Timothy Van Zandt


Research on Information Processing in Organizations

Surveys: Real-Time Hierarchical Resource Allocation: Other Decentralized Real-Time Information Processing: Decentralized Batch Processing: Other:


Surveys:


Decentralized Information Processing in the Theory of Organizations

Published: (1999) Contemporary Economic Issues, Vol. 4: Economic Design and Behavior, edited by Murat Sertel. London: MacMillan Press Ltd. Chapter 7, pages 125-160.

Description: A broad historical survey. 36 pages.

Abstract: Bounded rationality has been an important theme throughout the history of the theory of organizations, because it explains the sharing of information processing tasks and the existence of administrative staffs that coordinate large organizations. This article broadly surveys the theories of organizations that model such bounded rationality and decentralized information processing.

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Organizations with an Endogenous Number of Information Processing Agents

Published: (1998) Organizations with Incomplete Information, edited by Mukul Majumdar. Cambridge: Cambridge University Press. Chapter 7, pages 239-305.

Description: A narrow, detailed exposition. 63 pages.

Abstract: This paper examines recent research on bounded rationality in organizations which features (i) the explicit modeling of the computation constraints of individual agents and (ii) the endogenous determination of the number of information processing agents. This literature attempts to explain the existence and activities of the administrative apparatus of large organizations and the benefits and costs of decentralization. It has also addressed the questions of how information processing constraints affect the structure and returns to scale of organizations.

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Supplementary notes: These are unpublished supplementary notes that complement the paper.

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Hierarchical Computation of the Resource Allocation Problem

Published: (1995) European Economic Review. 39:700-708.

Abstract: Some recent research on information processing in organizations has treated the agents who process information as endogenous. This paper discusses a sample of models in this area, which differ in their methodology but are unified by the fact that they study the resource allocation problem. Computational constraints are related to the structure and returns to scale of hierarchies.

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Real-Time Hierarchical Resource Allocation


Real-Time Hierarchical Resource Allocation

Date: 12 June 2003

Abstract: This paper presents a model that distinguishes between decentralized information processing and decentralized decision making in organizations; it shows that decentralized decision making can be advantageous due to computational delay, even in the absence of communication costs. The key feature of the model, which makes this result possible, is that decisions in a stochastic control problem are calculated in real time by boundedly rational members of an administrative staff. The control problem is to allocate resources in a changing environment. We consider a class of hierarchical procedures in which information about payoffs flows up and is aggregated by the hierarchy, while allocations flow down and are disaggregated by the hierarchy. Nodes of the hierarchy correspond not to a single person but to decision-making units within which there may be decentralized information processing. The lower tiers of multitier hierarchies can allocate resources quickly within small groups, while higher tiers are still able to exploit gains from trade between the groups (although on the basis of older information).

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Real-Time Hierarchical Resource Allocation with Quadratic Payoffs

Date: 23 July 2003

Abstract: This paper presents a model in which resource allocations are calculated in real time by boundedly rational members of an administrative staff. We consider a class of hierarchical procedures in which information about payoff functions flows up and is aggregated by a hierarchy, while allocations flow down and are disaggregated by the hierarchy with decentralized decision making. We assume that the payoff functions are quadratic and that the payoff parameters follow first-order autoregressive processes. We define a team statistical optimality condition that formalizes the notion of decentralized decision making. We derive a reduced form that can be used to address specific questions about organizational structure and returns to scale.

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Balancedness of Real-Time Hierarchical Resource Allocation

Date: 23 July 2003

Abstract: We take the hierarchical resource allocation model in Van Zandt (2003) and derive a simpler, reduced-form model of balanced hierarchies. This model uses continuous approximations; we derive bounds on the errors due to these approximations. We then give results that indicate that optimal hierarchies in the general model of are approximately balanced. In particular, we show that aggregation should be balanced if the hierarchical structure is balanced and we show the hierarchical structure should be balanced if aggregation is balanced.

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Structure and Returns to Scale of Real-Time Hierarchical Resource Allocation

Date: 23 July 2003

Abstract: Companion papers develop a model of real-time hierarchical computation of resource allocations by boundedly rational members of an administrative staff. The nodes of a hierarchy are multiperson decision-making units offices. The current paper uses a reduced form to address specific questions about organizational structure and returns to scale. We find that the possibility of decentralizing decision making within these hierarchical organizations allows for larger hierarchies. However, organization size is still bounded because the combined effect of cumulative delay and administrative costs means that in large enough hierarchies, the value of the root office's information processing is less than the office's administrative costs. We also find that as the environment changes more rapidly, optimal hierarchies become smaller and more internally decentralized. A speed-up of managerial processing, such as through improved information technology, has the opposite effect.

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Other Decentralized Real-Time Information Processing:


Hierarchy Size and Environmental Uncertainty

Coauthors:
Kieron Meagher, University of New South Wales, k.meagher@unsw.edu.au.
Hakan Orbay, Sabanci University, hakan@sabanciuniv.edu.

Published: 2003, Advances in Economic Design, M.R. Sertel and S. Koray (Eds.), Springer-Verlag.

Abstract: We examine how a firm's changing environment and the information constraints of its managers interact as determinants of the size of the firm's administration. Following the recent decentralized information processing literature, we assume that it takes individual managers time to process information. A consequence is that it takes time for a firm to aggregate information, even when this task is shared. This delay increases with the amount of information that is aggregated, leading to the following trade-off: the more data the firm samples each period (and hence the larger its managerial staff), the more precisely it can estimate the state that its environment was in when the sample was taken but the more the environment has changed by the time these data are used to estimate the current state. We explore this trade-off for two computation models and for both a benchmark case of costless managers and the case of costly managers. When managers are costless, the size of the administrative staff increases monotonically as the environment becomes more stable. In contrast, when managers are costly, optimal managerial size first increases and then decreases as a function of environmental stability.

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Real-Time Decentralized Information Processing as a Model of Organizations with Boundedly Rational Agents

Published: (1999) Review of Economic Studies, 66:633-658.

Abstract: This paper studies the properties of real-time decentralized information processing as a model of human information processing in organizations. Real-time decentralized processing---which models the computation of decision rules in a temporal decision problem by members of an organization---captures both the cost of computation in terms of the members' time and the constraints imposed by computational delay on the use of recent information. Unlike a batch processing model, it has no single measure of delay because decisions are computed from data of heterogeneous lags. Furthermore, decentralization does not unambiguously reduce delay, because processing a message precludes processing current data.

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Real-Time Decentralized Information Processing and Returns to Scale

Coauthor: Roy Radner, Stern School of Business, New York University, rradner@stern.nyu.edu.

Published: 2001, Economic Theory, 17:497-544.

Abstract: We use a model of real-time decentralized information processing to understand how constraints on human information processing affect the returns to scale of organizations. We identify three informational (dis)economies of scale: diversification of heterogeneous risks (positive), sharing of information and of costs (positive), and crowding out of recent information due to information processing delay (negative). Because decision rules are endogenous, delay does not inexorably lead to decreasing returns to scale. However, returns are more likely to be decreasing when computation constraints, rather than sampling costs, limit the information upon which decisions are conditioned. The results illustrate how information processing constraints together with the requirement of informational integration cause a breakdown of the replication arguments that have been used to establish nondecreasing technological returns to scale.

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Supplementary notes: These are supplementary notes that provide technical details for various steps, claims, and lemmas in the main paper.

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Information Processing in Firms and Returns to Scale

Coauthor: Roy Radner, Stern School of Business, New York University, rradner@stern.nyu.edu.

Published: 1992. Annales d'economie et de statistique. 25/26:265-298.

Abstract: What are the returns to scale in decision-making, when information processing is costly? In a parallel-processing model of a firm, we characterize efficient networks for associative operations, where efficiency is measured in terms of the number of individual processors (of given capacity) and the information-processing delay. We then embed this structure in a model of decision-making under uncertainty, and find that returns to scale can vary from increasing to sharply decreasing, depending on the intercorrelation of the data and on the loss function for incorrect decisions.

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Batch processing:


The Scheduling and Organization of Periodic Associative Computation: Efficient Networks

Published: 1998. Review of Economic Design, 3:93-127.

Abstract: This paper characterizes the efficient decentralized networks for calculating the associative aggregate of cohorts of data of a fixed size that arrive periodically. Radner (1993) proposed this problem of periodic parallel associative computation as a model of the ongoing information processing and communication by the administrative staff of a large organization. For a simpler model in which the organization processes a single cohort of data---which is equivalent to the periodic model when the agents are paid only when busy---he found that the efficient networks are hierarchical but quite irregular, even though the computation problem and technology are each symmetric. In the periodic model in which managers are paid even when idle, it becomes important to minimize idle time when scheduling managers to processing tasks. Such scheduling appears more difficult when each problem is processed by an irregular hierarchy, which suggest that hierarchies might be more regular in the periodic model. However, we show that in a class of efficient networks for periodic computation that spans the efficiency frontier, the processing of each cohort is similar to the efficient processing of a single cohort, and the overall organizational structure is not even hierarchical.

Note: This paper presumes you have read or have access to the companion paper, ``The Scheduling and Organization of Periodic Associative Computation: Essential Networks''

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The Scheduling and Organization of Periodic Associative Computation: Essential Networks

Published: (1997) Review of Economic Design, 3:15-27.

Abstract: This paper defines and characterizes essential decentralized networks for calculating the associative aggregate of one or more cohorts of data. A network is essential if it is not possible to eliminate an instruction or manager and still calculate the aggregate of each cohort. We show that for essential networks, the graphs that depict the operations and data dependencies are trees or forests. These results assist in the characterization of efficient networks.

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Managerial Costs for One-Shot Decentralized Information Processing

Coauthor: Kieron Meagher, Economics Program, Australian National University, kmeagher@unsw.edu.au.

Published: (1998) Review of Economic Design, 3:329-345.

Abstract: Radner (1993) proposed a model of decentralized associative computation as a means to understand information processing in organizations. In the model, in which an organization processes a single cohort of data, resources are measured by the number of managers. This paper (i) explains why resources should instead be measured by the time the managers are busy, (ii) shows that, nevertheless, the characterization of sufficient conditions for efficient networks in Radner (1993) is valid for either measure, (iii) shows that measuring resources by the number of operations leads to sharper results on necessary conditions for efficiency, (iv) strengthens Radner's results on the irregularity of efficient hierarchies, and (v) compares the relative costs of parallelization under the two measures.

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Other:


Continuous Approximations in the Study of Hierarchies

Published: (1995) RAND Journal of Economics, 26:575-590.

Abstract: Large organizations are typically modeled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this paper is to study the validity of these approximations. I show that modeling hierarchies with a continuum of tiers is not a good approximation. I also show, for a particular model of balanced hierarchies, that ignoring rounding operators and integer constraints in formulae derived from the discrete model can be a valid approximation, when hierarchies are suitably large. This is made precise by bounds on the relative errors of the approximations.

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