Timothy Van Zandt

- Decentralized Information Processing in the Theory of Organizations
- Organizations that Process Information with an Endogenous Number of Agents
- Hierarchical Computation of the Resource Allocation Problem

- Real-Time Hierarchical Resource Allocation
- Real-Time Hierarchical Resource Allocation with Quadratic Payoffs
- Balancedness of Real-Time Hierarchical Resource Allocation
- Structure and Returns to Scale of Real-Time Hierarchical Resource Allocation

- Hierarchy Size and Environmental Uncertainty
- Real-Time Decentralized Information Processing as a Model of Organizations with Boundedly Rational Agents
- Real-Time Decentralized Information Processing and Returns to Scale
- Information Processing in Firms and Returns to Scale

- The Scheduling and Organization of Periodic Associative Computation: Efficient Networks
- The Scheduling and Organization of Periodic Associative Computation: Essential Networks
- Managerial Costs for One-Shot Decentralized Information Processing

**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.

Request hard copyDownload pdf file

**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.

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These are unpublished supplementary notes that complement the paper.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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).

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

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

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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''

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file

**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.

Request hard copyDownload pdf file