1The Walrasian model of perfectly competitive general equilibrium (from now on, the ‘Perfect Competition Paradigm,’ PCP) has provided the benchmark for almost any research in price-production-distribution theories over a period of more than one century in the history of modern economics. It has always been clear, however, that the model does not analyse competition as such—the kind of activity usually called ‘competition’—but only the alleged final outcome brought about by competition once its work has been completed, so to speak. Consequently, the epistemological status of the PCP, as the foundation of a scientific theory of the functioning of a market-based competitive economy, has been uncertain ever since its beginnings: what kind of knowledge is it supposed to convey? Even a summary survey such as the present one is enough to make us realize that there is no universally accepted answer. Add to this the consideration that the PCP has ethical and political implications, which different authors have interpreted in different ways, so that a general agreement is also missing from this point of view. Indeed, the optimality property of perfectly competitive equilibrium has not convinced all economists that perfect competition is completely in line with the objectives of a fair and well-functioning society: in the last section I shall focus on the reservations of two eminent founding fathers of modern economics, Pareto and Marshall. Now that a widespread feeling exists that the age of the PCP as the sole benchmark is over, we may pause a moment to wonder what has happened to all the ambiguities that were attached to it in today’s new theoretical situation. Have we done away with them, or are they still with us but in a metamorphosed shape? In this paper I shall argue that the latter seems to be the case, and that the metamorphosis follows from the fact that economic theory has developed better instruments to deal with those ambiguities so that, as a result, we now have a better understanding of the nature of the underlying problems.
2To begin with, I try to summarize what the PCP has yielded in terms of propositions concerning competitive economies. It is generally agreed that the PCP does not tell us much about how perfect competition works, but only (1) what its final consequences are supposed to be, and how they may vary as a function of structural (preferences and technology) and nonstructural (initial endowments) characteristics of the economy;  (2) that such consequences are logically viable in the sense that perfect competition does not clash with any inevitable in-built contradiction; and (3) that such consequences cannot be improved without conflict, in the sense that modifications that all traders would perceive as being improvements, or at least neutral, are not available. All of these points are now well understood, thanks to the huge amount of literature that deals with them. Since the common object of this literature is equilibrium defined as a state of affairs in which all incentives to what is normally considered competitive action are absent—traders have no better alternative than to carry out the plans that are most advantageous at the ruling prices—one might be tempted to conclude that one of the PCP’s teachings is that competition is a type of activity that, in ideally perfect conditions, ends by wiping out the prerequisites for its own continuation, a finally self-effacing activity.
3Besides the obvious ‘invisible hand’ associations, this conclusion also has a somewhat Kantian flavour, which may explain why its fascination goes beyond the amount of light that it throws on real-world competition. If propositions (1) to (3) are proved to be true, then competitive behaviour, in spite of all its aggressive and disorderly associations, passes the Kantian test of universalization brilliantly: if it becomes the general rule of behaviour, it results in a peaceful and orderly social state in which everybody pursues his/ her own happiness in the best possible way, with the awareness that everybody else is doing the same thing, and that nobody’s accomplishments are an obstacle to the others’. This normative side of the story has led economists from opposite ends of the political spectrum—one may cite Walras himself from the socialist end, and ultra-liberals such as Pantaleoni and Hayek from the other—to consider PCP as the demonstration that an ideal state based on a very advanced level of decentralization is possible, although opinions as to the political routes leading to it may differ.
4This construction, it may be argued, is vulnerable in at least two respects. First, the supposition under (1) above has never been demonstrated in a convincing way. Secondly, the non-improvability property under (3) refers to those components of happiness that can be the object of private transactions alone, and does not generally exhaust all the relevant components nor exclude negative interactions between ‘tradable’ and ‘non-tradable’ components. The two points are independent of each other: the first accounts for some of the epistemological ambiguities of PCP, and the second, for some of the ethical and political ambiguities. I shall discuss the two in order.
5In assuming that competition would lead to a state of general equilibrium from which competition was in fact removed, Walras relied on a peculiar kind of market organization that precluded competition not only in equilibrium but in all the states of the system, by allowing traders to communicate their intended transactions to an impersonal, computer-like clearing house instead of vying with each other for the best contracts. Even if he had been able to show the tâtonnement stability of equilibrium, therefore, this would have told us nothing as to whether and how actual competition is eventually able to turn into the sort of ‘spontaneous order’ postulated by PCP.  But he was unable to do so in any case, and later work on tâtonnement stability has shown that his argument was unwarranted unless restrictions are introduced that reduce the scope of the theory considerably. Pareto, who had no particular sympathy for tâtonnement,  and found the dynamics of general equilibrium still beyond the reach of the theory of his time, contented himself with expressing the unsupported belief that real systems lie in close vicinity to their equilibrium at all times, moving instantaneously with all the changes of the data on which equilibrium is based. As Donzelli  has argued, this changed the interpretation of equilibrium from Walras’s original static interpretation to that of a temporary position that moves in time. But apart from this further ambiguity, it is the very nature and way of operating of competition that both authors left unconnected to their general equilibrium theories.
6In a seminal paper of 1959, Arrow made it clear that the claims of PCP to provide an understanding of real-world competition make sense only if they are founded on an actual decentralization of allocation processes with all their uncertainties and strategic possibilities, and not on Walras’s semblance of decentralization. Out of equilibrium, therefore, non-tâtonnement stability is the only relevant kind of stability. But this involves dealing with the dynamics of a market in which some traders are price setters, some are rationed according to rationing schemes that defy general modelling, Jevons’ law of indifference does not apply, and which plans are optimal depends on each agent’s beliefs and information on what is going on in the whole economy. Either a Walrasian equilibrium can be shown to have a chance of emerging out of this world of imperfect competition, uncertainty and learning, or it remains a virtual state lacking in sufficient reasons for becoming true. A robust line of research in the 1960s and 1970s, and one that for a while seemed to offer the possibility of a much sought-after synthesis between micro and macro analysis, the study of non-tâtonnement stability finally came to a halt with somewhat disappointing results. Convergence can be proved to occur only under rather artificial restrictions, and in any case all attempts to model out-of-equilibrium behaviour with even a moderate amount of realistic detail lead to explosive complexity quite soon. Once again, the clarification of the epistemological status of PCP was delayed to a better occasion.
7Approximately during the same period, the formalist turn in general equilibrium theory seemed to provide a way out by explicitly disowning all pretensions to empirical descriptive accuracy on the part of the theory. In the preface to his 1959 masterpiece, Debreu made a frank statement of complete disconnection between theory and interpretations, with the former being an object subject only to mathematical rules, while the latter is the result of an activity that comes into play only after the theory has been constructed [Debreu, 1959: x–xi]. As he explained a few years later, this ‘complete surrender to the embrace of mathematics’ was intended to compensate for the unreliable empirical basis of economics which, unlike physics, cannot afford to be guided by controlled observation even to an occasional violation of the canons of logical rigor [Debreu, 1991: 2–3]. By continuing along this line, it has been authoritatively said that perfect competition should be considered ‘as an organizing concept and certainly not as an innocuous descriptive category for the real world.’ [Mas-Colell, 1980: 123] This is a striking statement, since it sees PCP in exactly the same role of organizational device that Hilbert assigned to the axiomatisation of mathematics, thus consigning PCP to a world of abstract algebraic structures perfectly isolated from facts. But this was not what the founders of general equilibrium theory had in mind. Walras thought of it as the normative model of a just economy, and Pareto, the more matter-of-fact of the two, saw it as the first step in the construction of a science of society that was no different from any natural science based on observation and reasoning. Although both Walras’s idealism and Pareto’s positivism are now out of fashion, there is no doubt PCP is still used by contemporary economists in fields of semi-applied economics (including macroeconomics and public economics) as if it were an adequate enough description of features of the real world. Just to offset the previous quotation from Mas-Colell with a reference going in the opposite direction, see the defence of the role of the general equilibrium model in empirical development studies by Acemoglu . In looking at these two texts side by side, one realizes that all the uncertainties surrounding the epistemological status of PCP are still there.
8While this remains true, however, two kinds of improvements in our ‘tooled knowledge’ (I take the Schumpeterian quotation from Makowski and Ostroy ) that have occurred over the last two decades or so have considerably changed our view of the whole theoretical situation, including the role and interpretation of PCP. I am referring, first, to the importation of dynamic methods from physics, engineering and computer science which, together with the availability of low-cost computing technology usable in simulations, make it possible to explore processes that exhibit what are now known as ‘complexity’ features. Secondly, the application of game-theoretic methods of solution to schemes of economic interaction, that were previously treated in terms of equilibrium or not treated at all. Both improvements help to deflate the unique importance of PCP as the fundamental benchmark of economic theory. The former seems also to be exempt from the epistemological ambiguities of PCP, while the latter shifts them from market dynamics to agents’ beliefs—not a real clarification, in fact, but arguably a more meaningful insight into the nature of the problems we are facing. I will deal with these two aspects briefly in the following paragraphs.
9With hindsight, it is not difficult to understand why the non-tâtonnement stability research program died out about thirty years ago. At the time, models of strategic interaction with or without imperfect information and/or learning were already widely applied in market analysis; the Santa Fe research program in the sciences of complexity was beginning its course, and the range of market forms, transaction technologies, contracts, mechanisms and dynamic processes subjected to modelling grew beyond limits. With so many novelties going on, no wonder that any interest in the stability of what was by then becoming a very special kind of market form dwindled.  Moreover, agent-based models of decentralized exchange intended to reproduce one feature or another of competitive trading show that convergence to a Walrasian general equilibrium may be confirmed as, e.g., in Gintis , or disconfirmed [Axtell, 2005], depending on the details of the out-of-equilibrium process. The effect is that of both clarifying the empirical status of PCP and of stripping it of its distinctive uniqueness. Point (1) of section 1—is Walrasian equilibrium the final outcome of some sort of competitive process?—may be warranted, but only on condition that the process follows precisely defined rules in a precisely specified environment. Otherwise, competition may not converge or converge on equilibria that are still competitive but do not have all the Walrasian characteristics. In the case of Axtell , to quote an example, equilibria are path-dependent, redistribute wealth during the trading process, and are generally non-Pareto efficient. Moreover, the flexibility of the tool is such that it may possibly generate a variety of competitive patterns that are still unexplored. Perhaps this announces the dawning of a new ‘emerging social economics’ as has been said with some emphasis [Durlauf and Young, 2001], or may be simply one of many possible lines of research supported by new tools. But in any case, all these dynamically-based approaches go in the direction of a theory of competition with a strong descriptive bent, in accordance with the empirical demands of many classical and contemporary economists, and are willing to face up to the collapse of the single-paradigm pre-existing situation.
10Game theory, too, is a flexible enough tool to generate many forms of competitive outcomes beyond the classical PCP—think only of the varieties of possibilities afforded by the concept of ‘strategy’ in modelling the interaction between the parties to a contract. Thus, pluralism is guaranteed along this line of research as well. But the shift from equilibrium to game-solving is less radical than it may appear at first sight, while the implications are perhaps subtler and more far-reaching. One may say that an alternative, crypto-game-theoretic way of looking at competition had always been available even before the official birth of game theory, at least since Cournot in 1838 and Edgeworth in 1881 analysed competition directly in terms of strategic interaction, and argued that the case of price-taking equilibrium could be considered as the limit of a sequence of solutions generated by a sequence of ‘replica markets’ with numbers of participants tending to infinity. In fact, these two theories of competitive markets have been the main channels through which more robust foundations of PCP have been attempted in recent years, by re-interpreting it as an approximation either of the Cournot-Nash solution of a large enough non-cooperative market game (see the JET symposium introduced by Mas-Colell ) or of the core of an equally large coalitional game.  Thus, on the one hand it might be said that the move to game theory has not been such a revolution for the established view of perfect competition. But on the other, it has resulted in a profound change in the questions connected with point (1) above, namely those that we have seen to be at the basis of the epistemological ambiguity of PCP. And while this ambiguity has not been removed—if PCP is now seen as the limit of a sequence of solutions, we still do not know whether each solution of the sequence is a reliable prediction of the outcome of the corresponding market game, or is just a theoretical recommendation that the players have no compelling reason to follow—it has, however, taken on a different shape. By re-interpreting the (mechanical) equilibrium of a market model as the solution to the market game put in its place, the focus is shifted from the features of the dynamical field underlying equilibrium to the epistemic foundations of the solution concepts applied to market games.
11This change in perspective has many implications, one of which may be noted here in passing. In analysing market games, there is a formal difference between using solution concepts of the non-cooperative or cooperative kind, but from the point of view of the foundations this does not make a substantial difference. Thanks to insights into the non-cooperative foundations of cooperative behaviour provided by game theory, we now see more clearly that the classical competition/cooperation opposition is a false one, perhaps induced or favoured by Walras’s disregard of interpersonal trading as necessarily leading to agreements in the form of contracts. Edgeworth, who was more alert than Walras to the fact that competition is basically a rivalry in contracting, had a clear notion of its mixed nature, ‘pax or pact between contractors during contract, war, when some of the contractors without the consent of others recontract.’ [Edgeworth, 1881: 17] This mixed nature is well mirrored in game-theoretic solutions of both the cooperative and non-cooperative kind. In both cases, a solution is a potential agreement among individuals or among coalitions as concerns the outcome of what in effect is a social choice problem involving enormous amounts of distributed information. The question is, what kind of reasoning leads the participants in the market game to the conviction that doing their part in a given solution is the best thing they can do? And what basis of common knowledge and beliefs must be assumed in order to support that reasoning? This issue, that has generated a vast literature in recent years, cannot be pursued further here. I simply observe that the fact of redirecting our interest from the features of out-of-equilibrium dynamics to the epistemic conditions underlying the strategic choices of market agents has taken us nearer to what seems to be the root of the problem, namely the emerging of a community of information and beliefs out of repeated and uniformly regulated interaction.
12While ‘new generation’ dynamics and simulations take care of the complexity of observed market processes, game theory provides a framework for dealing with the subtler epistemic issues involved in the analysis of the behaviour of market participants. At present, this seems to be the scheme of the division of labour that has emerged from the collapse of PCP as the main benchmark of economic theory.
13Lastly, a few remarks about the ethical and political implications of PCP in the present-day state of the art. The lack of a convincing theory regarding the emergence of perfectly competitive equilibria somehow deflates the claim that may be attached to competition as a form of action leading to the establishment of a relatively optimal social order. But even if we ignore this difficulty, there is a further reason for questioning the substance of the claim. For a committed utilitarian like Edgeworth, relative optimality was enough to qualify a perfectly competitive equilibrium (in his own sense) as a sort of ethical baseline, joining ‘egoistic’ to ‘universalistic’ or ‘Benthamite hedonism’ in a way that depends only on the initial endowments and the given utility functions, i.e. on impersonal factors and chance alone. ‘Of justice and humanity there was no pretence; but there seemed to command respect the majestic neutrality of Nature.’ [Edgeworth, 1881: 50] But there was also a more sceptical line of thought that, from the very beginning, pointed out that mixing positive analysis of the price system and ethical judgement might result in unacceptable confusion. Just to keep to eminent names, we may recall here the positions of such different authors as Pareto and Marshall.  The former disagreed with almost everything that the latter stood for, but the two had one common opinion concerning the optimality of competitive equilibrium: this was an optimum according to the evaluation of the individuals involved as to what is good for them, but not according to an objective assessment as to what is good for society as a whole. Marshall expressed this idea in the shape of criticism of the fact that equilibrium gives excessive prominence to the desires of those in control of relatively large amounts of purchasing power, whatever the importance of the sacrificed desires may be in the eyes, for example, of a moral philosopher concerned with opportunities for human development [Marshall, 1897 (1925): 302– 5]. Pareto dealt with the same point when he introduced the well-known distinction between ophelimity and utility in his 1896-7 Cours d’économie politique, utility being the field for the judgement of the sociologist who has a clearer notion of what is good or bad for society than its individual members, biased as they normally are by their primary concern with personal ophelimity and by poor understanding of collective interests. In different ways, these authors emphasized the fact that the kind of satisfactions or utilities that are consciously pursued by means of the contractual activity carried out in markets are only a part, even if an important one, of the utilities that are relevant for the well-being of the market agents themselves and of the social groups to which they belong. Competitive markets provide a method, based on prices, for weighting the individual assessments of these, so to speak, ‘tradable’ utilities. But other methods are possible that take ‘non-tradable’ utilities into account and lead to outcomes that may be judged more desirable although some individuals may disagree. Provided all methods avoid ‘inflicting unnecessary sacrifices on the entire collectivity,’ as Pareto put it in a concise treatment of the issue [Pareto, 1913: 341], that is, provided they do not give up available utilities to nobody’s advantage, there is nothing to recommend the competitive method as being more worthy than any of the others or as being deserving of a special position among the others.
14Pareto’s and Marshall’s misgivings about the virtues of perfect competition touch upon two distinct aspects that have subsequently been developed in different lines of the literature originating from PCP. One is the issue of the ‘non-tradable’ utilities that has been at least partially captured by the notion of externalities and has become one of the main objects of welfare economics. The other, the scarce reliability of market agents in the task of assessing their own, and their social group’s interests—an issue that has led a branch of social choice theory to question whether Pareto optimality is a defensible criterion in comparison with other collective values. A watershed in the former development is represented by Coase’s approach to externalities as signals of gaps in the normative order that call for alternative institutional solutions, with property rights and market transactions being only one of these. Continuing along this line, non-tradable utilities have become a part of the more general theme of the non-completeness of the market structure, a theme that originated from PCP but which eventually contributed to highlighting its limitations. Indeed, the PCP assumption that agents take the existing markets as an unmodifiable datum of the economy is less conspicuous but possibly more inhibitive than the identification of competition with price-taking [Makowski and Ostroy, 2001: 489–90]. The removal of the ‘market-taking’ assumption has played a significant role in obtaining a better understanding of the overall welfare implications of alternative institutional solutions to market failures [Newbery, 1990]. It also casts light on the creative side of competition by emphasising the opening up of new markets as a consequence of innovation.
15In all this we are still taking Pareto optimality as the ultimate criterion for social evaluation. The other development mentioned above is, instead, more radical in questioning the social relevance of the notion that underpins that criterion, i.e. individual preference. Whereas Pareto and Marshall envisaged an authoritarian [Pareto, 1913: 340–1] or paternalistic rule (see the Marshallian manuscripts published in Dardi ) to remedy the shortcomings of a mechanism overly exposed to the arbitrariness of individual tastes, discussions in social choice theory triggered by Arrow’s well-known impossibility theorem have taken directions that are politically more palatable.  Amartya Sen has emphasized the overly narrow informational basis of Pareto optimality as one of the sources of conflict between it and other desirable requisites of a social choice function.  In his view, the scope, context and background of expressed preferences should also be considered, especially when incompatibilities between them and widelyaccepted collective values surface. In the conclusions which he appended to a symposium on the ‘impossibility of a Paretian liberal’ [Sen, 1996]— concerning the possible conflict between Pareto optimality and a condition of minimal individual liberty—he insisted on conscious reflection on the part of individuals and public discussion as ways toward a democratic solution to such crises. This is not the place to expand on this theme. To us, it simply serves to mark another watershed in discussions about the ethical and political implications of PCP. Sen brings the issue back to where it belongs, the field of ethics and political philosophy, dispelling the illusion engendered by PCP that a decentralized automatic mechanism, however efficient, may perform the task of solving our problems of collective choice for us.
Dipartimento Scienze Economiche, University of Florence. email@example.com I am grateful to Ivan Moscati and to a referee of this journal for useful comments on a previous version.
Since an economy may have multiple equilibria, the function will generally be a multivalued function or a correspondence.
One further difficulty, one of which Walras did not seem to be aware, was due to the fact that, once equilibrium has been reached and traders are finally free to carry on their exchanges, the implementation of the equilibrium allocation raises a complex problem of coordination, the solution to which may vary, depending on the transaction technology adopted. To the best of my knowledge, Clower  was the first to point out this difficulty that gave rise to an abundant stream of literature focused on the role of money in general equilibrium.
He publicly defended Walras against Edgeworth’s attack on tâtonnement, out of his sense of loyalty to the French school and hostility to the British, but in his private correspondence with Pantaleoni expressed all his dislike of the device—see the letter of 19 February 1897 “in [Pareto, 1960: II, 35 ff]—and never used it in published writings.”
I am of course not implying that this was the only reason for the decline of that research program. In a 1982 survey of stability theory Hahn mentioned the ‘distressing ad hoc aspect’ of the whole subject and acknowledged the disturbing effect of the Sonnenschein-Mantel-Debreu findings on the properties of excess demand functions [Hahn, 1982: 747, 763].
The classical reference is Debreu and Scarf . But note that the similarity between the game-theoretic notion of the ‘core’ and the set of Edgeworth’s ‘final settlements’ can be disputed, see Vind .
As PCP is identified here with general equilibrium theory in the Walrasian version, considering the case of Marshall may appear out of place. It should be remembered, however, that while rejecting general equilibrium in favour of a partial equilibrium approach to value, Marshall referred to the simultaneous occurring of all equilibrium conditions as a frame for checking the logical determinacy of his own theory [Marshall, 1961, I: 855–6]. Besides, independently of Pareto, he provided complete verbal proof of the first fundamental theorem of welfare economics [ibid.: 470–1]. He was thus enough of an insider for his comments on the ethical implications of PCP to be taken seriously.
The discussion on ‘light’ or ‘libertarian’ paternalism induced by the recent wave of interest in behavioural economics may also be mentioned in this connection. For a survey of the arguments see Loewenstein and Haisley .
Although from a different point of view, also Bernheim and Rangel  explore the implications for normative welfare economics of enlarging the informative basis of individual preference judgements.