Innovation in networks and alliance management Small world networks & Trust

1. Innovationin networksandalliance managementSmall worldnetworks & Trust

2. Course aim knowledge about concepts in network theory, and being able to apply that knowledge

3. The setup in some more detail Network theory and background • Introduction: what are they, why important … • Four basic network arguments • Kinds of network data (collection) • Network properties (and a bit on trust) • Business networks

4. Two approaches to network theory • 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 (2ndhour, 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)

5. What kind of structures do empirical networks have?(answer: 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 (pairs of) nodes • Clustering coefficient (“cliquishness”) The probability that 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 this formula, for some value of gamma:

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 urbanmyth? • Milgramusedonly part of the data, actuallymainly the onessupporting his claim • Many packages didnot end up at the Boston address • Follow up studies typicallysmall 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 Canbeplayed at: http://oracleofbacon.org Kevin Bacon number (data might have changedbynow) Jack Nicholson: 1 (A few good men) Robert de Niro: 1 (Sleepers) Rutger Hauer (NL): 2 [Nick Stahl] Famke Janssen (NL): 2 [Nick Stahl] Bruce Willis: 2 [Patrick Michael Strange] 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… (2011) (Kevin Bacon at place 444) (RutgerHauer at place 43, J.Krabbé 867)

18. “Elvis has left the building …”

19. We find small average path lengths in all kinds of places… • CaenorhabditisElegans 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

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. And if we consider all three…

29. … then we find this: Wang & Chen (2003) Complex networks: Small-world, Scale-free and beyond

30. 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)

31. Examples of interestingproperties of small world networks

32. 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”)

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

34. 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)

35. 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 Watts asked: what happens along the way with APL and Clustering?

36. 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

37. And now the third characteristic

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

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

40. 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

41. (more) open problemsand related issues

42. 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

43. “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

44. The general approach … understandhow STRUCTURE can arise 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, …

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

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

47. 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”

48. The Trust Game as the measurement vehicle

49. 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

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