Transcript Document

Innovation in networks
and alliance management
Small world networks & Trust
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Course aim
knowledge about concepts in
network theory, and being able to
apply that knowledge
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The setup in some more detail
Network theory and background
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Introduction: what are they, why important …
Four basic network arguments
Kinds of network data (collection)
Network properties (and a bit on trust)
Business networks
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Two approaches to network theory
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Bottom up (let’s try to understand network
characteristics and arguments)
as in … “Four network arguments” we saw before
and in the trust topic today (2nd hour, if we make
it)
Top down (let’s have a look at many networks,
and try to deduce what is happening from what
we see)
as in “small world networks” (now)
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What kind of structures do
empirical networks have?
(answer: often small-world,
and often also scale-free)
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3 important network properties
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Average Path Length (APL) (<l>)
Shortest path between two nodes i and j of a network,
averaged across all (pairs of) nodes
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Clustering coefficient (“cliquishness”)
The probability that two of my friends are friends of each
other
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(Shape of the) degree distribution
A distribution is “scale free” when P(k), the proportion of
nodes with degree k follows this formula, for some value of
gamma:
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Example 1 - Small world networks
NOTE
Edge of network theory
Not fully understood yet …
… but interesting findings
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The small world phenomenon –
Milgram´s (1967) original study
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Milgram sent packages to a couple hundred people
in Nebraska and Kansas.
Aim was “get this package to <address of person
in Boston>”
Rule: only send this package to someone whom
you know on a first name basis. Try to make the
chain as short as possible.
Result: average length of chain is only six
“six degrees of separation”
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Milgram’s original study (2)
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An urban myth?
Milgram used only part of
the data, actually mainly
the ones supporting his
claim
 Many packages did not
end up at the Boston
address
 Follow up studies
typically small scale

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The small world phenomenon (cont.)
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“Small world project” has been testing this assertion (not
anymore, see http://smallworld.columbia.edu)
Email to <address>, otherwise same rules. Addresses were
American college professor, Indian technology consultant,
Estonian archival inspector, …
Conclusion:
 Low completion rate (384 out of 24,163 = 1.5%)
 Succesful chains more often through professional ties
 Succesful chains more often through weak ties (weak ties
mentioned about 10% more often)
 Chain size 5, 6 or 7.
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Ongoing Milgram follow-ups…
6.6!
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Two approaches to network theory

Bottom up (let’s try to understand network
characteristics and arguments)
as in … “Four network arguments” last week

Top down (let’s have a look at many networks,
and try to deduce what is happening from what
we see)
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The Kevin Bacon experiment –
Tjaden (+/- 1996)
Actors = actors
Ties = “has played in a movie with”
Small world networks:
- short average distance between pairs
…
- … but relatively high “cliquishness”
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The Kevin Bacon game
Can be played at:
http://oracleofbacon.org
Kevin Bacon
number
(data might have changed by now)
Jack Nicholson:
Robert de Niro:
Rutger Hauer (NL):
Famke Janssen (NL):
Bruce Willis:
Kl.M. Brandauer (AU):
Arn. Schwarzenegger:
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2
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2
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(A few good men)
(Sleepers)
[Nick Stahl]
[Nick Stahl]
[Patrick Michael Strange]
[Robert Redford]
[Kevin Pollak]
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A search for high Kevin Bacon numbers…
3
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Bacon / Hauer / Connery
(numbers now changed a bit)
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The best centers… (2011)
(Kevin Bacon at place 444)
(Rutger Hauer at place 43, J.Krabbé 867)
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“Elvis has left the building …”
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We find small average path lengths in all kinds
of places…
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Caenorhabditis Elegans
959 cells
Genome sequenced 1998
Nervous system mapped
 low average path length
+ cliquishness = small world network
Power grid network of Western States
5,000 power plants with high-voltage lines
 low average path length +
cliquishness = small world network
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How weird is that?
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Consider a random network: each pair of
nodes is connected with a given probability
p.
This is called an Erdos-Renyi network.
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APL is small in random networks
[Slide copied from Jari_Chennai2010.pdf]
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[Slide copied from Jari_Chennai2010.pdf]
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But let’s move on to the second network
characteristic …
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This is how small-world networks
are defined:
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A short Average Path Length and
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A high clustering coefficient
… and a random network does NOT lead to
these small-world properties
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Source: Leskovec & Faloutsos
Networks of the Real-world (1)
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Information networks:
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Social networks: people +
interactions
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World Wide Web:
hyperlinks
Citation networks
Blog networks
Florence families
Organizational networks
Communication networks
Collaboration networks
Sexual networks
Collaboration networks
Karate club network
Technological networks:
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Power grid
Airline, road, river
networks
Telephone networks
Internet
Autonomous systems
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Friendship network
Collaboration network
Source: Leskovec & Faloutsos
Networks of the Real-world (2)
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Biological networks
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Language networks
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metabolic networks
food web
neural networks
gene regulatory
networks
Yeast protein
interactions
Semantic network
Semantic networks
Software networks
…
Language network
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Software network
And if we consider all three…
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… then we find this:
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Wang & Chen (2003) Complex networks: Small-world, Scale-free and beyond
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Small world networks … so what?
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You see it a lot around us: for instance in road
maps, food chains, electric power grids,
metabolite processing networks, neural networks,
telephone call graphs and social influence
networks  may be useful to study them
They seem to be useful for a lot
of things, and there are reasons
to believe they might be useful
for innovation purposes (and hence
we might want to create them)
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Examples of interesting
properties of
small world networks
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Combining game theory and networks –
Axelrod (1980), Watts & Strogatz (1998?)
1.
2.
3.
4.
5.
Consider a given network.
All connected actors play the repeated Prisoner’s Dilemma
for some rounds
After a given number of rounds, the strategies “reproduce”
in the sense that the proportion of the more succesful
strategies increases in the network, whereas the less
succesful strategies decrease or die
Repeat 2 and 3 until a stable state is reached.
Conclusion: to sustain cooperation, you need a short
average distance, and cliquishness (“small worlds”)
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Synchronizing fireflies …
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<go to NetLogo>
Synchronization speed depends on small-world
properties of the network
 Network characteristics important for “integrating
local nodes”
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If small-world networks are so
interesting and we see them
everywhere, how do they arise?
(potential answer: through random
rewiring of a given structure)
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Strogatz and Watts
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6 billion nodes on a circle
Each connected to nearest 1,000 neighbors
Start rewiring links randomly
Calculate average path length and clustering as
the network starts to change
Network changes from structured to random
APL: starts at 3 million, decreases to 4 (!)
Clustering: starts at 0.75, decreases to zero
(actually to 1 in 6 million)
Strogatz and Watts asked: what happens along
the way with APL and Clustering?
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Strogatz and Watts (2)
“We move in tight circles yet
we are all bound together by
remarkably short chains”
(Strogatz, 2003)
 Implications for, for instance,
research on the spread of
diseases...
The general hint:
-If networks start from relatively
structured …
-… and tend to progress sort of
randomly …
-- … then you might get small
world networks a large part of the
time
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And now the third characteristic
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Same thing … we see “scale-freeness” all over
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… and it can’t be based on an ER-network
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Another BIG question:
How do scale free networks arise?
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Potential answer: Perhaps through “preferential
attachment”
< show NetLogo simulation here>
Critique to this approach:
it ignores ties created by those in the network
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(more) open problems
and related issues
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Applications to
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Spread of diseases (AIDS, foot-and-mouth
disease, computer viruses)
Spread of fashions
Spread of knowledge
Especially scale-free networks are:
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Robust to random problems/mistakes
Vulnerable to selectively targeted attacks
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“The tipping point” (Watts*)
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Consider a network in which each node determines
whether or not to adopt, based on what his direct
connections do.
Nodes have different thresholds to adopt
(randomly distributed)
Question: when do you get cascades of adoption?
Answer: two phase transitions or tipping points:
 in sparse networks no cascades
 as networks get more dense, a sudden jump in
the likelihood of cascades
 as networks get more dense, the likelihood of
cascades decreases and suddenly goes to zero
* Watts, D.J. (2002) A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences USA 99, 5766-5771
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The general approach … understand
how STRUCTURE can arise from
underlying DYNAMICS
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Scientists are trying to connect the structural
properties …
Scale-free, small-world, locally clustered, bow-tie,
hubs and authorities, communities, bipartite cores,
network motifs, highly optimized tolerance, …
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… to processes
(Erdos-Renyi) Random graphs, Exponential random
graphs, Small-world model, Preferential
attachment,
Edge copying model, Community guided
attachment,
Forest fire models, Kronecker graphs, …
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Part 2 – Trust
A journey into social psychology,
sociology and experimental economics
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Often, trust is a key ingredient of a tie
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Alliance formation
Friendship formation
Knowledge sharing
Cooperative endeavours
...
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Trust
Working definition: handing over the control of the situation
to someone else, who can in principle choose to behave in
an opportunistic way
“the lubricant of society: it is what makes interaction run
smoothly”
Example:
Robert Putnam’s
“Bowling alone”
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The Trust Game as the measurement vehicle
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Ego characteristics: trustors
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Gentle and cooperative individuals
Blood donors, charity givers, etc
Non-economists
Religious people
Males
...
Note: results differ
somewhat depending
on which kind of
trust you are
interested in.
 Effects tend to be relatively small, or at least not
systematic
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Alter characteristics: some are trusted more
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Appearance
Nationality
We tend to like individuals from some countries,
not others.
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Alter characteristics: some are trusted more
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Appearance
- we form subjective judgments easily...
- ... but they are not related to actual behavior
- we tend to trust:
+pretty faces
+average faces
+faces with characteristics similar to our own
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Alter characteristics: some are trusted more
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Nationality
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Some results on trust between countries
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There are large differences between countries:
some are trusted, some are not
There is a large degree of consensus within
countries about the extent to which they trust
other countries
Inter-country trust is symmetrical: the Dutch do
not trust Italians much, and the Italians do not
trust us much
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The effect of payoffs on behavior
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The Trust Game – general format
P
P
S
T
R
R
S<P<R<T
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Trust Games: utility transformations
P P
S T
RR
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The effect of payoffs on behavior
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Trustworthy behavior: temptation explains
behavior well
Trustful behavior: risk ((35–5)/(75–5)) explains
behavior well, temptation ((95–75)/(95–5)) does not
People are less good at choosing their behavior in
interdependent situations such as this one
Nevertheless: strong effects of the payoffs on
trustful and trustworthy behavior
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Trust shows all the signs of what is
generally called the
“disposition effect”
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Example applications to alliance networks
Take as given that firms (having to) trust each
other. Then trust research suggests, for instance:
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It is not so much that firms themselves tend to
differ "by nature" in the extent to which they trust
each other.
Dealing with overcoming opportunistic behavior
might be difficult, given that people are relatively
poor at using the other parties incentives to
predict their behavior.
Dealings between firms from countries with low
trust, need to invest more in safeguarding the
transaction.
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… and …
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Knowing how trust issues work, some kinds of
networks might be more appropriate to tackle
issues of trust
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To Do:
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Read and comprehend the papers on small world
networks, scale-free networks, and trust (see
website).
Think about applications of these results in the
area of alliance networks !!
WARNING: online survey coming up next week …
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