before. This is due both to the rise of biology as a rigorous science and to the rise of computation and computer science. Even mathematics is shifting in
this direction. Gregory Chaitin (2012) speaks of a mathematics that is shift-
ing away from continuous formulations, differential equations, and static out-
comes, to one based on discrete formulations, combinatorial reasoning, and
algorithmic thinking. “The computer,” he says, “is not just a tremendously useful technology, it is a revolutionary new kind of mathematics with profound
philosophical consequences. It reveals a new world.” Science and mathematics
are shedding their certainties and embracing openness and procedural think-
ing, and there is no reason to expect that economics will differ in this regard.
Complexity economics is not a special case of neoclassical economics. On the
contrary, equilibrium economics is a special case of nonequilibrium and hence
complexity economics. Complexity economics, we can say, is economics done
in a more general way. Equilibrium of course will remain a useful first-order
approximation, useful for situations in economics that are well-defined, ratio-nalizable, and reasonably static, but it can no longer claim to be the center of economics. Moving steadily to the center32 is an economics that can handle
interactions more generally, that can recognize nonequilibrium phenomena,
that can deal with novelty, formation and change.
Complexity economics is still in its early days and many economists are
pushing its boundaries outward. It shows us an economy perpetually invent-
ing itself, perpetually creating possibilities for exploitation, perpetually open to response. An economy that is not dead, static, timeless, and perfect, but
one that is alive, ever-changing, organic, and full of messy vitality.
32. See Holt et al. (2010); Davis (2008).
comPlexi t y economics [ 25 ]
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comPlexi t y economics [ 29 ]
CHAPTER 2
Inductive Reasoning and Bounded
Rationality
The El Farol Problem
W. BRIAN ARTHUR*
In 1993 I was experimenting with ways to model inductive choice behavior in the economy and came upon a seeming paradox. There was a bar in Santa Fe, El Farol on Canyon Road, to which people would go on a Thursday night if they expected few people to be there, but would avoid if they expected it to be crowded. I realized this represented a decision problem where expectations (forecasts) that many would attend would lead to few attending, and expectations that few would attend would lead to many attending: expectations would lead to outcomes that would negate these expectations. In particular, rational expectations (by definition forecasts that are on average correct or valid) would lead to their own incorrectness—a logical self-contradiction not unlike the Liar’s Paradox.
The paper was taken up by physicists and became well known in complexity circles; later it was generalized and put into game form by Zhang and Challet as the Minority Game.
In its original and minority game versions it has spawned very many “solutions,” variants, and further papers. The paper appeared in the American Economic Review Papers & Proceedings, 84, 406–411, 1994.
* Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, NM 87501, and Stanford
University. I thank particularly John Holland, whose work inspired many of the ideas here. I also thank Kenneth Arrow, David Lane, David Rumelhart, Roger Shepard, Glen Swindle, Nick Vriend, and colleagues at Santa Fe and Stanford for discussions.
A lengthier version is given in Arthur (1992). For parallel work on bounded rationality and induction, but applied to macroeconomics, see Thomas J. Sargent (1994).
The type of rationality assumed 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 one 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 one can readily fin
d a perfectly rational, minimax solution to it; but rational “solutions” are not found 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 level of complexity human logical capacity ceases to cope—human rationality is bounded. The other is that in interactive situations of complication, agents cannot 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.
Economists, of course, are well aware of this. The question is not whether perfect rationality works, but rather what to put in its place. How does one 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 con-
vergence 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.
I. THINKING INDUCTIVELY
How do humans reason in situations that are complicated or ill-defined? Modern psychology tells us that as humans we are only moderately good at deductive
logic, and we make only moderate use of it. But we are superb at seeing or recognizing or matching patterns—behaviors that confer obvious evolutionary ben-
efits. In problems of complication then, we look for patterns; and we simplify the problem by using these to construct temporary internal models or hypotheses or schemata to work with.1 We carry out localized deductions based on our 1. For accounts in the psychological literature, see R. Schank and R. P. Abelson (1977), David Rumelhart (1980), Gordon H. Bower and Ernest R. Hilgard (1981), and John H. Holland et al. (1986). Of course, not all decision problems work this way. Most t He el farol ProBlem [ 31 ]
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