# Organization Theory

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_1620

## Abstract

Since all the social sciences deal with human organizations (families, bureaucracies, tribes, corporations, armies), the term ‘organization theory’ appears in all of them. What has distinguished the economists’ pursuit of organization theory from that of sociologists, of political scientists and of psychologists (say those psychologists working in the field called ‘organizational behaviour’)? First, the real organizations that have inspired the theorizing of economists are the economy, the market and the firm. Second, economists, with their customary taste for rigour, have sought to define formally and precisely the vague terms used in informal discourse about organizations, in such a way as to capture the users’ intent. They have sought to test plausible propositions about organizations – either by proving that they follow from simple, reasonable and precisely stated assumptions, or (rarely) by formulating the propositions as statements about observable variables on which systematic rather than anecdotal data can be collected, and then applying the normal statistical procedures of empirical economics. (Here we shall only consider testing of the first type). Third, much of the economists’ organization theory is not descriptive but normative; it concerns not what is, but what could be. It takes the viewpoint of an organization *designer*. The organization is to respond to a changing and uncertain environment. The designer has to balance the ‘benefits’ of these responses against the organization’s *informational costs*; good responses may be costly to obtain. In addition, the designer may require the responses to be *incentive-compatible*: each member of the organization must *want* to carry out his/her part of the total organizational response in just the way the designer intends.

Since all the social sciences deal with human organizations (families, bureaucracies, tribes, corporations, armies), the term ‘organization theory’ appears in all of them. What has distinguished the economists’ pursuit of organization theory from that of sociologists, of political scientists and of psychologists (say those psychologists working in the field called ‘organizational behaviour’)? First, the real organizations that have inspired the theorizing of economists are the economy, the market and the firm. Second, economists, with their customary taste for rigour, have sought to define formally and precisely the vague terms used in informal discourse about organizations, in such a way as to capture the users’ intent. They have sought to test plausible propositions about organizations – either by proving that they follow from simple, reasonable and precisely stated assumptions, or (rarely) by formulating the propositions as statements about observable variables on which systematic rather than anecdotal data can be collected, and then applying the normal statistical procedures of empirical economics. (Here we shall only consider testing of the first type). Third, much of the economists’ organization theory is not descriptive but normative; it concerns not what is, but what could be. It takes the viewpoint of an organization *designer*. The organization is to respond to a changing and uncertain environment. The designer has to balance the ‘benefits’ of these responses against the organization’s *informational costs*; good responses may be costly to obtain. In addition, the designer may require the responses to be *incentive-compatible*: each member of the organization must *want* to carry out his/her part of the total organizational response in just the way the designer intends.

The design point of view has old and deep roots in economics. Adam Smith’s ‘invisible hand’ proposition is a statement about the achievements of markets as resource-allocating devices. If one reinterprets it as a comparative conjecture about alternative designs for a resource-allocating organization – namely, that a design using prices is superior to other possible designs – then it becomes an ancestor of the organization-design point of view. In any case, that point of view appears very clearly in Barone’s ‘The Ministry of Production in the Collective State’ (1908), and in the debates about ‘the possibility of socialism’ (i.e., of a centrally directed economy) in the 1930s and 1940s (Hayek 1935; Lange 1938; Dobb 1940; Lerner 1944).

Nearly all the debaters agreed that if the designer of resource-allocating schemes for an economy has a clean slate and can construct any scheme at all, then he must end up choosing some form of the price mechanism; for example, a scheme of the Lange–Lerner sort. Here a Centre announces successive trial prices; in response to each announcement, profit-maximizing demands are anonymously sent to the Centre by managers, and utility-maximizing demands are sent by consumers; in response to the totals of intended demands, the Centre announces new prices; the final announced prices are those which evoke zero excess demands, and the corresponding intended productions and consumptions are then carried out. The debate dealt largely with the informational virtues of such a price scheme as compared to an extreme centralized alternative scheme. The alternative scheme (never made very explicit) appears to be one wherein managers and consumers report technologies, tastes and endowments to the Centre, which thereupon computes the economy’s consumptions and productions; those become commands to be followed.

In retrospect, the extreme centralized alternative seems an unimaginative straw man, since one can imagine a whole spectrum of designs lying between extreme centralization, on the one hand, and the price scheme, on the other; namely, designs in which some of the agents’ private information is centrally collected (or pooled), but not all of it. In any case, the debaters agreed that the price scheme is informationally superior to the centralized alternative because (1) in the former, small computations are performed simultaneously by very many agents (though possibly many times), whereas in the latter an immense central computation is required (though required only once), and (2) the messages required in the former (prices and excess demands) are small (though sent many times) while in the latter a monstrously large information transmission is required (though only once).

Persuasive as this claim may appear, a moment’s thought reveals how very many gaps need to be filled before the claim becomes provable or disprovable. If a proposed scheme is to be operated afresh at regular intervals (in response, say, to new and randomly changing tastes, technologies and endowments), then what is the designer’s measure of a proposed allocation scheme’s gross performance (against which a scheme’s cost must be balanced)? Is it, for example, the expected value of the gross national product in the period which follows each operation of the scheme? Or is it perhaps a two-valued measure which takes the value one when the scheme’s final allocation is Pareto-optimal and individually rational (i.e., every consumer ends up with a bundle at least as good as his/her endowment) and takes the value zero otherwise? When is the scheme to be terminated if it comprises a sequence (possibly infinite) of steps? What interim action (resource allocation) is in force while the proposed scheme is in operation and before it yields a final action? For alternative investments in information-processing facilities, how long does the sequence’s typical step take? (The longer a step takes, the longer one waits until a given terminal step is reached and the longer an unsatisfactory interim action is in force.)

Once such gaps are filled in, the claim becomes, in principle, a verifiable conjecture. Without venturing to fill them in, economists were nevertheless sufficiently intrigued by the intuitive (but quite unverified) informational appeal of the Lange–Lerner scheme so that they proceeded to construct many more schemes of a similar kind in a variety of settings, including multidivisional firms, for example, as well as planned economies with technologies less well behaved than the classic (convex) ones (see Heal 1986). These efforts were partly stimulated by (and, in turn, stimulated) the development of algorithms for general constrained optimization, which often had a natural interpretation as schemes wherein a ‘Centre’ makes announcements and other ‘persons’ respond without directly revealing their private information. (One can so interpret, for example, certain gradient methods for constrained optimization, as well as the ‘decomposed’ version of the simplex algorithm for linear programming.)

If the informational appeal of schemes of the Lange–Lerner type was powerful but unverified, what of the incentive side? Here the ‘possibility-of-socialism’ writers were divided. A sceptic like Hayek (1935, pp. 219–20) asked why a manager would want to follow the Lange–Lerner rules. One (unsupported) reply – hinted at in various places in the debate – is that to induce a manager to follow the rules we need only pay him a reward which is some nondecreasing function of his enterprise’s profit. The incentive question becomes acute when one turns to the scheme that is the analogue of the Lange–Lerner scheme if there are public goods; namely, the Lindahl scheme (Lindahl 1919), when that is given a central-price-announcer interpretation. (The scheme was developed before the possibility-of-socialism debates but appears to have been unknown to the debaters). For here, as Samuelson (1954) was the first to note, the prospective consumer of a public good may perceive an advantage in falsifying his demand for it; that is, in disobeying the designer’s rules. (In fact, it turned out later (Hurwicz 1972) that the same difficulty can arise without public goods; that is, in the original Lange–Lerner scheme itself). It took about three decades after the possibility-of-socialism debate until one had the framework to study with precision the question of when incentive-compatible schemes of the price-announcer type – or indeed of any type – can be constructed for economies or for organizations in general.

On the informational side of the design question, a 1959 paper by Hurwicz (Hurwicz 1960) proved to be a major step towards precise conjectures (as opposed to broadly appealing but unverifiable claims) about the informational merits of alternative resource-allocating schemes for economies, or indeed alternative designs for organizations in general. The key notion is that of an *adjustment process*, to be used by an *n*-person organization confronting a changing environment *e* = (*e*_{1}, …, *e*_{n}), lying always in some set *E* of possible environments. Here *e*_{i} is that aspect of the environment *e* observed by person *i*. Assume that the possible values of *e*_{i} comprise a set *E*_{i} and that *E = E*_{1} × … × *E*_{n}. If, for example, the organization is an exchange economy, then *e*_{i} is composed of *i*’s endowment and *i*’s preference ordering on alternative resource allocations; if *n* = 2, then *E* might be the set of classic Edgeworth-box economies. An adjustment process is a quadruple, π = (*M*, *m*_{0}, *f, h*),where *M* is a set called a *language* and is the cartesian product of *n individual language M*_{i}; *f* is an *n*-tuple (*f*_{1}, …, *f*_{n}); *f*_{i} is a function from *M*× *E*_{i} to *M*_{i};*m*_{0} = (*m*_{01},…,*m*_{0n}) is an *initial* message *n*-tuple in *M*; *h* is a function, called the *outcome function*, from *M* × *E* to *A*; and *A* is a set or organization *actions* or *outcomes* (e.g., resource allocations). Imagine the environment to change at regular intervals. Following each new environment, person *i* emits the initial message *m*_{1i} = *f*_{i} (*m*_{0},*ε*_{i}) in **M**_{i}. At step 1, person *i* emits the message *m*_{1i} = *f*_{i}(*m*_{0},*ε*_{i}) in **M**_{i} and at the typical subsequent step *t*, person *i* emits *m*_{ti} = *f*_{i} (*m*_{t−1}, *ε*_{i}), where *m*_{ti} ∈ *M*_{i} and *m*_{t−1} denotes an element of *M*; namely,(*m*_{t−1},1,…,*m*_{t−1,n}). At a terminal step *T*, the organization takes the action (or puts into effect the outcome) *h*(*m*_{T}, *e*) in *A* which is its final response to the environment *e*. The process is *privacy-preserving* in the sense that *e* enters *i*’s function *f*_{i} only through *e*_{i} which is *i*’s private knowledge. One might require a similar property for *h*, that is, that *h* be an *n*-tuple (*h*_{1},…,*h*_{n}) where *h*_{i} is a function from *M*× *E*_{i} to a set *A*_{i} of possible values of *i*’s *individual action* (thus *A* is the cartesian product *A*_{1} × … × *A*_{n}). In the useful special case of a ‘non-parametric’ outcome function, where *h* does not depend on *e* at all, such privacy-preservation for action selection holds trivially.

Note that we can endow person *i* with a memory. To do so, let every element *m*_{i} of the set *M*_{i} be a *pair* (*m*_{i}^{*}, *m*_{i}^{* *}), where *m*_{i}^{*} denotes memory and *m*_{i}^{* *} denotes a message sent to (noticed by) others; specify that for *k* ≠ *i, f*_{k} is insensitive to (its value does not depend on) *m*_{i}^{*}. By making the set in which *m*_{i}^{*} lies sufficiently large, we can let *i* remember, at every step, all that he has observed of the organization’s messages thus far. We can, moreover, let *i* send messages always to *j* and to no one else by specifying that for *k* ≠ *i, k* ≠ *j, f*_{k} is insensitive to the *i*th component of *m*. We can let *i* send a message to *j* and to no one else *at some specific step t*^{*} by specifying that when all persons’ memories tell them that *t*^{*} has been reached, then for *k* ≠ *i, k* ≠ *j, f*_{k} is insensitive to the *i*th component of *m*.

The adjustment process, as the object to be chosen by the designer, is a concept sufficiently broad and flexible to accommodate all the economists’ iterative resource allocation schemes for economies as well as a rich variety of designs for other organizations. All organizations, after all, respond to a changing environment of which each member observes only some aspect in which he/she is the specialist, and the environment’s successive values are unknown to the designer when a design is to be chosen. If those values *were* known (e.g., if the environment were constant), then there would be no need for message exchanges at all: each member could simply be programmed once and for all to take a correct (a best) action or sequence of actions. In all organizations, moreover, members engage in dialogue that evèntually yields an organizational response to the current environment (an action).

With regard to the classic claim that price schemes are informationally superior designs when the organization is an economy, the adjustment-process concept has permitted a first rigorous test. The test takes the view that we can (as a reasonable starting place) ignore the preequilibrium performance of a price scheme (formulated as an adjustment process), and can focus entirely on its *equilibrium* achievements. For any *e* in *E* let *M*^{e} denote the set of *equilibrium messages*; that is, every \( {m}^{\mathrm{e}}=\left({m}_i^e,\dots, {m}_n^e\right) \mathrm{in} {M}^{\mathrm{e}} \) satisfies \( {f}_{\mathrm{i}}\left({m}^e,{e}_{\mathrm{i}}\right)={m}_1^e \) for all *i*. Confine attention to processes with non-parametric outcome functions *h* (i.e., *h* depends only on *m*, not on *e*) and, for the case where *E* is a set of exchange economies, formulate the competitive (the Walrasian) mechanism as a non-parametric process, say \( {\pi}^{\ast }=\left({M}^{\ast },{m}_0^{\ast },{f}^{\ast },{h}^{\ast}\right) \). The typical element *m* of *M*^{*} comprises a vector of proposed prices and an (*n* − 1)-tuple of proposed trade vectors; *f*_{i} yields *i*’s intended trade vector – or, in an alternative version, a *set* of acceptable trade vectors – at the just-announced prices; and *h* is a projection function yielding the ‘trade’ portion of *m*. For the process *π*^{*} and for every *e* in a classical set *E*, all the *equilibrium outcomes for e* – that is, all those allocations (trade (*n* − 1)-tuples) *a* satisfying *a* = *h*^{*} (*m*) for all *m* in *M*^{*e} – are Pareto-optimal and individually rational. One now asks the following question: does there exist any other process *π* = (*M*, *m*_{0}, *f*, *h*) such that (i) for all *e* in the same set *E* every equilibrium outcome is again Pareto-optimal and individually rational, and (ii) the process *π* is informationally ‘cheaper’ than *π*^{*}? A natural starting place for the assessment of informational cost is size of the language. If one confines oneself to processes *π* in which *M* is in a finite Euclidean space, then a natural measure of language size is dimension. But then the question just posed has a trivial Yes as its answer, since one can always code a message of arbitrary dimension as a one-dimensional message. To rule out such coding, one imposes ‘smoothness’ on the process *π*. For example, one considers the mapping *t* from *A* (the set of outcomes), to the subsets of *E*, such that for every *e* in *t*(*a*), *a* is an equilibrium outcome for *e*, and one requires that *t* contain a Lipschitzian selection. It turns out that for classic sets *E* and for language dimension as the cost measure, no smooth process satisfying (i) and (ii) exists (Hurwicz 1972). The result extends (for more general sorts of smoothness requirements) to processes with non-Euclidean languages and language-size measures more general than dimension (Mount and Reiter 1974; Walker 1977; Jordan 1982).

These results are clearly a first step towards vindicating the classic claim that the price process is informationally superior. To go further, one would like to consider pre-equilibrium outcomes – so that the final allocation is the one attained at a fixed, but well-chosen, terminal step – and to take account of the change in the time required to reach that terminal step as one varies the investment in the information-processing facilities available for carrying out the typical step. It seems plausible that a version of the competitive process that converges rapidly to its equilibrium messages will rank high relative to other processes once this complication is added. One would like the ‘smoothness’ requirement to arise naturally from a model of a wellbehaved information technology rather than being introduced (as at present) in an ad-hoc manner. One would like to leave the setting just sketched, wherein messages and outcomes are points of a continuum, to see whether analogous results hold when both messages and outcomes (allocations) have to be rounded off to a chosen precision. (A limited analogue of the dimensional-minimality result just sketched has in fact been obtained in such a discrete setting (Hurwicz and Marschak 1985).

For organizations in general, the requirements of Pareto-optimality and individual rationality are replaced by some given set of desired (and equally acceptable) responses to every possible given environment. The problem facing a designer who is unconcerned about incentive aspects can then be put as follows. Given a set *E* and a *desired-performance correspondence ϕ* from *E* to the subsets of an outcome (action) set *A*, find an adjustment process *π* = (*M*, *m*_{0}, *f*, *h*) which *realizes ϕ* that is, which satisfies *a* ∈ *ϕ* (*e*) if *a* = *h*(*m*, *e)* and m∈*M*^{e} – and *whose* informational costs (suitably measured) are no less than those of any other process which realizes *ϕ*.

Note that a far more ambitious task could be given the designer instead. Let the designer have preferences over alternative environment/outcome/cost triples and let the preferences be represented by a utility function. The ambitious task is then to find a process *π*, and an accompanying selection function, which chooses a unique equilibrium outcome in the set *M*^{e} for every *e*, so as to maximize the designer’s expected utility (expectation being taken with respect to the random variable *e*). It seems clear that such unbounded designer’s rationality is too ambitious a standard; organization theory would freeze in its tracks if it adopted such a standard. The realization of a given performance correspondence at minimum informational cost is a reasonable step towards bounded rationality, especially if the performance correspondence is not stringent. (Thus *ϕ* might assign to *e* all outcomes which are within a certain specified distance of an outcome that is ‘ideal’ for *e* – say an outcome that maximizes some pay-off function).

The preceding bounded-rationality version of the designer’s task can again be modified by allowing some ‘dynamics’; that is, permitting choice of terminal step rather than focusing on equilibrium outcomes. Whether we do so or not, we now have a precise version of the general performance-versus-cost problem which we claimed at the start to be a distinctively ‘economists’, contribution to organization theory. (The problem is surveyed in more detail in Marschak 1986).

When one turns to incentive issues, a certain ‘contraction’ of the adjustment-process concept has proven useful. The object chosen by the designer now becomes a *game form* (*S*, *g*), where *S* = *S*_{1} × … × *S*_{n};*S*_{i} is the set of person *i*’s possible *strategies s*_{i}; and *g* is an outcome function from *S* to *A* (the set of organizational actions or outcomes). Person *i*’s local environment *e*_{i} specifies (among other things) *i*’s preferences over the alternative organizational outcomes. The set of Nash-equilibrium strategy *n*-tuples *s* = (*s*_{1},…,*s*_{n}) such that given *e* = (*e*_{1},…,*e*_{n}) each person *i* regards the outcome *g*(*s*) to be at least as good as the outcome, \( g\left({s}_1,\dots, {s}_{i-1},{\overline{s}}_i,{s}_{i+1},\dots, {s}_n\right) \) for all \( \overline{s} \)_{i} in *S*_{i}. Suppose the designer is again given a desired-performance correspondence *ϕ* from *E* to the subsets of *A*. Then the incentive problem may be put this way: find a game form (*S*, *g*) such that for every *e* in *E* and every *s* in *N*_{sg}*(e)*, the outcome *g*(*s*) is contained in the set *ϕ* (*e*). Such a game form *Nash-implements ϕ*. We can trivially find an adjustment process(*M,m*_{0},*f*,*h*) whose equilibrium outcomes for every *e* comprise exactly the set {*a*:*a* = *g*(*s*); *s*∈*N*_{sg}*(e*)} (To do so, let *M* = *M*_{1} × … × *M*_{n} = *S*_{1} × … × *S*_{n}; let *f*_{i} satisfy *f*_{i}()(*s*_{1},*…,s*_{n}),*e*_{i}) = *s*_{i} if and only if, given *e*_{i}, *i* regards the outcome *g*(*s*) to be at least as good as the outcome \( g\left({s}_1,\dots, {s}_{i-1},{\overline{s}}_i,{s}_{i+1},\dots, {s}_n\right) \) for all \( \overline{s} \)_{i} in *S*_{i}; and let *h*(*s*) = *g*(*s*).) Much has now been learned about what sorts of performance functions *ϕ* (including economically interesting ones) can be implemented and what sorts cannot (for a survey, see Hurwicz 1986). We again have the ‘dynamic’ shortcoming noted before: if, for every *e*, an outcome in the set{*a*∈*N*_{gs} (*e*):*s*∈*S*} is indeed to be reached by operating an adjustment process (as in the economists’ allocation mechanisms), then the behaviour of the process prior to equilibrium must be studied. Doing so may, moreover, introduce quite new strategic considerations, since a fresh incentive problem may arise at each step of the process: at each step a member may ask whether carrying out the designer’s instructions (applying *f*_{i}) is what he/she really wants to do.

Thus both on the informational and the incentive sides, a very large research agenda stretches before the economic organization theorist. Moreover, the abstract theorizing we have sketched is very far indeed from making good contact with the institutional facts about real organizations. One may take the design point of view, but even a designer is constrained by those facts.

In particular, the notion of *hierarchy* (the ‘organization chart’), which appears so often in popular discourse, is very hard indeed to pin down in the adjustment-process framework. To define ‘hierarchy’, we first have to define ‘authority’. When does an adjustment process have the property that person 1 is in authority over person 2? Probably the best one can hope for (Hurwicz 1971) is this: person 1 is in authority over person 2 if (1) at the terminal step *T*,*m*_{T2} depends only on *m*_{T−1,1}, and (2) *m*_{T−1,1} is sensitive to *e1*. If we did not add requirement (2), then person 1’s apparent terminal instruction to person 2 (embodied in the pre-terminal message *m*_{T−1,1}) might in fact be a robot-like repetition (perhaps in recoded form) of a ‘command’ that 2 gave to 1 at step *T* − 2. On the other hand, we might satisfy the sensitivity required by (2) in such a trival way that we have not really succeeded in ruling out person 2 as the ‘true’ (though somewhat disguised) commander. Authority is, in short, a very fragile concept from a formal point of view.

Yet it is a central concept in influential writings like those of Williamson (1975). His book is a rich source of institutionally motivated conjectures about how organizations work, but it teems with terms, concepts and conjectures that the formal theorist must struggle mightily to make precise. The task of precise pinning down is so daunting that the stage of testing the conjectures (trying to prove them) seems unlikely to be reached. The book argues for these conjectures nevertheless, and many of them appear, at some level, to be plausible. Here is one example: ‘it is elementary that the advantages of centralization vary with the degree of independence among the members, being … almost certainly great in an integrated task group’ (p. 51). To the formal theorist, that is not ‘elementary’ at all. One requires five or six definitions before one even knows what is being claimed.

Nevertheless, such informal but insightful institution-based essays are an essential challenge to formal theory. The economists’ organization theory of the future will grow out of the tension between highly imprecise but widely believed and institutionally grounded claims and the harsh demands of formal argument.

## See Also

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