Innovation in networks and alliance management Lecture 3 Small world networks & Trust

1. Innovation in networks and alliance managementLecture 3Small world networks & Trust

2. Course aim knowledge about concepts in network theory, and being able to apply that knowledge (with an emphasis on innovation and alliances)

3. 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

4. Two approaches to network theory • Bottom up (let’s try to understand network characteristics and arguments) as in … “Four network arguments” last week and 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)

5. What kind of structures do empirical networks have?(often small-world, and often also scale-free)

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

7. Example 1 - Small world networks NOTE • Edge of network theory • Not fully understood yet … • … but interesting findings

8. 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”

9. 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

10. 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.

11. Ongoing Milgram follow-ups… 6.6!

12. 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)

13. 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”

14. 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]

15. A search for high Kevin Bacon numbers… 3 2

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

17. The best centers… (2009) (Kevin Bacon at place 507) (Rutger Hauer at place 48)

18. “Elvis has left the building …”

19. We find small average path lengths in all kinds of places… • Caenorhabditis Elegans 959 cells Genome sequenced 1998 Nervous system mapped  small world network • Power grid network of Western States 5,000 power plants with high-voltage lines  small world network

20. 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.

21. APL is small in random networks [Slide copied from Jari_Chennai2010.pdf]

22. [Slide copied from Jari_Chennai2010.pdf]

23. But let’s move on to the second network characteristic …

25. 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

26. 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 Source: Leskovec & Faloutsos Networks of the Real-world (1) Florence families Karate club network Collaboration network Friendship network

27. Biological networks metabolic networks food web neural networks gene regulatory networks Language networks Semantic networks Software networks … Source: Leskovec & Faloutsos Networks of the Real-world (2) Semantic network Yeast protein interactions Language network Software network

28. 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 hence we might want to create them)

29. Examples of interestingproperties of small world networks

30. Combining game theory and networks – Axelrod (1980), Watts & Strogatz (1998?) • 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”)

31. Synchronizing fireflies … • <go to NetLogo> • Synchronization speed depends on small-world properties of the network  Network characteristics important for “integrating local nodes”

32. If small-world networks are so interesting and we see them everywhere, how do they arise?(potential answer: through random rewiring of given structures)

33. 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?

34. 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

35. And now the third characteristic

36. Same thing … we see “scale-freeness” all over

37. … and it can’t be based on an ER-network

38. 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

39. (more) open problemsand related issues

40. 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

41. “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

42. The general approach … understandSTRUCTURE from underlying DYNAMICS • 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, … • … 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, …

43. Part 2 – Trust A journey into social psychology, sociology and experimental economics

44. Often, trust is a key ingredient of a tie • Alliance formation • Friendship formation • Knowledge sharing • Cooperative endeavours • ... Trust

45. 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”

46. P P S T R R The Trust Game – general format S < P < R < T

47. The Trust Game as the measurement vehicle

48. Ego characteristics: trustors Note: results differ somewhat depending on which kind of trust you are interested in. • 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

49. Alter characteristics: some are trusted more • Appearance • Nationality We tend to like individuals from some countries, not others.

50. 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