nature, organisms and species coexist in an ecosystem, where each species has its own place or niche in the system. The environment contains a limited number and amount of resources, and the various species must compete for access to those resources, where successive adaptations in one group put pressure on another group to catch up (e.g., the coupled phenomena of speed in the cheetah and evasive agility in the gazelle). Through these interactions, species grow and change, each influencing the others evolutionary development [7]. This process of bi-adaptive relationship (in some cases can also assume a form of cooperation and mutualism) or reciprocal adaptation is know as Co-evolution, i.e. the evolution of two or more competing populations with coupled fitness.
The phenomena has several interesting features that may potentially enhance the adaptive power of artificial evolution [7], or other types of bio-inspired learning systems. In particular, competing populations may reciprocally drive one another to increasing levels of complexity by producing an evolutionary “arms race”, where each group may become bigger, faster, more lethal, more intelligent, etc. Co-Evolution can then happen either between a learner (e.g., single population) and its environment (i.e. based on competitions among individuals in the population) or between learning species (two populations evolving), where the fitness of individuals is based on their behaviour in the context of the individuals of the other population [7]. This latter type of co-evolutionary search is often described as “host-parasite”, or “predator-prey” co-evolution. A good example and application of co-evolutionary learning include the pioneering work by Hillis in 1990 [1] on sorting networks.
It can occur at multiple levels of biology: it can be as microscopic as correlated mutations between amino acids in a protein, or as macroscopic as co-varying traits between different species in an environment. Being biological Co-Evolution, in a broad sense, “the change of a biological object triggered by the change of a related object” [2], his visualization however, could be profoundly hard. In fact, attempting to define and monitor “progress” in the context of Co-Evolutionary systems can be a somewhat nightmarish experience , as stated in [4]. It’s exactly here where Scottish-kilts come into play.
In 1995 [3], two researchers had a simple, yet powerful idea. In order to monitor the dynamics of artificial competitive co-evolutionary systems between two populations, Dave Cliff and Geoffrey Miller [3,4,5] proposed evaluating the performance of an individual from the current population in a series of trials against opponents from all previous generations. while visualizing the results as 2D grids of shaded cells or pixels: qualitative patterns in the shading can thus indicate different classes of co-evolutionary dynamic. Since their technique involves pitting a Current Individual (CI) against Ancestral Opponents (AO), they referred to the visualizations as CIAO plots (fig. above [3]).
Important Co-Evolutionary dynamics such as limited evolutionary memory, “Red Queen” effects or intransitive dominance cycling, will then be revealed like a fingerprint as certain qualitative patterns. Dominance cycling, for instance, it’s a major factor on Co-Evolution, wish could appear or not, during the entire co-evolutionary process. Imagine, for instance, 3 individuals (A,B,C) or strategies. Like over the well known “Rock, Paper, Scissors” game, strategy B could beat strategy A, strategy C could beat B, and strategy A could beat C, over and over in an eternal cycling, where only “arms race” specialized learning will emerge, at the cost of a limited learning generalization against a possible fourth individual-strategy D. If you play poker, you certainly know what I am talking about, since 2 poker players are constantly trying to broke this behavioural cycle, or entering it, depending on their so-far success.
Above (left and right figures – [3]), two idealised typical CIAO plot patterns can be observed, where darker shading denotes higher scores. On the left figure, however, co-evolutionary intransitive dominance cycling is a constant, where current elites (population A elites) score highly against population B opponents from 3, 8 and 13 generations ago, but not so well against generations in between. On the other hand (right figure), the behavioural pattern is completely different: over here we do observe limited evolutionary memory, where the current elites do well against opponents from 3,4 and 5 generations ago, but much less well against more distant ancestral opponents.
“For to win one hundred victories in one hundred battles is not the acme of skill. To subdue the enemy without fighting is the acme of skill.” ~ Sun Tzu
Of course, in increasingly complex real-world situations Scottish-kilt like CIAO plots are much noisy than this (fig. above -[7]) where banded tartans could be less prominent, while the same could happen in irregular dominance cycling as elegantly showed by Cartlidge and Bullock in 2004 [6]. Above, some of my own experiences can be observed (submitted work). Over here I decided to co-evolve a AI agent strategy to play against a pool of 15 different strategies (6 of those confronts are presented above), and as a result, 6 different behavioural patterns emerged between them. All in all, the full spectrum of co-evolving dynamics could be observed, from the “Red Queen” effect, till alternate dominant cycles, and limited or long evolutionary memory. Even if some dynamics seem counter-productive in one-by-one confronts, in fact, all of these dynamics are useful in some way, as when you play Poker or the “Rock, Paper, Scissors” game. A typical confront between game memory (exploitation) and the ability to generalize (exploration). Where against precise opponents limited evolutionary memory was found, the same effect produced dominant cycles or long evolutionary memory against other strategies. The idea of course, is not to co-evolve a super-strategy to win all one-by-one battles (something that would be rather impossible; e.g. No free Lunch Theorem) but instead to win the whole round-robin tournament, by being highly adaptive and/or exaptive.
So next time you see someone wearing a banded tartan Scottish-kilt do remind yourself that, while getting trapped in traffic, that precise pattern could be the result of your long year co-evolved strategies to find the quickest way home, while confronting other commuters doing the same. And that, somewhere, somehow, Charles Darwin is envying your observations…
.
[1] W. Daniel Hillis (1990), “Co-Evolving Parasites improve Simulated Evolution as an Optimization Procedure”, Physica D, Vol. 42, pp. 228-234 (later in, C. Langton et al. (Eds.) (1992), Procs. Artificial Life II, Addison-Welsey, pp. 313-324).
[2] Yip et al.; Patel, P; Kim, PM; Engelman, DM; McDermott, D; Gerstein, M (2008). “An integrated system for studying residue Coevolution in Proteins“. Bioinformatics 24 (2): 290-292. doi:10.1093/bioinformatics/btm584. PMID 18056067.
[3] Dave Cliff, Geoffrey F. Miller, (1995), “Tracking the Red Queen: Methods for measuring co-evolutionary progress in open-ended simulations“. In F. Moran, A. Moreno, J. J. Merelo, & P. Cachon (Eds.), Advances in artificial life: Proceedings of the Third European Conference on Artificial Life (pp. 200-218). Berlin: Springer-Verlag.
[4] Dave Cliff, Geoffrey F. Miller, (2006), “Visualizing Co-Evolution with CIAO plots“, Artificial Life, 12(2), 199-202
[5] Dave Cliff, Geoffrey F. Miller (1996). “Co-evolution of pursuit and evasion II: Simulation methods and results“. In P. Maes, M. J. Mataric, J.-A. Meyer, J. Pollack, & S. W. Wilson (Eds.), From Animals to Animats 4: Proceedings of the Fourth International Conference on Simulation of Adaptive Behavior (pp. 506-515). Cambridge, MA: MIT Press.
[6] Cartlidge, J. and Bullock S., (2004), “Unpicking Tartan CIAO plots: Understanding irregular Co-Evolutionary Cycling“, Adaptive Behavior Journal, 12: 69-92, 2004.
[7] Ramos, Vitorino, (2007), “Co-Cognition, Neural Ensembles and Self-Organization“, extended abstract for a seminar talk at ISR – Institute for Systems and Robotics, Technical Univ. of Lisbon (IST), Lisbon, PORTUGAL. May 31, 2007.
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.
Last year, at the beginning of October I decided to dedicate my second post on financial markets (I, II) to Black Swans. Swans are beautiful animals, but while white swans are vulgar and omnipresent at every pond, black swans are rare! Meanwhile, 2 days ago (June 1) the Wall Street Journal comes with this very awkward – and by all means for that precise reason – interesting article written by journalist Scott Patterson, where Mr. Taleb’s name pops-up again (image below).
Well, … let’s face it: you could put your money in the bank and have – let’s say – a 3% revenue at the end of your fiscal year. Or you could apply it to raise a new fancy gourmet restaurant at your local vicinity. Restaurants and local food stores are known to have 5-7% revenues in one year, not to speak on the immense burden they represent as well as for some associated risks – specially these days. But then you may think – better than banks, right? Right! Or, just to give you another example on this increasing scale – raising a little bit the risk -, on the other hand you could apply your money in stock markets. Main financial indexes (Dow Jones, NASDAQ, etc) are known to have an annual average revenue of 10-12% (since 1918). Not these days of course, where high volatility and entropy in the markets are installed. Well, emergent countries like China are raising themselves at 12%/year also. We could go on and on with so many other examples. Some say that Eolic parks could achieve 40%. Normally the cost of one eolic tower is around 1 million euros, which could be paid back after one year producing energy trough wind at normal operating conditions. The rest are maintenance costs, as well as initial investment in terrains, etc. So, what’s new? Consider this. For moments imagine yourself having 100% in revenues, just last year, at this precise dramatic context. That’s 10 times what the market does in regular years, 20 times what your favorite restaurant does. Moreover, there is a substantial difference between all these examples. If you keep dropping money at the restaurant (for instance the revenue you have earned in the last year), still liquid revenues will be the same in the next year (unless you open a new dinner room next to the first one, while the awful burden keeps increasing). Some business are static and linear in time while others are exponential. As Alice in the wonderland, you will need to keep running twice as faster in order to be at the same place. Amazing those differences, no? Well, not for those “lovely” animal creatures known as Black Swans. According to Patterson, … Funds run by Universa, which is managed and owned by Mr. Taleb’s long-time collaborator Mark Spitznagel, last year gained more than 100% thanks to its bearish bets. Universa now runs about $6 billion, up from the $300 million it began with in January 2007. Excerpts from the Wall Street Journal article (Black Swan Fund Makes a Big Bet on Inflation) follow below. So, why the hell I do not feel at all surprised by this?! Really, I am not. Let me just say, I do have my own reasons:
[…] A hedge fund firm that reaped huge rewards betting against the market last year is about to open a fund premised on another wager: that the massive stimulus efforts of global governments will lead to hyperinflation. The firm, Universa Investments L.P., is known for its ties to gloomy investor Nassim Nicholas Taleb, author of the 2007 bestseller “The Black Swan,” which describes the impact of extreme events on the world and financial markets.
Funds run by Universa, which is managed and owned by Mr. Taleb’s long-time collaborator Mark Spitznagel, last year gained more than 100% thanks to its bearish bets. Universa now runs about $6 billion, up from the $300 million it began with in January 2007. Earlier this year, Mr. Spitznagel closed several funds to new investors….
Mr. Taleb doesn’t have an ownership interest in the Santa Monica, Calif., firm, but he has significant investments in it and helps shape its strategies. The term “black swan,” which has become a market catchphrase in the last few years, alludes to the once-widespread belief in the West that all swans are white. The notion was proven false when European explorers discovered black swans in Australia. A black-swan event, according to Mr. Taleb, is something that is extreme and highly unexpected. … […]
Many man made and naturally occurring phenomena (being inherently complex systems), including city sizes, incomes, word frequencies, internet links, social networks and earthquake magnitudes, are distributed according to a power-law distribution. One under f Zipf’s law follows the same characteristic, or pink noise. Here is a possible long list, collected year after year, since the 1910’s up to now – 2008 (which I vividly recommend). From vacuum tubes to trading activities in world financial markets. Even, we could easily found them on Pollock’s paintings (recently here). Back in 2002, I have addressed some of his painting features (mostly fractal) regarding the theme “Emergent Aesthetics in Autonomous Collective Systems“. Astonishingly, without having a clue what fractal dimension’s would be, Jackson increased his fractal signatures year over year, while getting old. Indeed, “Action painting”, has he call it, mainly using his body motion and a bucket, were largely enough.
Financial markets are indeed complex systems, even if they are far from being self-regulated. Much after this recent black Monday, I have made here some notes regarding Self-Organization and finance, over two weeks or so. Their basic features – as I see it. However- essentially what brings me here today is-, what happens to their frequency? Are phenomena like the current financial crisis, frequent? Well, much of that depends on our knowledge on power-laws. Good news is that we know how many of them will occur in a very large time window, bad news is that, we don’t know when will they precisely occur. As in Earthquakes (check this out). Does this impel us to do nothing? Not at all. We can’t do anything about earthquakes (at least for now – except prevent them), however we can establish some ground smart rules in order to avoid financial systems to collapse in turmoil (that is, tune them in the precise physical regime). Power-laws are not only our wake-up call, as they are a signature. For good or for worse. It seems that we are all playing across the planet, a reversed El Farol Bar problem. If that’s somehow true we all should ask new questions like: In what frequency should we go to a bar ?! In other words, should we all run to the banks now, asking for our deposits?
Any polynomial relationship that exhibits the property of scale invariance is a Power-Law. Power-law implies that small occurrences are extremely common, whereas large instances are extremely rare (similarly over maps and cities – if you have time, found out the foundation of Berlin city over time). As the large quantity of small dots + low frequency of large dots we may found on Jackson Pollock paintings. The same goes for Black-Swans.
Jackson Pollock in action - As reported somehow recently by Nature magazine (Sept., 13, 2000), research suggests that the abstract works of artists such as Jackson Pollock are esthetically pleasing because they obey fractal rules similar to those found on the natural world. Pollock was known to have swung his paint back and forth like a pendulum, using a can on the end of a string with a hole punched in it. Researchers (Jensen) have found that if a swinging pendulum is hit with a hammer at just the right frequency (slightly less than the natural rhythm of the pendulum), its motion becomes chaotic and the paint traces out very convincing "fake Pollocks". However, the artist had no idea of fractals or chaotic motion, while dot distribution over Pollock's paintings indeed follow a power-law.
A Black Swan is a highly improbable event that has three characteristics: It is unpredictable, it has incredible impact, and after it happens we invent a reason for it that makes it seem less probable. For those of you that did not have read 2007 Taleb’s book (picture above), wondering what a Black Swan is, or question yourself from where the name arises, just jump for a quick look over here. Nassim started to wrote his book in 2003. Finished it in 2006. So, in what way this “funny” distribution regards financial markets? Well, for many of us now, it his surprising that he have wrote this, back then:
[…] Globalization creates interlocking fragility, while reducing volatility and giving the appearance of stability. In other words it creates devastating Black Swans. We have never lived before under the threat of a global collapse. Financial Institutions have been merging into a smaller number of very large banks. Almost all banks are interrelated. So the financial ecology is swelling into gigantic, incestuous, bureaucratic banks – when one fails, they all fall. The increased concentration among banks seems to have the effect of making financial crises less likely, but when they happen they are more global in scale and hit us very hard. We have moved from a diversified ecology of small banks, with varied lending policies, to a more homogeneous framework of firms that all resemble one another. True, we now have fewer failures, but when they occur ….I shiver at the thought. […]
Were these words a Black Swan within the Black Swan book itself? Rather not. He continues directly to something we now know and face it in precise context. Please note that this was written in the period 2003-2006:
[…] Banks hire dull people and train them to be even more dull. If they look conservative, it’s only because their loans go bust on rare, very rare occasions. But (…) bankers are not conservative at all. They are just phenomenally skilled at self-deception by burying the possibility of a large, devastating loss under the rug. […] The government-sponsored institution Fannie Mae, when I look at its risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: their large staff of scientists deemed these events “unlikely”. […]
What about the costs, and the memory of them? Yes, indeed memory is important while playing game-theory-like games, as his mainly in our daily reality, but in one-two generations it will be probably lost (I hope not), and once again all will start:
[…] the real-estate collapse of the early 1990s in which the now defunct savings and loan industry required a taxpayer-funded bailout of more than half a trillion dollars. The Federal Reserve bank protected them at our expense: when “conservative” bankers make profits, they get the benefits; when they are hurt, we pay the costs.
Should we be surprised? In fact, this is not new. Somehow, fallacy goes on (as George Monbiot tackle it with extreme precision over Guardian Journal very recently – Sep. 30). Not only we were not reacting to these power-law consequences, as many of those economic agents playing within the systems core itself, were thinking of something else:
[…] Once again, recall the story of banks hiding explosive risks in their portfolios. It is not a good idea to trust corporations with matters such as rare events because the performance of these executives is not observable on a short-term basis, and they will game the system by showing good performance so they can get their yearly bonus. The Achilles’ heel of capitalism is that if you make corporations compete, it is sometimes the one that is most exposed to the negative Black Swan that will appear to be the most for survival.[…] As if we did not have enough problems, banks are now more vulnerable to the Black Swan and the ludic fallacy than ever before with “scientists” among their staff taking care of exposures. The giant J. P. Morgan put the entire world at risk by introducing in the nineties RiskMetrics, a phony method aiming at managing people’s risks, causing the generalized use of the ludic fallacy, and bringing Dr. Johns into power in place of the skeptical Fat Tonys. (a related method called “Value-at-Risk,” which relies on the quantitative measurement of risk, has been spreading.) […]
Starting with the distribution and frequency of these kind of events (among many others), all of these words were written in the period 2003-2006. Since then, you could follow Taleb’s war on “Value at Risk” over here. Or here, at Edge.org which I highly recommend.
Meanwhile, apart from what markets are suffering and complex science may enlightened us, life goes on. Not necessarily as we supposed. As we know, reality, many times excels fiction; one single video frame could value one thousand words. Right at your neighborhood. As you may see below, consequences could be much worse than a tornado:
Vodpod videos no longer available.
more about “Foreclosure Alley – SoCal Connected“, posted with vodpod
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. […]
[…] 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.
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.
Chemoton § Vitorino Ramos' research notebook 
Recent Comments