A Companion to the History of Economic Thought - Chapter 24 pps

Constrained optimization had been a hallmark of neoclassical theory, at least since the work of Vilfredo Pareto, who stated: “The principal subject of our study is economic equilibrium..

C H A P T E R T W E N T Y - F O U R Postwar Neoclassical

Microeconomics

S Abu Turab Rizvi

24.1 INTRODUCTION

Postwar neoclassical microeconomic theory was a curious mixture of successes and problems Its successes include widespread use, as both a basis for all areas

of economics and a growing method in other social sciences The ideas that constrained optimization is the embodiment of individual rationality and that individually rational behavior should be the building block of all social theory have proved very popular This popularity is belied, however, by very serious churning in the underlying formal theory of neoclassical microeconomics in the postwar period Indeed, the formal theory can be characterized as having a series

of impossibility results that imply a demonstrable lack of progress on the main problems set for the theory The theory had to be reinvented regularly in re-sponse to problems, and applications of the theory are often tenuous inasmuch

as the theory is not firm While this protean character has allowed the theory to survive and become widespread, many of the main interests of microeconomists have been sidestepped The overall result is breadth of application and use combined with troubling lack of depth The resulting dynamic is best seen historically

The topic is vast In order to keep this presentation manageable, this chapter focuses on the main aspects of general equilibrium theory and the pluralist approaches that have come, increasingly, to replace it

24.2 SAMUELSON’S FOUNDATIONS AND ITS SETTING

Postwar neoclassical microeconomics began confidently with Paul Samuelson’s

Foundations of Economic Analysis (1947) The book arose from Samuelson’s Harvard

Ph.D dissertation As Samuelson’s career advanced, the book’s main mathemat-ical device – the formulation of nearly every economic matter as a constrained optimization problem – became commonplace Constrained optimization came

to represent the economic problem, subsuming Lionel Robbins’s formulation of

economics as the allocation of scarce resources among competing ends Scarcity was represented as constraint and the allocation process involved optimization Constrained optimization had been a hallmark of neoclassical theory, at least since the work of Vilfredo Pareto, who stated: “The principal subject of our study

is economic equilibrium We shall see shortly that this equilibrium results from the opposition between men’s tastes and the obstacles to satisfying them Our study includes, then, three distinct parts: 1° the study of tastes; 2° the study of obstacles; 3° the study of the way in which these two elements combine to reach equilibrium” (Pareto, 1971 [1906], p 106)

Maximization (of something good or valuable) and minimization (of some-thing bad or undesirable) often imply goal-directed behavior; constrained optim-ization became seen as the embodiment of individually rational choice As such, constrained optimization has reverberated and replicated throughout economics and into related fields (Heilbroner, 1991) The success of neoclassical micro-economics in taking over nearly all of micro-economics and spreading into sociology, political science, and other areas not ordinarily seen as economic rested on the portability and usefulness of constrained optimization as an expression of indi-vidual rationality The basic, fecund mathematical technique used by Samuelson

in constrained optimization was the Lagrange multiplier method of differenti-able calculus An indication of Samuelson’s influence is found in Robert Lucas’ Nobel lecture:

It was lucky for me that one of my undergraduate texts referred to Paul Samuelson’s

the war.” Both the mathematics and the economics in Foundations were way over

my head, but I was too ambitious to spend my summer on the second most import-ant book in economics, and Samuelson’s confident and engaging style kept me going All my spare time that summer went in to working through the first four chapters, line by line, going back to my calculus books when I needed to By the beginning of fall quarter I was as good an economic technician as anyone on the Chicago faculty Even more important, I had internalized Samuelson’s standards for when an economic question had been properly posed and when it had been answered, and was in a position to take charge of my own economic education (Lucas, 1995)

As useful and original as Samuelson’s work was, it might best be situated as part of a revival of neoclassical microeconomics that took place in the 1930s and 1940s Mathematical microeconomics again became prominent after the initial activity – associated with Menger, Jevons, Walras, Pareto, and others – in the latter nineteenth and early twentieth centuries (Mirowski, 1989) This revival took place at Harvard and Chicago in the United States, at the London School

of Economics, and as part of French planning It was associated with the names

of Oskar Lange, Harold Hotelling, John Hicks, Maurice Allais, Abba Lerner, and,

of course, Samuelson They and many other contributors published their works

in the Economic Journal, the Journal of Political Economy, the Review of Economic

Studies , and Econometrica – the prestigious publications in neoclassical economics The culminating statement of the results was Samuelson’s Foundations It

de-rived demand curves from utility functions and based the production side of the economy on the profit-maximization decisions of firms, both using the calculus Samuelson and his colleagues provided a basis for the demand and supply sides

of the economy with a single method, constrained optimization While these authors did not successfully solve the general equilibrium equations resulting from these optimizations, they were able to state them They identified, though they did not successfully pursue, some of the key desiderata of microeconomic general equilibrium theory: the existence, stability, and uniqueness of equilibrium, and the long-sought relations thereof to the theories of money, capital, and growth These issues were to centrally occupy neoclassical microeconomics for the next forty-odd years

The establishment of equilibria of demand and supply is an important feature

of neoclassical microeconomics An equally important preoccupation has been

the welfare properties of the equilibrium allocations Prior to Samuelson’s

Foun-dations, Lerner, Lange, and Allais demonstrated what became known as the two Fundamental Theorems of Welfare Economics: that every competitive equilib-rium is Pareto-optimal, such that no one can be made better off without making someone else worse off, and that any Pareto-optimal allocation can be achieved

as a competitive equilibrium with some redistribution of the agents’ initial endowments Lerner and Lange had used these results to argue for economic planning and market-based socialism, and engaged with Austrian thinkers in what became known as the Socialist Calculation debate (Lavoie, 1985) But many Pareto-optimal allocations remained from which to choose; an important research project became the determination of the best Pareto optimum The approach favored by Samuelson, building on the work of Abram Bergson (1938), posited

a social welfare function ordering all allocations The Bergson–Samuelson social-welfare-function approach was to receive a fatal blow, however, due to the Impossibility Theorem of Kenneth Arrow (1951b) Arrow and his associates, Gerard Debreu and Tjalling Koopmans, also challenged the use of calculus in microeconomic theory

24.3 ARROW’S IMPOSSIBILITY THEOREM

Postwar activity in microeconomic theory began with Samuelson’s Foundations The 1950s were ushered in by Kenneth Arrow’s Social Choice and Individual

Values (1951b), also begun as a Ph.D dissertation Contributing to the Cowles Foundation monograph edited by Tjalling Koopmans on activity analysis (Arrow, 1951a), Arrow deployed the Cowles Foundation’s axiomatic approach

to economic theorizing After moving to the Rand Corporation, he explored when supra-individual entities such as societies and nations could be said to have well-behaved preferences of the sort attributed to individuals in neoclassical

economics (the importance of Cowles and Rand in the development of the economics of this period is discussed by Mirowski, 2002; see also Leonard, forthcoming) Arrow’s exploration led him to his Impossibility Theorem, which concluded that under fairly innocuous conditions, including one on nondictator-ship according to which no single individual’s preferences would dominate the social ranking, there were no such well-behaved preferences This proved to be a remarkably durable result

It is also a negative result and has important consequences for the neoclassical project Much of economics and politics – and social science generally – is con-cerned with making statements about collectivities: countries, societies, groups, and institutions The hope that such statements could have solid microeconomic foundations in individual optimization was devastated by Arrow’s Impossibility Theorem It also had other important consequences For example, the Bergson– Samuelson social welfare function – an attempt to make a statement about which economic allocations were best, as opposed to the imperfect ranking given by the Pareto criterion – was a direct casualty of the Impossibility Theorem Neoclas-sical economics could not presume to say much about the overall ranking of allocations except in terms of the quite partial ordering implied by the First Welfare Theorem and its emphasis on (Pareto) efficiency The usefulness of the Second Welfare Theorem was also limited: asserting that any competitive equi-librium could be obtained with a suitable configuration of endowments, the theory was unable to develop a coherent comparative statics by which changes in endowments could relate to changes in equilibria, and this assertion could never approach practical implementation

Arrow’s theorem announced two further troubling and interrelated themes for neoclassical theory The first is its problem with the aggregation of individual economic relations; this surfaced in Arrow’s theorem itself, in the capital contro-versies of the 1960s (Harcourt, 1972) and in the Sonnenschein–Mantel–Debreu results on the arbitrariness of aggregate excess demands (discussed in section 24.5) The inability to address aggregated economic relations means that the legitimate scope of the theory is circumscribed and its usefulness is bounded The second, related problem is that the course of neoclassical theory has often been thwarted by internally generated impossibility results By “internally generated”

is meant that it is results of the neoclassical theorists themselves that often have shown the limits of the theory But this is to get ahead of ourselves The heady and confident days of neoclassical microeconomic theory continued, as general equilibrium theorists achieved successes in establishing the existence of competi-tive equilibrium

24.4 THE EXISTENCE OF COMPETITIVE EQUILIBRIUM

Authors in the 1930s and 1940s did not pay much attention to rigorous demon-stration of the existence of a general equilibrium In the early 1950s, this issue received considerable attention The existence issue had already been examined

by the theorists of the Vienna Colloquium around 1930 (Weintraub, 1983), when

they explored the equations that Gustav Cassell derived from Walras’s work (this strand of general equilibrium theory is often called neo-Walrasian) Frederik Zeuthen, Hans Neisser, and Heinrich von Stackelberg noted problems with the Walras–Cassell equations, including the possibility that prices might be negat-ive in a proposed solution Karl Schlesinger proposed complementary slackness conditions, and Abraham Wald fashioned a general equilibrium proof using inequalities rather than equations John von Neumann’s work on other issues resulted in the introduction of fixed-point theorems into economics that would become important in existence proofs The German invasion of Austria, however, meant the end of the Vienna Colloquium, whose members, in large part, fled Vienna into exile in the United Kingdom and the United States

The efforts to demonstrate the existence of competitive equilibrium continued

in the United States under the auspices of the Cowles Commission, which began

in Chicago (later moving to New Haven) The general equilibrium theorists (Arrow, Debreu, Tjalling Koopmans, Lionel McKenzie, and others) used math-ematical techniques resembling those employed by the Vienna group rather than the calculus methods of Hicks and Samuelson The Cowles economists, including Arrow (1951b), used axiomatic reasoning (which had also played a prominent

role in von Neumann and Morgenstern’s 1944 Theory of Games and Economic

Beha-vior) They also employed set theory, especially as it analyzed convex structures (Koopmans, 1957; Debreu, 1959) Many of the economic issues that they exam-ined were similar to those considered by Samuelson: consumer theory, producer theory, and the theorems of welfare economics These were reconsidered with the new mathematical methods, often exaggeratedly contrasted with the earlier calculus: Debreu wrote disparagingly of “calculus and other compromises with logic” (Debreu, 1959) The basic tenets of this approach were given in the meth-odological treatment of Koopmans (1957) and the summary statement of Debreu (1959)

These authors referred to existence proofs of Arrow and Debreu (1954), Lionel McKenzie (1954), David Gale (1955), and Hukukane Nikaido (1956) In these proofs, the general equilibrium theorists demonstrated the existence of com-petitive equilibrium using fixed-point theorems, such as that of Kakutani, which was related to the fixed-point theorem introduced to the economics literature by von Neumann (1937) in his growth model, printed in English translation in 1945 These accomplishments were important in moving the general equilibrium pro-gram forward Problems were immediately recognized, however For example, the economic models with which the theorists’ demonstrated existence did not demonstrate the specialization taken for granted in market economies (Rizvi, 1991) However, the most important set of problems was that of the definiteness

of the competitive equilibria

While the existence proofs demonstrated that the general equilibrium equations had some solution, they did not show that there was just one equilib-rium (uniqueness), that the economy would converge to an equilibequilib-rium if it were not in one or were perturbed while in one (stability), and that the precise characteristics of the equilibrium could be found once the data of preferences, endowments, and technology had been given (computability) These important

concerns had been broached by Hicks (1939), Samuelson, and others, and then by the axiomatic general equilibrium school (Koopmans, 1957; Scarf, 1967) Other important concerns were not addressed in the existence work, but had to be if general equilibrium theory were to be a progressive research program One was the issue of comparative statics, which answered the question: If an aspect of the data of the problem (preferences, endowments, or technology) changed in some direction, how would the equilibrium change and could we expect this change to

be uniformly in a particular direction? This was clearly related to uniqueness Other questions were: Could existence of equilibrium be proved for imperfectly competitive economies? Could the general equilibrium project help to identify econometric equations? Could general equilibrium theory underpin the the-ories of money and of macroeconomics more generally? What about capital and growth? In this sense, the demonstration of existence raised more questions than

it answered

It was difficult to make progress on these questions during the later 1950s and 1960s; many new ideas emerged, which nevertheless did not conclusively settle matters For example, the stability of equilibrium was examined by Arrow and Leonid Hurwicz (1958), Arrow, Block, and Hurwicz (1959), and Lionel McKenzie (1960) No sooner had this work begun than counterexamples to the kind of stability sought began to appear: by Herbert Scarf (1960), for instance The re-sponse was to reformulate the concept of stability, as in the work on

non-tâtonnement stability (Frank Hahn and Takashi Negishi, 1962) A similar dynamic

is seen in work trying to meld the theories of money and of general equilib-rium Donald Patinkin’s (1956) initial attempt was criticized by Hahn (1965) along strictly general equilibrium lines In response to his own critique, Hahn – along with others – tried to develop an equilibrium theory of money based on transaction costs and sequence economies (Hahn, 1971, 1973; Grandmont, 1977) Likewise, when Edmond Malinvaud (1953) was able to incorporate aspect of capital into the general equilibrium framework, he did so by incorporating an intertemporal equilibrium framework (Milgate, 1979) In each of these cases – from more usual

stability concepts to non-tâtonnement stability, from straightforward approaches

to money to transactions cost and sequence economy approaches, and from synchronous to intertemporal equilibrium – changes arose because of a lack of progress on the basis of the earlier, more clear-cut concepts The result was a theory that became increasingly abstruse and rarefied, such that the average practitioner increasingly became disenchanted with and unable to understand

or use general equilibrium theory This process continued throughout the 1960s and 1970s and beyond, as conceptual innovation and ever-greater mathematical sophistication was applied to seemingly fundamental aspects of microeconomics for which clear and simple answers ought to have been available

This trend bears some examination In the pages of Econometrica, Review of

Economic Studies , Journal of Mathematical Economics, and Journal of Economic Theory,

numerous articles seemed to have little relevance to the main concerns of most economists The mathematics employed was high-powered and arcane One ex-ample was the many works aimed at demonstrating that the core of an economy would converge to its competitive equilibria as the number of agents in the

economy increased without limit In establishing this Edgeworthian conjecture, economists used the mathematically sophisticated tools of measure theory and nonstandard analysis It was impossible for many economists to read this liter-ature Debreu and Scarf (1963) demonstrated this conjecture for a case where the set of agents was repeatedly replicated in its entirety Robert Aumann (1964) did the same for a case in which the economy had a continuum of agents, akin

to points on a line A key mathematical device from measure theory, Lyapunov’s Theorem, came to be widely used Edgeworth’s conjecture was developed for more and more general cases by Truman Bewley (1973), Werner Hildenbrand (1974), Donald Brown and Abraham Robinson (1972), and Robert Anderson (1978) With each development, the mathematics became harder to understand and the additional insight gained was arguably decreasing

This pattern was seen in several other areas of general equilibrium endeavor First, general equilibrium theorists became concerned with the existence of gen-eral equilibrium with an infinite number of goods This meant the use of infinite-dimensional vector space theory The problem was first set by Debreu (1954) and followed up by Truman Bewley (1991 [1969], 1972), Bezalel Peleg and Menahem Yaari (1970), and many others Secondly, Debreu (1970) realized that some pro-gress on uniqueness could be made if the differentiability assumptions he had once disparaged were applied in very particular settings He employed Sard’s Theorem from differentiable topology to demonstrate that, in such settings, equi-libria are locally unique, such that there is usually a finite number of equiequi-libria Egbert Dierker (1974) and many others then applied the methods of global ana-lysis to the problem of uniqueness In these and many other cases, sophisticated mathematics, comprehensible to a few and used in very restricted domains, was employed to pursue a topic that did not really speak to the main concerns of economists

Consequently, a pressing need existed for clarity and progress in general equilibrium theory In an attempt to provide these, Arrow and Hahn (1971)

wrote their epochal textbook, General Competitive Analysis, which heralded the

beginning of a decade that was to prove fateful for microeconomic theory

24.5 THE ARBITRARINESS RESULTS

In General Competitive Analysis, Arrow and Hahn restated and summarized the

main results of the general equilibrium efforts of the 1950s and 1960s, and formu-lated a series of research questions that would have to be answered for the theory

to make progress The problems were stability, uniqueness, comparative statics, econometric identification, imperfectly competitive general equilibrium, and the microfoundations of macroeconomics

This last topic shows how central microeconomic theory had become to all aspects of economics In the neoclassical approach, theoretical development proceeded on the basis of individualist foundations This implied that for a theory

to be well founded, it had to have a microeconomic basis Since all of the formal theory of economics was evidently at the microeconomic level, and formalist

general equilibrium theory was microeconomics par excellence, no sub-field of

economics could be said to have an adequate foundation without becoming, as

it were, an applied field of general equilibrium theory Thus macroeconomics – as a conceptually distinct field from microeconomics – nearly disappeared, except as serving as a label, during this time E Roy Weintraub (1979, p 5) stated quite correctly for the time he wrote in that “even those few economists who

argue that current microeconomics does not generate macroeconomics have been

extremely shy in their attempts to convince their colleagues of the seriousness

of their concerns.” Allan Drazen (1980, p 293) similarly expressed a common view when he held that “explanations of macroeconomic phenomena will be complete only when such explanations are consistent with microeconomic choice theoretic behavior and can be phrased in the language of general equilibrium theory.” Many economists today recall the period of 1970–85 as one in which nearly every economic statement was considered suspect without some sort of microfoundations; this thinking continues in large measure to this day, albeit with significant exceptions (Rizvi, 1994b) A curious feature of this period was the reliance on representative agent models that purported to demonstrate microfoundations with the use of a single agent or very few types of agent This particular approach has been criticized very effectively (Kirman, 1992)

Suffice it to say, general equilibrium theory as it emerged in the time following Arrow and Hahn’s book had a very large burden to bear It proved unequal to this task Such became clear in a spectacular series of impossibility results that might be called Sonnenschein–Mantel–Debreu (SMD) theory after its main promulgators (Rizvi, 1994b, 1997b) In the 1970s, it was established that despite the availability of well-behaved axioms at the individual level, the aggregate excess demands arising in Walrasian formalist general equilibrium models were arbitrary, except that they satisfied Walras’s Law and a form of continuity These two properties were needed to establish existence of the general equilib-rium solutions, but all of the Arrow–Hahn desiderata mentioned at the beginning

of this section required well-behaved aggregate excess demands Economists eventually came to see that there could be no general results on uniqueness (Mas-Colell, 1977), stability (Sonnenschein, 1973), comparative statics (Kehoe, 1985), econometric identification (Diewert, 1977; Stoker, 1984a,b), imperfectly com-petitive general equilibrium (Roberts and Sonnenschein, 1977; Grodal, 1996), and microfoundations of macroeconomics (Rizvi, 1994b) The SMD articles showed that formalist general equilibrium theory had reached a dead end: no general results beyond existence of equilibrium were possible

Consequently, when SMD theory became well known by the early 1980s (for example, through the survey by Shafer and Sonnenschein, 1982), it became increasingly clear to many economists that general equilibrium theory could not fulfill a promise of over 30 years This realization had serious and unsettling consequences Werner Hildenbrand wrote that:

When I read in the seventies the publications of Sonnenschein, Mantel and Debreu

on the structure of the excess demand function of an exchange economy, I was deeply consternated Up to that time I had the nạve illusion that the microeconomic

foundation of the general equilibrium model, which I had admired so much, does not only allow us to prove that the model and the concept of equilibrium are logically consistent (existence of equilibria), but also allows us to show that the equilibrium is well determined This illusion, or should I say rather, this hope, was destroyed, once and for all, at least for the traditional model of exchange economies (Hildenbrand, 1994, ix)

It is difficult to overstate the importance of the arbitrariness results for neo-classical microeconomic theory Arrow’s Impossibility Theorem meant that general progress on welfare economics in the neoclassical vein was unattainable; the SMD theory meant that microeconomics could not yield determinateness

to general equilibrium Importantly, it also meant that the project of providing aggregate phenomena with a basis in general equilibrium microeconomics had come to an end (Rizvi, 1994b) The results had an epoch-ending impact Erst-while champions of general equilibrium theory have had to abandon the field Christopher Bliss thus wrote, “The near emptiness of general equilibrium theory

is a theorem of the theory” (Bliss, 1993, p 227)

Once the arbitrariness results called into question the central status of general equilibrium theory, a stage of pluralism in microeconomics ensued (Rizvi, 1994a, pp 2–6; 1997b, pp 275–6) Strictly, the arbitrariness results put an end to neoclassical general equilibrium theory of the Arrow–Debreu–McKenzie variety Many neoclassical ways of thinking – partial equilibrium arguments, textbook presentations, many applications, and much of economic practice – still persist, even if they might explicitly or implicitly make reference to an underlying general equilibrium model More in keeping with the emphasis of this essay on theoretical developments, it is notable that rational-choice game theory, experi-mental economics, and other developments arose in the early- to mid-1980s In each case, no significant theoretical or methodological innovations were deep enough to have caused this upsurge Rather, general equilibrium theory vacated the dominant position it had enjoyed since the early 1950s, and these alternative approaches were able to develop and to receive a hearing on issues that the previous theory could not

24.6 GAME THEORY AND EXPERIMENTAL ECONOMICS

The still-continuing wave of pluralism in economic theory, begun in the wake of general equilibrium theory’s collapse, is seen in the work on complexity (Mirowski, 2002), experimental economics, the market demand approach championed by Hildenbrand, Grandmont, and others, and other approaches (Rizvi, 1997b) The most prominent of the pluralist approaches became rational-choice game the-ory (Rational-choice game theory contrasts with game theory that emphasizes rule-following behavior, such as evolutionary game theory.) In the early 1980s,

as increasing numbers of economists accepted the gravity of the arbitrariness results, game theory seemed to have certain things in its favor (see contributors

to Weintraub, 1992) It dealt with strategic interactions, had a history of dealing with imperfect competition, and had recently been revivified with Harsanyi’s

(1973) reinterpretation of mixed-strategy equilibrium and Rubinstein’s bargain-ing result (1982) It is arguable, however, that its ascendance occurred mainly because of the vacuum created by the collapse of general equilibrium theory An example illuminating this transition may be seen in comments by Sonnenschein –

a key figure in establishing the problems with general equilibrium theory – who showed a way out of the older theory and toward game theory, despite reserva-tions (Rizvi, 1994a) In commenting on a paper by Oliver Hart that surveyed the unsuccessful attempts at demonstrating an imperfectly competitive general equilibrium, Sonnenschein (1985, p 176) argued that there was a need for “new blood” and that this was to be provided by rational-choice game theory He also mentioned his students, Dilip Abreu, Vijay Krishna, David Pearce, Motty Perry, and Leo Simon – who were to be influential in the new trajectory – as influencing his thinking Sonnenschein quite explicitly linked the need for game theory to the problems with general equilibrium He wrote that game theory has ideas “that are useful for the theory of monopolistic competition My feeling is that the Negishi line [of approaching imperfect competition via general equilibrium theory], which builds on the Arrow–Debreu–McKenzie theory, has been pretty much played out” (Sonnenschein, 1985, p 176)

This turn toward the theory of games in economic theory gained enormous momentum at this time Fisher (1989, p 113) correctly asserted that “game theory [had come] to the ascendant as the premier fashionable tool of microtheorists That ascendancy appears fairly complete.” Very shortly after Fisher wrote, the textbooks and treatises by Kreps (1990a,b) and Fudenberg and Tirole (1991) cemented the position of game theory in economic theory Rational-choice game theory reached beyond pure theory, however, transforming many fields, including industrial organization and international economics Industrial organization in particular was thoroughly changed; Tirole’s (1988) game-based treatment became the leading textbook in the field This trend was documented by Peltzman (1991) Rational-choice game theory came to dominate microeconomics and its applied fields (Rizvi, 1994a)

Unfortunately, rational-choice game theory suffered from key foundational problems Once again, the cycle of theoretical difficulty following theoretical transformation arose in neoclassical microeconomics A key problem for rational-choice game theory was the very concept of rationality in a game-theoretic setting (Rizvi, forthcoming) The primary difficulty is that its common solution concepts (prescriptions as to how to play a game), such as Nash equilibrium, are burdened with extremely implausible common-knowledge assumptions (Brandenburger, 1992; Bicchieri, 1993) Common knowledge means that each player knows that each player knows that each player knows (and so on) each player’s rationality and structure of the game With such an immense structure of know-ledge being assumed, the idea of strategizing, which involves guesswork in the face of a lack of knowledge, is nearly rendered incoherent

Common knowledge also has important negative implications for the eco-nomics of asymmetric information, on which a large edifice has been built, usually

in the context of game-theoretic models (Riley, 2001) Asymmetric information models are used to illuminate areas as diverse as incentives, auctions, insurance,