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Innovation in networks and alliance management

Lecture 3

Small world networks & Trust

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Course aim

knowledge about concepts in network theory, and being able to apply that knowledge

(with an emphasis on innovation and alliances)

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The setup in some more detail

Network theory and background

- Introduction: what are they, why important …- Four basic network arguments- Network properties (and a bit on trust)- Kinds of network data (collection)- Typical network concepts- Visualization and analysis

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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 weekand the trust topic today (2nd hour)

Top down (let’s have a look at many networks, and try to deduce what is happening from the observations)as in “small world networks” (now)

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What kind of structures do

empirical networks have?

(often small-world, and often also scale-free)

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3 important network properties

Average Path Length (APL) (<l>)Shortest path between two nodes i and j of a network, averaged across all nodes

Clustering coefficient (“cliquishness”)The probability that a two of my friends are friends of each other

(Shape of the) degree distributionA distribution is “scale free” when P(k), the proportion of nodes with degree k follows:

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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

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)

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 all small scale

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The small world phenomenon (cont.)

“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…

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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: 1 (A few good men)

Robert de Niro: 1 (Sleepers)

Rutger Hauer (NL): 2 [Jackie Burroughs]

Famke Janssen (NL): 2 [Donna Goodhand]

Bruce Willis: 2 [David Hayman]

Kl.M. Brandauer (AU): 2 [Robert Redford]

Arn. Schwarzenegger: 2 [Kevin Pollak]

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A search for high Kevin Bacon numbers…

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Bacon / Hauer / Connery (numbers now changed a bit)

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The best centers… (2009)

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(Kevin Bacon at place 507)(Rutger Hauer at place 48)

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“Elvis has left the building …”

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We find small average path lengths in all kinds of places…

Caenorhabditis Elegans959 cellsGenome sequenced 1998Nervous system mapped small world network

Power grid network of Western States5,000 power plants with high-voltage lines small world network

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How weird is that?

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

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[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:

A short Average Path Length and

A high clustering coefficient

… and a random network does NOT lead to these small-world properties

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Networks of the Real-world (1) Information networks:

World Wide Web: hyperlinks

Citation networks Blog networks

Social networks: people + interactions

Organizational networks Communication networks Collaboration networks Sexual networks Collaboration networks

Technological networks: Power grid Airline, road, river

networks Telephone networks Internet Autonomous systems

Florence families Karate club network

Collaboration networkFriendship network

Source: Leskovec & Faloutsos

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Networks of the Real-world (2)

Biological networks metabolic networks food web neural networks gene regulatory

networks Language networks

Semantic networks Software networks …

Yeast proteininteractions

Semantic network

Language network Software network

Source: Leskovec & Faloutsos

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Small world networks … so what?

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 hencewe 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. Consider a given network.

2. All connected actors play the repeated Prisoner’s Dilemma for some rounds

3. 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

4. Repeat 2 and 3 until a stable state is reached.

5. Conclusion: to sustain cooperation, you need a short average distance, and cliquishness (“small worlds”)

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Synchronizing fireflies …

<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 given structures)

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Strogatz and Watts

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 Wats 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?

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 problemsand related issues

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Applications to

Spread of diseases (AIDS, foot-and-mouth disease, computer viruses)

Spread of fashions Spread of knowledge

Especially scale-free networks are:

Robust to random problems/mistakes Vulnerable to selectively targeted attacks

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“The tipping point” (Watts*)

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

STRUCTURE from underlying DYNAMICS

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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

- 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 – general format

P P

S T

R R

S < P < R < T

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The Trust Game as the measurement vehicle

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Ego characteristics: trustors

Gentle and cooperative individuals Blood donors, charity givers, etc Non-economists Religious people Males ...

Effects tend to be relatively small, or at least not systematic

Note: results differ somewhat depending

on which kind of trust you are interested in.

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Alter characteristics: some are trusted more

Appearance

NationalityWe tend to like individuals from some countries, not others.

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Alter characteristics: some are trusted more

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

Nationality

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Some results on trust between countries

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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Trust Games: utility transformations

P P

S TR R

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The effect of payoffs on behavior

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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Application to alliance networks

Take as given that firms (having to) trust each other. Then trust research suggests:

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 …

Some kinds of networks might be more appropriate to tackle issues of trust

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To Do:

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 …