Communication Networks and the Rise of an Information Elite: 
Do Computers Help the Rich Get Richer?

Copyright © 1996
Marshall W. Van Alstyne 
Erik Brynjolfsson
Version 1.0 96/04/30

This notebook contains graphical illustrations of propositions found in a paper of the same title.  The basic question examined is what happens to a universe of agents (self interested people, firms, or regions) as you increase the access they have to one another and as they share information resources.  Our main implication is one of "Cyber-Stratification" -- increasing access and decreasing search costs enable elites to cooperate when geography might have limited their interaction beforehand.  The code used to generate these images is available free from the authors to allow you to explore these results for yourself.  In the interest of advancing research on this topic and encouraging policy debate, we support the Free Software Foundatin's idea of a "Copyleft":  you are welcome to use, modify, and distribute these materials free of charge provided that (1) you retain acknowledgment of both original and any subsequent authors' contributions, noting any modifications you make and (2) you understand that these materials are provided without warranty either expressed or implied.  We encourage you to contact us with  comments, suggestions, or new additions which we might include in subsequent releases.

Marshall Van Alstyne
Erik Brynjolfsson
Cambridge, MA 1996
marshall@mit.edu

Open any group of cells by double clicking on the right hand bracket with the down arrow.  Double click again to close the group.

Setting & Instructions

Overview

With  the emergence of the Internet, geographically separated populations have gained the ability to communicate and to coordinate their activities in ways that were once too difficult to manage over large distances.  In particular, people can reach new information resources and share information among their network of associates in an attempt to improve their collective resource base.  Before advanced information technologies, this might have required face-to-face communication or the use of sluggish low bandwidth telecommunications (or very expensive high bandwidth communications).  This notebook illustrates what happens as agents (self-interested persons, firms, or regions) attempt to improve their information resources by networking with each other.

Demonstration Instructions & Conventions

This is an interactive demonstration.  You can animate many of the graphics by double clicking on the face of the graphic.  If you also have access to Mathematica, you can even run the code that accompanies this notebook to create entirely new scenarios.  These are a few of the conventions that will help with the demonstration.

Animation

Graphics with a grey box underneath can be animated...

Commands

If you wish to create your own demonstrations, the commands in the bordered boxes can be executed at your computer to create images similar to those shown here.  You will need to load the source code available from the URL at the bottom of this notebook and you will need access to a copy of Mathematica.  The free reader displays graphics and animation but does not execute symbolic commands.  Instructions for using individual commands and help documentation are included within the source code.

In[1]:= Commands that look like this can be executed at your computer.

The "In[1]:=" just tells you which input we typed on the command line. If you are using the free Reader, however, you will only be able to run the animation.

Modeling Assumptions

We make four basic assumptions about information interactions which we use to construct a model.  First, people cannot talk to or listen to everyone else at once.  As a proxy for bounded rationality, this means that they will need to select some subset of the population with whom to communicate.  It's been suggested that we might be able to communicate with as many as 3000 people but out of 270 million in the US alone, this is a pretty small fraction (see the paper for this and all subsequent references).  Second, we assume that information isn't lost, consumed, or destroyed when it is shared with others. In economic terms, information goods are "nonrival."  If one person gives another a favorite recipe, for example, that information doesn' t necessarily become unavailable to the giver -- information isn't destroyed and multiple agents can still use it.  This also allows us to model the possibility, however, that people may lose strategic advantage if resources are transfered.  Third, private resources differ in quality, amount, value etc.  That is, people know different things and private resources as distinct from public resources are heterogeneous.  It has also been suggested that information which might once have been public is becoming increasingly privatized as people recognize its value.  For example, trade secrets, patents and copyrights increasingly privatize software, genetic codes, and protein manufacturing.  Fourth, people can improve their resources based on the resources to which they can gain access.  If one person can gain access to a Nobel prize winner for example, but another cannot, then the first  is likely to have access to a richer source of information.  This implies that social networks or networks of connections can become very important in improving resources over time.  Only the first two assumptions are important to our observation that increasing access and decreasing search costs brought on by information technology are likely to increase "cyber-stratification."   The other assumptions help us make a few observations about the improvements to resources over time.

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Observation 1 -- Increasing Access and Decreasing Search Costs Increase Stratification

Create the Population & Local Neighborhoods

This command populates a universe with agents.  Each agent is given an endowment of information resources which is illustrated both by color and by size.  Larger cyan circles represent more resources and smaller red circles represent fewer resources with differences being purely relative not absolute. All endowments are randomly generated numbers initially falling between 0 and 1.  Here we make 11 agents and give them 2 channels each to communicate with other agents.

In[1]:= makeAgents[11, ChannelCount->2]

Let's start with a situation of purely local neighborhoods in which no one can reach more than two other agents in their neighborhood. Agents want to reach one another but are restricted by access. The situation looks something like this:

In[2]:= connectAgents[Access->Local]

These numbers indicate that there are a total of four networks, that their endowments start with the sixth richest and end with the tenth, that their indices run clockwise starting at 12 o'clock from one to eleven, and that they are members of one of four networks consisting of local partners {1, 2 , 3}, {4, 5, 6}, {7, 8, 9}, and {10, 11}.  The range of endowments for all agents is .9272 with an average of .3315 while the range in network 1, for example, is .5201 with an average endowment of .3388.  Note that with everyone restricted to local access, the networks all have average endowments which are not too far from the norm overall.  The highest average is only .529 while the lowest average is .2235.

Agents' private knowledge bases look like the following (counting clockwise):

In[3]:= aPKBases

Out[3]={0.243, 0.646, 0.126, 0.225, 0.124, 0.320, 0.376, 0.046, 0.478, 0.973, 0.084}

Show Effects of Universal Access

Consider that "access" is the fraction of the population that any given agent can reach because they also have access to information technology infrastructure.  Ideally, "Universal Access" would mean that everyone can reach everyone else.  Since it's possible to reach everyone in a virtual neighborhood, not just a physical neighborhood, agents across the system can reach one another.  But, if agents only have two channels (i.e. they can only talk to a fraction of the population) then who talks to whom?

In[4]:= connectAgents[Access->Global]

This implies that agents can leave their physical neighborhoods behind to participate with virtual neighbors anywhere else.  Access to other agents also doesn't necessarily imply availability.  In theory, for example, the telephone allows any of us to speak with Vice President Al Gore but in practice, we'd probably need to be a head of state or captain of industry to get through to him.  Agents at, say 3 o'clock, can in theory reach a Nobel prize winner agent 10 but they can't get through if she's busy talking to agents 2 and 9.

The real point, however, is the new potential for "cyber-stratification."  Notice how the average resources tend to be more concentrated by network.

In[5]:= showGaps[]

After global access, the highest average network has average resources of .6997 and the lowest is .0654.  With no growth in resources, the top has changed by +32% and the bottom has changed by -71% simply by allowing virtual networks to form instead of geographic networks.  Neighborhoods have become more stratified.

Observation 2 -- Universal Access Facilitates Winner-Take-All Markets

Consider that "access" is the portion of the entire population that can communicate over an information technology backbone.  Alternatively, it's the portion of the population that any single agent can reach by such an IT backbone.  Ideally, "Universal Access" would mean that everyone can talk to everyone else.  This is plotted below in the case where there are no constraints on the number of channels available.  So, as access increases, the probability of being able to reach any given agent climbs to one.

In[6]:= plotProbAccess3D[
	           Constrained->False,
	           PlotLabel->"Full Access with No Capacity  
	           Constraints"]

The agents we created, however, actually have a limitation of only two channels.  This affects the partnerships that form with universal access.  Now that everyone can reach everyone else, which networks form? If C represents the number of channels you have, the new question becomes "What are the chances that the agents you can reach are among your top C choices?"  You can only talk to at most C others at once.  The graphic below animates what happens as the channel capacity (or bounded rationality) constraint falls to the 2 we originally assigned.

This command plots the same chart several times dropping the number of channels from 11 (the size of the population) down to 2.

In[7]:= Map[plotProbAccess3D[Constrained->True,
                     		      NumChannels->#]&, 
            {11, 10, 9, 8, 7, 6, 5, 4, 3, 2}]

This effect has been called a "Winner-Take-All" market ([Frank & Cook '95] see the paper for more details and references). In fact, with only two connections, almost everyone prefers to allocate their attention to the two richest sources.

Suppose we gave agents more channels and also had a bigger population.  The same distribution plotted with 25 agents and 5 channels each looks like this:

In[8]:=plotProbAccess3D[NumAgents->25,NumChannels->5]

The pattern is pretty similar.  Increasing access benefits everyone until the capacity constraint binds.  Then the top agents benefit most.  The last row, representing universal access, is particularly interesting since the probability that any agent is in the top C choices is either 0 or 1. The information "middle class" initially benefit from increased access until the capacity constraint binds for them too.

If the top C agents can actually serve the entire market, as in the case of broadcast technology, then they are the ones who gather the most benefits, i.e. the winners take all.  Kurt Vonnegut describes a story in which a local musician was once a neighborhood treasure but then telecommunications technoloy put him in competition with the world's best musicians.  Then he loses his opportunity to perform.  That is one of the phenomena we model here.

Observation 3 -- Strategic Competition Among Agents Leads Them to Stop Sharing Information

Although information is a nonrival good that can be shared without depleting it, agents sometimes value not how much they have, but how much of an advantage they have over their neighbors -- they look at the relative differences not the absolute value.

In[9]:= connectAgents[Strategy->Relative]

With two channels each, four networks could form just as before but agents might lose any relative advantage by sharing information so they stop cooperating.

In[10]:= showGaps[]

A study of groupware information sharing technology found exactly this kind of behavior.  Consultants were promoted to partner inside the firm based on relative skill levels.  Only a handful, however, ever received the promotion and the rest usually left the consulting practice.  Despite the availability of tools to facilitate sharing, consultants resisted trading information fearing the loss of a distinctive competitive advantage.  This model suggests that incentives can be important to getting a different kind of behavior.

Observation 4 -- Agents In The Same Network Grow Towards One Another Over Time While Agents In Different Networks Grow Away From One Another Over Time

The next command shows that network members who share information tend to have resources that approach one another over time.  Since resources improve partly as a function of one's network of connections, richer networks tend to improve faster.  The following command runs time forward by 15 periods assuming that resource growth rates and sharing rates are the same for all networks.

In[1]:= run[20, PlotTimes->4]

Note that the ranges of values between network members has decreased for all networks from where they stood under Observation 1.   The average in the highest level network has also increased to 9.34.  Agent 10 is still at the top but her two partners are converging on the same level of resources.  The last network, with only two members, grows much more slowly.  As always, colors show relative distances with the spectrum anchoring the two endpoints in terms of total resources.

This next plot shows the absolute values, not just the relative positions.  The following command creates a list of all agents from 1 to 11 then plots their resource histories.

In[12]:= plotHist[Table[x,{x,1,11}]]

Clearly the resources of members in the same network converge even as the networks themselves diverge.   Thus an initial advantage can become compounded over time.

Observation 5 -- Even If Learning or Information Production Exhibits Diminishing Returns to Scale, the Information State Exhibits Increasing Returns to Scale.

The final graph under Observation 4 showed how groups tend to move apart from one another.  It might be possible to raise an objection that these results depend on our particular choice of a learning function which we modeled as linearly compounding.  In fact, however, this is not the case.  Even if the rate of change in information exhibits diminishing returns, results analogous to those of Observation 4, where groups move apart from one another, still hold (a formal proof is provided in the paper).  The linear learning rate looks like the following:

In[13]:= ?learnFn

In[14]:= aLearning

These two inputs merely show that all 11 agents can change their resources at the same rate which is simply set at 10%.  The vector of learning functions associates one function with each agent.  We can change this to diminishing returns, however, and still get the same kinds of results -- it just takes longer.  Below we plot the conventional learnFn against a concave (diminishing returns) learning function.  We first define the concave function, then plot both over a range of 0-20, one in red, the other in blue.

In[15]:= concaveLearn[x_] := x^.1

In[16]:= Show[Plot[learnFn[x], {x,0,20},     
																			PlotStyle->{RGBColor[1,0,0]}],
              Plot[concaveLearn[x], {x,0,20},       
                   PlotStyle->{RGBColor[0,0,1]}],
              AxesLabel->{Input, Output},
              PlotLabel->"Linear & Diminishing 
                          Returns"]

Thus the new function produces less output per each additional unit of input.  Now, we'll reset agents' resources to where we started then assign new learning functions and run the whole process forward again.  The undo[] function can be quite helpful in this regard.

In[17]:= undo[]

This command undoes changes we made under Observation 4.  (The undo[n] command will reverse n changes with a default of 1.)  Now we give everyone the same concave learning function which increases at a much slower and diminishing rate.  This creates 11 copies of the function and assigns it to the learning vector.

In[18]:= aLearning=Table[concaveLearn, {11}]

Then we run time forward by 50 periods only plotting at intervals of 10.

In[19]:= run[50,PlotTimes->10]

Note that the top and bottom colors don't  spread further since we can only show relative positions.  Showing absolute positions would take color representations outside the color scale. The averages, however, have certainly spread apart.  To see the absolute differences, we plot the output histories for all 11 agents over the 50 periods.

In[20]:= plotHist[Table[x,{x,1,11}]]

Here, the different agents' plots have grown so close together that only their networks are distinct.  Notice, however, that the concave (diminishing returns) generation rate still gives rise to a convex (increasing returns) information state.  This is a rather unusual property of nonrival goods -- you can recover all the inputs  after using them so diminishing returns to scale need not necessarily apply.

Observation 6 -- A Network Can Improve its Resources Faster By Sharing More

Let's take the final network resource state provided by the last operation in Observation 4 which we show below.  What we want to show, is how much better off a network can be by improving its sharing rate.

This command undoes the last operations (bringing the network back to time 0) then runs it forward by 20 steps only printing at time 20.

In[21]:= Undo[]; run[20, PlotTimes->20]

As with the learning functions, we set everyone to be equal in terms of their baseline rates.  The vector of sharing functions shows the following:

In[22]:= aSharing

In[23]:= ?shareFn

Here agents only share about 10% of their private information.  What we now wish to do is to increase the sharing rate of the third tier network who has average resources of less that 1/4 those of the top tier network.  The following shows what happens in more open environments when agents are willing to share more of their private information.

First we create a sharing function which helps the agents share 80% of their private resources not just 10%.  Then we assign it to the vector location for each member of the third tier network.

In[24]:= shareMore[x_]:=.8*x

In[25]:= aPartners

In[26]:= setSharing[aPartners[[3]], shareMore]

In[27]:= run[25]

The third tier network has outstripped the other two by a substantial margin over the 25 periods.  Increasing the sharing rate has substantially increased the growth in overall resources and provides an indication of the advantages that are possible in more open environments or ones with groupware and other sharing systems in place.  We can also plot the relative resources of different agents in 3D absolute terms as well.

In[28]:= plotHist3D[Sorted->False]

In the above plot, the upper surface represents access to total resources by agent -- the sum of private resources and those resources shared by partners in their respective networks.  The lower surface represents purely private resources regardless of sharing. 

One particularly interesting feature of this plot is that along the lower envelope, the agents in network three i.e. {3,4,5} do not have particularly high numbers implying that their private resources aren't that remarkable compared to other agents.  In fact, a drop appears between agents 2 and 3.  But, along the upper envelope, their resources are as good if not better than those of every other agent.

A situation of growing resources suggested by this observation derives some empriical support from a case study of high technology firms in Massachusetts and in California [Saxenian 1995].  In 1975, firms in the two regions employed roughly the same number of people but 15 years later the firms in California had created three times as many net new technology jobs.  Additionally, in the last several years of the study, firms in Massachusetts had increased their market capitalization by roughly 1 billion dollars as compared to 25 billion in California.  The study suggests that (1) firms in New England were more vertically integrated so their business units traded less information with buyers and suppliers (2) these firms also had more defense contracts so they couldn't share their research and (3) scientists and engineers did more job hopping and traded more information in California leading to a greater distribution of knowledge in California.

Observation 7 -- Whom You Know Counts; In an Information Economy, One's Network of Connections is a Valuable Resource

Let's again go back to the situation at the end of Observation 4 when network members have converged in resources.  The situation looks something like this:

In[29]:= undo[]

What we're now going to do is connect Agent 3 to the top tier network to see what becomes of his resources.  We do this by indicating which partners form a particular network

In[30]:= aPartners

In[31]:= makeNetwork[{3,9,10}]

In[32]:= aPartners

Now we'll run time forward by 25 periods to see how the resources move.  Note, in particular, the resources of agents 2 (who is by himself) and 3 (who is in the new network together with agents 9 and 10.

In[33]:= run[25]

We can also plot the absolute resources of the agents to see how they have moved over time.  In the plot below, Agent 3's resources leaves the trajectory of the former network {3,4,5} and joins the trajectory of the new network {3,9,10}.  Agent 2, on the other hand, goes off on a different trajectory entirely.

In[34]:= plotHist[{2,3,4,10}]

The point of this illustration is a more formal accounting of the idea that "it's not just what you know but whom you know." Numerous studies, for example, have concluded that access to better schools can provide a network of contacts that is useful throughout one's career.  In an information economy, one's network of connections can prove to be a considerable asset.

Epilogue & Sources

These outcomes are based on a formal model with several assumptions which you can manipulate directly.  It is these assumptions and their implications which can help improve understanding, achieve different outcomes, and assist policy.  We also encourage you to read the paper to understand more formally the details of how the model works.  Research is progressing on several extensions to the basic model and new results will appear periodically at URL http://web.mit.edu//marshall/www/home.html.  Availability from this site is expected for at least one year or until June 1, 1997.  Pendng resource availability, updates might also appear after this date.