At Cowles: general equilibrium as a theory of organisation

Kenneth Arrow and Leonid Hurwicz first met at the Cowles Commission in the late 1940s, at a moment when postwar mathematical economics was undergoing a significant transformation. The publication of The Theory of Games and Economic Behavior (Reference Morgenstern and von Neumann1953) by von Neumann and Morgenstern opened a new approach to economic theory, one that could move beyond supply-and-demand analysis toward the broader realm of social interactions. New analytical tools promised novel insights, although their broader implications were not yet clear (Giocoli, Reference Giocoli2008). Efforts to extend mathematical analysis to the social sciences increasingly took shape around the emerging concept of organisation (Marschak, Reference Marschak, Thrall, Davis and Coombs1954; Morgenstern, Reference Morgenstern1951; Simon, Reference Simon1952).

At Cowles, under the directorship of Tjalling Koopmans (1948–1954), this transition involved a shift from the study of business cycles toward a research programme focused on rational decision-making and Walrasian general equilibrium theory (Düppe and Weintraub, Reference Düppe and Weintraub2014; Mirowski, Reference Mirowski2002: 264–65). This shift was not only methodological but also conceptual, involving a reframing of the economy as an organisational structure (Mirowski, Reference Mirowski2002: 355). In this transition, general equilibrium theory itself came to be viewed not merely as a theory of market exchange but as a general framework for analysing decentralised organisations (Boldyrev and Ushakov, Reference Boldyrev and Ushakov2016; Mirowski and Nik-Khah, Reference Mirowski and Nik-Khah2017; Mirowski, Reference Mirowski2002).

The term ‘organization’ was itself productively ambiguous, referring to a firm, an administrative unit, or an entire economic system seen as a network of decentralised decision-makers (Arrow, Reference Arrow1964). As one Cowles summary would note, the Commission’s work increasingly sought to analyse ‘economic organizations of various types’ – entities in which ‘the processes of decision-making and adjustment by individuals, firms, or public bodies are interdependent’. In this context, rational decision-making – whether individual or collective – became the central theoretical concern (Cowles Commission for Research in Economics, 1951: 15).

At the same time, the ambitions surrounding mathematical analysis widened (Arrow, Reference Arrow, Lerner and Lasswell1951b). Rather than focusing on markets, Cowles researchers increasingly viewed themselves, or at least presented themselves, as constructing a unified social science (Mirowski, Reference Mirowski2002: 265). As the Commission’s 1950–1951 report declared, ‘To determine the best economic organization in this wider sense is to study the central problem of our time (…) problems split between business administration, public administration, political science, and economics turn out to be special applications of the same general problem, that of optimal organization’ (Cowles Commission for Research in Economics, 1951: 14–15).

Cowles’ approach was explicitly opposed to the institutionalist tradition that had occupied a prominent position in interwar American economics (Mirowski, Reference Mirowski2002: 261–262; Rutherford, Reference Rutherford2011: 321–322). Yet this opposition did not imply a rejection of institutions as objects of economic analysis. Rather, in contrast to the historically specific mode of analysis associated with the older institutional tradition (Hodgson, Reference Hodgson1998), Cowles’s economists increasingly sought general analytical structures through which different forms of economic organisation could be described and compared.

This new ambition required a different conception of mathematics, and Cowles’s economists increasingly embraced abstract mathematical structures – optimisation, activity analysis, linear programming, and formal logic – rather than the calculus-based methods traditionally associated with neoclassical price theory. Following Koopmans’s emphasis on logic and structure, abstract mathematics was valued not merely for its rigour but because it appeared more suitable for analysing complex systems of social coordination extending beyond market exchange (Weintraub and Mirowski, Reference Weintraub and Mirowski1994).

As Arrow explained in a 1951 paper on mathematics in the social sciences, many critics assumed that mathematics was inherently quantitative and therefore unsuitable for social inquiry. Yet, Arrow argued, this view ignored the existence of mathematical fields – most notably symbolic logic – that were qualitative rather than quantitative in character (Arrow, Reference Arrow, Lerner and Lasswell1951b: 129–31).

This search for new formal tools unfolded along several directions. Game theory appeared promising because it shifted attention away from purely price-based interaction toward strategic and organisational relations, although its broader implications for social theory were not yet fully developed (Giocoli, Reference Giocoli, Arena and Lazaric2001, Reference Giocoli2008). Linear programming and activity analysis similarly attracted attention because they offered abstract approaches to optimisation under constraints that seemed applicable beyond conventional market settings (Düppe and Weintraub, Reference Düppe and Weintraub2014).

The intellectual trajectories of Kenneth Arrow and Leonid Hurwicz were shaped by this conceptual landscape. While Arrow’s early research ambitions, as evidenced by his initial doctoral plans, were directed toward constructing a realistic theory of competitive markets, his ultimate dissertation on social choice was celebrated at Cowles as a paradigmatic example of the new theoretical orientation toward abstract inquiry into collective decision-making (Cowles Commission for Research in Economics, 1951: 15). Indeed, in his monograph, Arrow suggested that a broad set of social organisations – from markets and democratic voting systems to customs and tradition – could all be analysed formally as modes of collective decision-making, understood as different methods of preference aggregation (Arrow, Reference Arrow1951c: 1–2).

For Hurwicz, Arrow’s work on social choice theory was particularly influential. Hurwicz’s own intellectual concerns had long extended beyond narrowly economic questions. As a Jewish émigré from Moscow who witnessed the political instability of interwar Europe, he was deeply concerned with the relationship between economic conditions and broader problems of social and political order (Hurwicz, Reference Hurwicz1940b). In an unpublished manuscript from the early 1940s, he argued that many major economic controversies ultimately derived from divergent underlying postulates – concerning competition, profit maximisation, or equilibrium stability – and called for a logical framework capable of clarifying the implications of alternative assumptions while integrating theoretical and empirical analysis (Hurwicz, Reference Hurwicz1940a).

Arrow’s early work provided Hurwicz with a powerful example of how such a framework might be constructed. Hurwicz later recalled being deeply impressed by Arrow’s ability to use abstract mathematical reasoning to define concepts rigorously and examine whether different normative and theoretical postulates could be logically reconciled (Hurwicz, Reference Hurwicz and Feiwel1987: 270). Inspired by this approach, Hurwicz began applying similar methods to what would become his lifelong project: the development of a general theory of economic organisation.

While ‘organization’ was a common theme at Cowles and RAND, Hurwicz’s project stood out for its ambition: he aimed to approach the question of optimal organisational structure in the most general and abstract terms, with the ambition of addressing the major economic controversies of his time (Hurwicz, Reference Hurwicz1953: 1). His first formulation, presented at the 1950 Econometric Society meeting, treated the ‘theory of organization’ as an extension of the theory of the firm: rather than a single manager, organisational systems involved multiple decentralised decision-makers whose interactions were constrained by limits of communication and information processing. Presented this way, economic organisation became an optimisation problem. The question was no longer simply how markets allocate resources but how different structures of decentralisation process and transmit information (Hurwicz, Reference Hurwicz1951b: 54).

At the same meeting, Arrow presented ‘An Extension of the Basic Theorems of Classical Welfare Economics’, the first in a series of contributions to Walrasian general equilibrium theory.

Although Arrow and Hurwicz appeared to address different problems, their concerns were closely related. Within the Cowles environment, general equilibrium theory was understood not simply as a theory of markets but as a general framework for decentralised organisation (Arrow and Hurwicz, Reference Arrow, Hurwicz and Pfouts1960: 35–36). Influenced by the socialist calculation debate, Cowles’s economists increasingly interpreted the price mechanism as a general informational device capable of transmitting signals and coordinating decentralised decisions across complex systems (Boldyrev and Ushakov, Reference Boldyrev and Ushakov2016; Mirowski and Nik-Khah, Reference Mirowski and Nik-Khah2017).

From this perspective, the study of the welfare properties of competitive equilibrium no longer represented the end point of the long debate over whether markets could achieve optimal allocation. Instead, it became the starting point for a broader investigation into the properties of the price mechanism as the paradigmatic form of decentralised coordination.

This reinterpretation formed the basis of Arrow’s and Hurwicz’s early collaboration, in which questions concerning equilibrium, adjustment, and optimality increasingly merged with problems of communication, information, and organisation. As Hurwicz later recalled, their joint work revolved around three interconnected themes: the mathematics of optimisation, the dynamics of equilibrium, and the design of economic mechanisms (Hurwicz, Reference Hurwicz and Feiwel1987: 258).

Their first major joint presentation, ‘Dynamic Aspects of Achieving Optimal Allocation of Resources’, delivered at the 1951 Econometric Society meeting, directly reflected this ambition. There, Arrow and Hurwicz presented the price mechanism as a ‘decentralized adjustment process through which optimal allocations could be achieved over time’ (Arrow and Hurwicz, Reference Arrow and Hurwicz1952: 86–87). Their collaboration combined Arrow’s computational and equilibrium-oriented methods with Hurwicz’s interpretation of adjustment processes as formal representations of communication and coordination in decentralised systems (Arrow, Reference Arrow1951d).

That work marked the first step in their broader attempt to transform general equilibrium theory from a theory of competitive markets into a general analytical framework for studying alternative forms of economic organisation. In this sense, it also marked the beginning of a process through which the abstraction of the market model would gradually make possible the reformulation of institutions into objects of mathematical economic inquiry.

Two paths beyond the competitive model

While Arrow and Hurwicz’s joint work explored alternatives to what they called the ‘competitive adjustment process’, it remained grounded in the logic of the price mechanism. In that sense, the work as eventually published largely explored the informational properties of the market mechanism itself (Arrow and Hurwicz, Reference Arrow and Hurwicz1958; Arrow et al., Reference Arrow, Block and Hurwicz1959).

Yet during the 1950s, both increasingly sought to reformulate the competitive mechanism in more abstract terms, with the aim of constructing a unified analytical framework for studying different forms of economic organisation.

This shared effort generated two distinct but related paths beyond the competitive model. Hurwicz gradually reinterpreted prices as one possible language for transmitting information across decentralised systems, while Arrow increasingly approached competitive equilibrium through the problem of uncertainty and the allocation of risks. Among the two, Hurwicz was more explicitly committed to the development of a general theory of economic organisation from an early stage. Already in ‘Optimal Properties of Decentralized Economic Systems’ (Hurwicz, Reference Hurwicz1951a), he sought to ask how alternative decentralised systems could be evaluated and compared – laying the foundations for his analytical approach to the study of institutions.

‘We may think of economic organization’, he wrote, ‘as a set of (legal or customary, say) rules imposed on human behavior’ (Hurwicz, Reference Hurwicz1953: 1). From Hurwicz’s perspective, familiar ideological oppositions – ‘laissez-faire versus intervention’, ‘capitalism versus socialism’, or ‘centralization versus decentralization’ – all concerned the same underlying problem: the desirability of alternative organisational structures (Hurwicz, Reference Hurwicz1953: 1).

Hurwicz argued that moving such debates beyond the level of ideology required economists to place the analysis on more abstract and analytical ground by developing ‘a conceptual and analytical framework for consideration of a broader class of structures’ (Hurwicz, Reference Hurwicz1953: 5). Within such a framework, ‘the theory of market phenomena fits in a natural manner as a special case of a more general theory’ (Hurwicz, Reference Hurwicz1953: 5). To make this possible, however, economists first had to reformulate market theory itself ‘in a more abstract and generalized manner than had previously been done’ (Hurwicz, Reference Hurwicz1953: 5). Such reformulation would allow market phenomena to be analysed in a ‘functional’, rather than merely ‘descriptive’, manner (Hurwicz, Reference Hurwicz1953: 6).

The direction Hurwicz found most fruitful for constructing this broader framework was the analysis of ‘decentralized resource allocation’, through which he attempted to provide, for the first time, ‘a rigorous formulation of the concept of decentralization of an adjustment process’ (Hurwicz, Reference Hurwicz1955b: 342–43).

To achieve this, Hurwicz introduced a basic distinction between ‘concrete’ and ‘abstract’ adjustment processes. ‘The difference between the two’, he explained, ‘lies in the fact that the language in which the units communicate is specified in the ‘concrete’ but not in the ‘abstract’ process’ (Hurwicz, Reference Hurwicz1955a: 1). According to Hurwicz, earlier theories of decentralisation had largely treated coordination as an iterative exchange of information encoded in prices. Hurwicz now redefined adjustment processes more generally – as procedures through which decentralised units transmit and respond to messagesaccording to pre-specified behavioural rules (Hurwicz, Reference Hurwicz1955a: 3)

Prices therefore became only one possible language among many. The price mechanism itself became a special case within a broader class of communicative and organisational mechanisms. Coordination problems were thus recast as more general informational and organisational problems that could potentially be studied across the social sciences. As Hurwicz suggested, this abstract framework could help ‘establish a bridge between the models of interest to economists and those arising in other fields’ (Hurwicz, Reference Hurwicz1955a: 1).

Arrow’s work during these years seemed at first to be directed toward a narrower set of questions within general equilibrium theory. Between 1951 and 1953 he produced three contributions that would fundamentally reshape the field. After publishing his extended proof of the welfare theorems (Arrow, Reference Arrow and Neyman1951a), he formulated a model of competitive equilibrium under uncertainty (Arrow, [Reference Arrow1952] Reference Arrow1964). Simultaneously, he and Gérard Debreu developed the general existence theorem, first presented at Cowles in December 1952 and submitted to Econometrica in May 1953 (Düppe, Reference Düppe2012: 492).

Taken together, these works are often read as establishing the view that optimal allocations are most effectively achieved through competitive markets (Blaug, Reference Blaug2007: 196; Weintraub, Reference Weintraub2002: 183–84). Yet Arrow himself was notably cautious about that interpretation (Maayan Yeshoron, Reference Maayan Yeshoron2025). In March 1953, Arrow presented a draft at the Cowles seminar titled ‘Why Are There Not More Markets for Future Delivery in Manufacturing Goods?’ (Cowles Commission Staff Meeting, 1953) – a question that he later identified as the central challenge to the idealised view of capitalism (Arrow, Reference Arrow1974a). This question concerned the gap between the arrangements required by the model for optimal allocation and their absence in the real world (Arrow, Reference Arrow1974b: 5–6).

To understand the significance of Arrow’s question, it is useful to note that, like Hurwicz, Arrow came to reinterpret the competitive mechanism in more abstract terms, though he did so by shifting attention to a different element of the model. Whereas Hurwicz’s abstraction focused on the price system as a mechanism for transmitting information, Arrow’s focused on the nature of commodities themselves, asking what kind of ‘goods’ markets actually allocate.

Rather than viewing the market as a mechanism for allocating physical commodities, Arrow ultimately came to understand it as a system for allocating risks among market participants. This abstraction was developed through his model of general equilibrium under uncertainty (Arrow, [Reference Arrow1952] Reference Arrow1964), which he later described as the most fully articulated version of the competitive market mechanism (Arrow, Reference Arrow and Feiwel1987). In this model, commodities were no longer defined solely by their physical characteristics but also by the states of the world in which they were delivered. In that sense, they could be interpreted as an insurance device.

Arrow’s 1952 paper showed that even under this extended structure, an optimal allocation could be achieved through a competitive mechanism. In the model, agents trade state-contingent contracts, and under standard assumptions a Pareto-efficient equilibrium emerges (Arrow, [Reference Arrow1952] Reference Arrow1964). Arrow also demonstrated that, in certain cases, the state-contingent structure could be implemented through appropriately organised financial markets (Arrow, [Reference Arrow1952] Reference Arrow1964: 92–93).

However, as the title of his 1953 presentation suggests, Arrow was sceptical that such mechanisms existed in actual economies. Rather than treating this absence as a mere empirical deviation from the model, he suggested that explaining why markets for future goods failed to emerge could reveal important features of the arrangements that govern real-world economies.

He returned to this issue in ‘The Allocation of Risk-Bearing’, presented at the 1954 Econometric Society meetings (Hurwicz Reference Hurwicz1955b: 27–30). At first glance, it seemed that the paper extended the 1952 general equilibrium under uncertainty model by incorporating production. Yet, it ultimately centred on an unexpected limitation: ‘Some difficulties arise… on the production side not in the formal validity of the conditions for optimal allocation but in their applicability to the real world’ (Hurwicz Reference Hurwicz1955b: 342). To explain this limitation, Arrow pointed to cognitive constraints: achieving efficiency in this framework required very fine commodity differentiation; even small variations – say, different probabilities of damage across otherwise identical inputs – would require distinct prices. As such distinctions multiply, the computational burden on agents becomes unrealistically large (Arrow, Reference Arrow1966).

Arrow pursued this problem of limited computational capacity throughout the second half of the 1950s. He turned to the study of economic decision-making under uncertainty and imperfect information. These efforts unfolded within a broader postwar research environment centred at Stanford and supported by Ford and Rockefeller Foundation initiatives aimed at developing formal approaches to problems of behaviour, learning, and organisation across the social sciences.

A particularly important setting was Stanford’s newly founded Centre for Advanced Study in the Behavioural Sciences (CASBS), where Arrow spent the academic year 1956–57. There he became involved in experimental work on learning and decision-making, seeking to adapt psychological models of information acquisition to economic situations involving uncertainty (Arrow, Reference Arrow1957).Footnote ¹

The following year, Arrow joined Patrick Suppes’s Ford-funded project on mathematical models in the social sciences, another interdisciplinary research programme.Footnote ²

This project sought to frame coordination, uncertainty, and decision-making as organisational and informational problems extending beyond market theory narrowly conceived. In a 1957 Rockefeller Foundation proposal, Arrow and Suppes described their aim as formalising ‘the organizational aspect of social science mathematical work’, linking experimental studies of investor behaviour under uncertainty to broader questions concerning the ‘ideal’ organisation of decentralised systems (Arrow and Suppes, Reference Arrow and Suppes1957).

In 1959, Arrow and Suppes jointly organised the Stanford Conference on Mathematical Methods in the Social Sciences. There, Hurwicz presented the first major synthesis of his decade-long effort to extend the logic of competitive adjustment beyond the market setting. The paper – ‘Optimality and Informational Efficiency in Resource Allocation Processes’ – offered the first systematic formulation of his broader project (Hurwicz, Reference Hurwicz, Arrow, Karlin and Suppes1960). In the paper, Hurwicz articulated the abstract adjustment framework and demonstrated how different allocation mechanisms could be formally analysed and compared according to their informational properties. In this approach, the market could finally appear not as a unique organisational arrangement but as one mechanism among many for coordinating decentralised decisions. Today, this paper is widely regarded as a foundational contribution to what would later become mechanism design (Myerson, Reference Myerson2009).

Market completeness and incentive compatibility: new lenses for institutional analysis

The collaboration between Arrow and Hurwicz on stability culminated in a series of publications between the late 1950s and early 1960s (Arrow, Reference Arrow, Hurwicz and Pfouts1960; Arrow and Hurwicz, Reference Arrow and Hurwicz1958). Yet by the early 1960s, Arrow increasingly appeared to view the earlier stability project as insufficient to address the questions that occupied him concerning the market mechanism. In a 1962 letter to Hurwicz, he admitted that ‘the stability book has gotten kind of cold in my mind’, adding that his ‘present inclination’ was instead to pursue work on ‘the foundations of the theory of competitive equilibria’ (Arrow, Reference Arrow1962b). He referred to recent developments in general equilibrium theory by Aumann, Scarf, and Debreu, which reconceptualised equilibrium through increasingly abstract formulations drawn from cooperative game theory (Aumann, Reference Aumann1961; Debreu and Scarf, Reference Debreu and Scarf1963).

Yet, Arrow’s trajectory moved in a different direction. Rather than exploring the foundations of general equilibrium theory through its mathematical structure, he sought to understand them by examining the relationship between the model and real-world markets. The question that had preoccupied him since the early 1950s – how uncertainty alters the welfare properties of competitive markets – gradually led him toward the analysis of the institutional arrangements through which societies allocate risk in practice. These concerns were already evident in his work at Stanford during the late 1950s, where he explored both decision-making under uncertainty and processes of disequilibrium adjustment, but their full conceptual significance emerged only in the early 1960s.

The opportunity emerged through another Ford Foundation initiative. In 1961, Robert Dorfman invited Arrow to join a project led by Victor Fuchs devoted to the economic analysis of social and welfare services – fields that, according to Fuchs, had been largely neglected by theoretical economists (Dorfman, Reference Dorfman1961; Fuchs, Reference Fuchs1960: 2). Each sector was assigned both a practitioner and a theorist; Arrow was asked to analyse the medical care industry, producing what became one of his most influential papers – ‘Uncertainty and the Welfare Economics of Medical Care’ (Arrow, Reference Arrow1963).

Although widely recognised as a pioneering contribution to health economics, for Arrow, this paper marked a more fundamental conceptual achievement – it allowed him to revisit the question that had occupied him for more than a decade: what does uncertainty imply for the welfare analysis of competitive markets? (Smith, Reference Smith2008).

To set up the analysis, Arrow returned to the question of applicability, using it to guide the logic of welfare economics itself. Competitive markets were valued because, under certain assumptions, they generated efficient outcomes. Empirical analysis, therefore, required comparing actual markets to this idealised benchmark and examining ‘the presence or absence of the preconditions for the equivalence of competitive equilibria’ (Arrow, Reference Arrow1963: 944). These preconditions included the existence of competitive equilibrium, the marketability of relevant goods and services, and non-increasing returns.

Arrow’s key observation was that uncertainty systematically undermines the conditions required by the welfare theorems because many risks cannot be fully marketised (Arrow, Reference Arrow1963: 944–45). At this stage, he no longer emphasised the problem of limited computational capacity. Instead, he pointed to a different source of difficulty: the actual arrangements required for trading risks – most notably insurance markets – are inherently incomplete.

Drawing on his practical experience in the insurance industry, Arrow argued that in reality, insurance contracts can never provide complete coverage. Problems such as moral hazard make it ‘impossible to draw up insurance policies that will sufficiently distinguish among risks’ (Arrow, Reference Arrow1963: 945).Footnote ³

From this seemingly practical observation, Arrow derived a much broader conclusion. Because full insurance is unattainable, markets are inherently limited in their ability to allocate risks efficiently. The assumptions required for complete markets therefore cannot be satisfied in practice, not because of imperfections in particular markets, but because of structural limitations in the organisation of risk itself.

Yet this was not the endpoint of Arrow’s analysis. The limitations of ideal competitive behaviour under uncertainty did not merely reveal a weakness of market theory; they also provided, in his view, a framework for explaining the existence of alternative mechanisms of social coordination. Where competitive markets fail to achieve efficient outcomes, other social institutions emerge to compensate for the resulting ‘optimality gap’ (Arrow, Reference Arrow1963: 947).

Among these institutions, Arrow highlighted arrangements based on delegation and trust, which are ‘designed to obviate the problem of informational inequality’ (Arrow, Reference Arrow1963: 965). Drawing on Talcott Parsons’s The Social System, he argued that professional ethics, entry restrictions, and distinctive pricing practices in medicine served to sustain forms of collective orientation that could not be maintained through ordinary market exchange alone (Parsons, Reference Parsons1991[Reference Parsons1951]; Arrow, Reference Arrow1963: 949). The doctor–patient relationship thus appeared not simply as a market transaction but as a socially organised response to the limits of market coordination under conditions of uncertainty.

Arrow therefore concluded that ‘the failure of the market to insure against uncertainties has led to the creation of many social institutions in which the usual assumptions of the market are contradicted to some extent’ (Arrow, Reference Arrow1963: 967). Following Parsons, Arrow suggested viewing social institutions as organisational arrangements that emerged to perform coordination functions that markets could not reliably achieve on their own.

Over the following years, Arrow extended this line of analysis beyond the specific case of medical care. Across a series of studies on insurance, uncertainty, and public policy, he increasingly explored how different institutional arrangements compensate for the limitations of market coordination (Arrow, Reference Arrow1964, Reference Arrow1965, Reference Arrow1966).

This effort culminated in ‘The Organization of Economic Activity: Issues Pertinent to the Choice of Market versus Non-Market Allocation’ (Reference Arrow1969), originally prepared as a study for the Joint Economic Committee of the United States Congress as part of a broader discussion of public expenditure and policy planning.

The paper presented Arrow’s increasingly unified framework for analysing economic organisation. The first step in this framework was the construction of a common analytical language for understanding market failures. Rather than treating increasing returns, externalities, uncertainty, and informational asymmetries as distinct problems, Arrow sought to subsume them under the broader category of missing markets. Missing markets, in turn, could be understood through the more general notion of transaction costs, particularly the communication and information costs involved in creating and sustaining exchange (Arrow, Reference Arrow1969: 59–60).Footnote ⁴

The second step was to extend this framework beyond markets themselves. Having reformulated a wide range of market failures within a common analytical language, Arrow turned to alternative forms of economic and social organisation, including firms, political institutions, and social norms. Rather than treating these as fundamentally different objects of inquiry, he analysed them through the same categories of information, communication, incentives, and coordination. Political representation appeared as a principal-agent problem, while norms and trust emerged as institutional responses to the limitations of contractual enforcement (Arrow, Reference Arrow1969: 62). The paper thus presented a remarkably broad analytical framework in which markets, firms, voting systems, and social norms appeared as alternative mechanisms for aggregating individual preferences via collective action or for organising decentralised activity under different informational conditions.

As we have already seen, the ambition to develop a general framework for analysing economic organisation had shaped Hurwicz’s work from the outset. Like Arrow, he viewed the central task of modern social science as bringing ‘order out of chaos’ through the analytical clarification of alternative organisational arrangements (Hurwicz, Reference Hurwicz1964: 4). These concerns culminated in ‘On the Concept and Possibility of Informational Decentralization’ (Reference Hurwicz1969), where Hurwicz recast earlier debates over markets, planning, and socialism as questions of informational structure. Drawing on Hayek’s problem of dispersed knowledge, he proposed a formal definition of informational decentralisation, distinguishing organisational forms according to the information exchanged among agents.

This framework made it possible to compare alternative forms of economic organisation in terms of informational efficiency, stability, and Pareto optimality. By the early 1970s, however, Hurwicz had turned to a different problem concerning the information exchanged within such systems: why would individuals truthfully reveal the information they possess? (Hurwicz, Reference Hurwicz and Feiwel1987: 272). To formalise this problem, Hurwicz represented economic organisation as a game between a planner and decentralised agents (Hurwicz, Reference Hurwicz and Eckstein1971: 86). The comparison of alternative forms of economic organisation thus shifted from the problem of information transmission to the problem of strategic interaction. This shift culminated in the principle of incentive compatibility, which integrated informational constraints and strategic behaviour within a single analytical framework. The central question was no longer simply what information is communicated through decentralised systems, but whether organisational arrangements provide individuals with incentives to use and reveal that information in ways consistent with the objectives of the system (Hurwicz, Reference Hurwicz, McGuire and Radner1972).Footnote ⁵

By this point, the projects through which Arrow and Hurwicz had sought to extend mathematical economic analysis beyond the market had acquired relatively clear analytical forms. The preceding discussion traced the emergence of their respective approaches through a series of conceptual and technical innovations, culminating in two central analytical lenses: Arrow’s notion of incomplete markets and Hurwicz’s notion of incentive compatibility. Yet these concepts did more than provide new analytical tools. They exemplified new ways of thinking about institutions by reformulating a framework initially developed around the competitive market into a more abstract analytical language within which markets and other forms of economic organisation could be compared.

To clarify this broader significance, the last part of this section turns to two more synthetic statements of these research programmes, one by Arrow and one by Hurwicz, in which their underlying conceptions of institutions are articulated most clearly.

Hurwicz presented perhaps the clearest statement of his approach in ‘The Design of Mechanisms for Resource Allocation’ (Reference Hurwicz1973). The title itself captured the central methodological move of his framework. Economists were invited to adopt the perspective of the planner, not as an alternative to the self-regulating market, but as a designer of decentralised mechanisms. The problem of economic organisation could now be approached through a unified analytical framework in which markets, planning systems, and other institutional arrangements appeared as different mechanisms for coordinating decentralised activity. Institutions were understood as configurations of rules, information structures, and incentive systems whose properties could be analysed within a common language centred on information, incentives, and outcomes.

In the paper, delivered as the Ely Lecture of 1973, Hurwicz interpreted this development as a possible reconciliation between mathematical and institutional economics by making institutions themselves objects of rigorous analytical comparison (Hurwicz, Reference Hurwicz1973).

In The Limits of Organization (1974), Arrow offered a different perspective for approaching the same analytical landscape. Rather than beginning from the design of institutions, he suggested approaching them through their limits. The central question, as he put it, was how to evaluate alternative social organisations. Markets, firms, governments, political organisations, and ethical norms could all be understood as different ways of organising collective action and coordinating decentralised activities. Their common analytical treatment rested on the recognition that each confronted characteristic informational and incentive constraints. The limitations of any particular form of social organisation thus became a guide to understanding the role of others.

In the book, Arrow stepped away from the formal language of economic theory and offered a broader reflection on social organisation. Yet, the underlying analytical framework remained the same: problems of information and incentives defined the limits of social coordination across markets, firms, governments, and professional organisations. Authority was linked to the alignment of incentives, while ethical norms appeared as mechanisms for reducing the costs of coordination.

Markets, firms, governments, and ethical systems differed in form, but they could all be evaluated in terms of Pareto efficiency: according to their ability to facilitate coordination and improve collective outcomes under conditions of informational and incentive constraints (Arrow, Reference Arrow1974c: 19).

Taken together, these developments can be read in two different ways. From the perspective suggested by Hurwicz, they represented a successful reconciliation between traditions long regarded as incompatible. Mathematical economics had moved beyond its earlier concentration on competitive markets and developed analytical tools capable of addressing a much broader range of institutions. Markets, firms, governments, professional organisations, and social norms could now be studied within a common analytical framework.

At the same time, this transformation also marked a significant shift in the meaning of institutions within economic analysis. Earlier institutional traditions had often approached institutions as historically evolving social formations, shaped by habits, customs, power relations, and cultural practices. By contrast, the frameworks developed by Arrow and Hurwicz increasingly rendered institutions intelligible through a common analytical language centred on coordination, information, incentives, and efficiency. The result was not a return to institutional analysis in its earlier form, but the emergence of a new way of thinking about institutions – one that expanded the scope of economic inquiry while simultaneously redefining the terms through which institutions could be understood and evaluated.

Epilogue – institutions and the mathematisation of economics

Today, when economists analyse institutions, they rarely do so through the language of general equilibrium theory. Instead, institutional analysis is largely conducted through frameworks grounded in game theory, including mechanism design, information economics, contract theory, and the study of repeated interaction. General equilibrium theory is often regarded as the antithesis of institutional analysis, a framework concerned with abstract market equilibrium, far removed from the study of institutions. From this perspective, the intellectual world reconstructed in this paper may seem distant from contemporary institutional analysis.

Yet this paper has suggested that the relationship was more complex. By following the work of Arrow and Hurwicz from the 1950s to the 1970s, I have argued that general equilibrium theory played an important role, at least in their intellectual trajectories, in the construction of an analytical language through which social institutions could become objects of mathematical economic analysis. For both Arrow and Hurwicz, mathematical abstraction offered a means of reformulating a framework initially developed around the competitive market for the more general study of social institutions. By recasting market phenomena in terms of information, coordination, communication, and incentives, they sought to place markets, planning systems, firms, political institutions, and social norms within a common analytical framework.

This paper did not seek to establish direct lines of influence. Nevertheless, several later developments appear closely related to the trajectories reconstructed here. Most obviously, Hurwicz’s notion of incentive compatibility became one of the central concepts of modern economics and of institutional analysis through the mechanism design tradition. Arrow’s contribution to social choice theory also appeared significant to this tradition, as questions of institutional design were increasingly reformulated in terms of implementable social objectives (Dasgupta et al., Reference Dasgupta, Hammond and Maskin1979).

A second trajectory can be associated with Arrow’s emphasis on information asymmetries and the limits of market organisation. The early 1970s witnessed a rapid expansion of information economics (Akerlof, Reference Akerlof1970; Stiglitz, Reference Stiglitz2017). In this context, Arrow offered a way of interpreting the new types of informational market failure as evidence for the necessity of alternative institutional arrangements. Rather than viewing information asymmetries as temporary deviations from an otherwise efficient market system, Arrow interpreted them as reasons why coordination often depends on organisations, norms, authority relations, and other non-market institutions. This perspective can be traced in the development of contract theory, in analyses of hierarchy within firms and labour markets, and in the growing economic interest in trust and social norms (Akerlof and Yellen, Reference Akerlof and Yellen1986; Bowles, Reference Bowles2016; Dasgupta, Reference Dasgupta and Gambetta2000; Williamson, Reference Williamson and Feiwel1987).

More broadly, the trajectories reconstructed in this paper offer a window into a wider transformation within postwar economics. Existing historiography has often described the mathematisation of economics in terms of the development and movement of new analytical tools across disciplinary boundaries (Amadae, Reference Amadae2003; Giocoli, Reference Giocoli, Arena and Lazaric2001; Mirowski, Reference Mirowski2002). The trajectories examined here draw attention to a complementary process: extending mathematical analysis to new domains also required economists to reconceptualise those domains in forms amenable to formal analysis. Market phenomena, organised around prices, quantities, and exchange, were relatively amenable to the mathematical framework of neoclassical economics; extending mathematical analysis beyond the market presented a different representational challenge. In the case examined here, this involved reformulating a framework initially developed around the competitive market into a more abstract language of information, incentives, coordination, and rules, through which markets and other institutional arrangements could be represented and compared.

This new way of thinking about institutions, I have argued, emerged through a long intellectual process that shaped the high-theory years of postwar economics. Mathematisation, from this perspective, involved not only the development and application of new analytical tools but also the construction of new ways of representing the social world.

What, then, drove efforts to develop a mathematical language capable of incorporating social institutions into economic analysis? While the cases examined here do not provide an answer to this question, they suggest three possible and complementary explanations that can only be briefly indicated here as directions for further investigation. First, as mathematical economists increasingly came to regard mathematics not as a supplement to economic reasoning but as its fundamental analytical language, that language had to be extended to a wider range of economic and social phenomena. Second, the funding and institutional structure of postwar American science encouraged competing efforts to develop scientific approaches to problems of social organisation and governance (Amadae, Reference Amadae2003; Bessner and Guilhot, Reference Bessner and Guilhot2018; Crowther-Heyck, Reference Crowther-Heyck2006). Economists seeking a place within this broader project had reason to demonstrate that their analytical expertise extended beyond markets – a claim visible in the rhetoric of both Arrow and Hurwicz. Finally, the growing role of economists as public experts, together with the applied turn of the 1960s and 1970s, confronted them with social problems and economic domains whose institutional features could not easily be accommodated within the standard market model. These intellectual, institutional, and practical explanations warrant further investigation.

The history traced here may also help illuminate the analytical shift separating older and newer forms of institutional economics. As many scholars have argued, the renewed engagement with institutions within mainstream economics was not simply a return to the older institutional tradition but involved a new way of making institutions analysable within economic theory (Hodgson, Reference Hodgson1998, Reference Hodgson2001). When Douglass North called for renewed attention to institutions, he defined them as ‘humanly devised constraints that structure political, economic, and social interaction’ (North, Reference North1991: 97), including norms, customs, traditions, and other historically evolved social practices. By that time, however, these phenomena were no longer treated as self-sufficient analytical categories. Instead, North proposed to understand them at a higher level of abstraction – as ‘the rules of the game’ that ‘provide the incentive structure of an economy’ (North, Reference North1991: 98). Viewed through this lens, institutions became intelligible through categories such as incentives, constraints, uncertainty, information, and coordination. The trajectories examined here shed light on the development of this broader framework for thinking about institutions not primarily as historically specific phenomena, but as abstract structures, and on some of the analytical categories through which this abstraction became possible.

Seen in retrospect, this transformation involved both a powerful analytical achievement and a particular reduction of social phenomena to a narrower set of analytical categories. A common language of coordination, information, incentives, and outcomes made heterogeneous institutions amenable to systematic comparison and formal analysis. Yet this abstraction came at a cost that resonates with Hodgson’s (Reference Hodgson2001) critique of the loss of historical specificity in twentieth-century economics: institutions were increasingly detached from the particular historical processes through which they emerged and changed and from the broader institutional configurations in which they were embedded.Footnote ⁶

Tracing this history also reminds us how much conceptual work was required before institutions could become objects of mathematical analysis. The social world did not simply present itself in a form readily incorporated into mathematical analysis. Extending neoclassical analysis beyond the market to the broader realm of social institutions required economists to develop new ways of conceptualising social organisation itself. The success of this effort transformed not only economic theory but also the broader language through which economists came to understand institutions and society. In this sense, the history examined here is not only a history of economic theory but also a history of changing ways of imagining and representing society itself.