1. Universiteit Utrecht QMSS seminar Groningen September 15, 2006 Social Context and Network Formation: Experimental Studies Martijn Burger Erasmus University Rotterdam Vincent Buskens Utrecht University

2. QMSS seminar Groningen September 15, 2006 2

3. 3 Research Questions What do specific arguments about the value of network positions imply for emergence of networks in a dynamic model? If contexts differ in how networks matter, what does this imply for the networks we expect to emerge? Can we experimentally show whether we can predict emerging network structures if we know the value of specific network positions?

4. Brokerage as Social CapitalClosure as Social Capital Static Value of non-redundant informationValue of redundant information Control through regulating the flow of information Control through sanctioning and amplification of existing opinion Center in a star-shaped structureDense local structure ‘Strength of weak ties’‘Strength of strong ties’ Dynamic Striving for non-redundant ties, brokerage positions, and open triads Striving for redundant ties and closed triads Preferring ties with unconnected alters Preferring ties with connected alters Social Context Competitive and entrepreneurial settings Cooperative and collaborative settings Acquisition of private goodsProduction of collective goods

5. QMSS seminar Groningen September 15, 2006 5 The Macro-Micro-Macro link The context determines which network positions are beneficial (Pairs of) individuals make decisions on who wants a relations with whom These interdependent decisions about relations determine which networks will emerge

6. QMSS seminar Groningen September 15, 2006 6 Three Contexts Actors have benefits of ties Actors have increasing marginal costs of ties Actors might have costs or benefits of closed triads Burt network formation context: Closed triads are costly Coleman network formation context: Closed triads are beneficial Neutral network formation context: Closed triads do not matter

7. QMSS seminar Groningen September 15, 2006 7 Utility Functions Burt Network Formation Context Coleman Network Formation Context Neutral Network Formation Context

8. QMSS seminar Groningen September 15, 2006 8 Stability Condition Pairwise stability No actor can increase his utility by removing a tie No actor can increase his utility by adding a tie without decreasing the utility of the actor he is adding a tie with OR No actor wants to remove a tie No pair of actors wants to add a tie

9. QMSS seminar Groningen September 15, 2006 9 Simulating Individual Decisions Start from an empty network Choose a random actor With probability ‘noise’, this actor changes a random tie With probability 1−`noise’, this actor changes the tie that gives him the largest improvement in terms of network position (or does nothing if no improvement is possible) We continue to choose actors until the network is pairwise stable

10. QMSS seminar Groningen September 15, 2006 10 Simulation Design ConditionValues Starting networkEmpty network Size of the network6 (156 different structures) Network formation contextBurt, Coleman, Neutral Linear Costs0.20 Quadratic Costs (max. number of ties actors want) 0.10 (4), 0.20 (2) Costs and benefits of closed triads0.20 Noise0.10, 0.40, and 0.70 Repetitions200

11. Stable Networks under High Quadratic Costs Square and Dyad (Burt, Neutral) Two triangles (Coleman, Neutral) Full pentagon and isolate (Coleman) Pentagon and Isolate (Burt, Neutral, Coleman) Hexagon (Burt, Neutral, Coleman) Full square and dyad (Coleman)

12. Stable Networks under Low Quadratic Costs 3,3-complete bipartite (Burt) 3-prism (Burt) 2,4-complete bipartite (Burt) Full hexagon (Coleman) Full pentagon and isolate (Coleman, Neutral) Single-crossed 3-prism (Neutral) Octahedron (Neutral) Tailed full pentagon (Neutral)

13. QMSS seminar Groningen September 15, 2006 13 Probability of Convergence by Noise Level for Low Costs Neutral contextNoise=.1Noise=.4Noise=.7 Two triangles 0.1650.1400.125 Square and dyad 0.1900.1100.130 Pentagon and isolate 0.2150.1900.205 Hexagon 0.4300.5600.540 Burt context Square and dyad 0.1900.1600.205 Pentagon and isolate 0.2250.2050.235 Hexagon 0.5850.6350.560 Coleman Context Full pentagon and isolate 0.000 0.005 Full square and dyad 0.0350.1050.190 Two triangles 0.6450.5950.465 Hexagon 0.1700.1950.260 Pentagon and Isolate 0.1500.1050.080

14. QMSS seminar Groningen September 15, 2006 14 Probability of Convergence by Noise Level for High Costs Noise=.1Noise=.4Noise=.7 Neutral Context Tailed full pentagon 0.2250.2200.345 Single-crossed 3-prism 0.4250.4000.295 Octahedron 0.2150.3400.345 Full pentagon and isolate 0.1350.0400.015 Burt Context 2,4-complete bipartite 0.1400.070 3,3-complete bipartite 0.7350.6200.495 3-prism 0.1250.3100.435 Coleman Context Full hexagon 0.7200.8600.875 Full pentagon and isolate 0.2800.1400.125

15. QMSS seminar Groningen September 15, 2006 15 Hypotheses Predicted mean network characteristics on basis of predicted pairwise stable networks: Density Proportion of full triads Centralization Segmentation Rank order of network formation contexts based on these predictions and determined by means of Wald test

16. QMSS seminar Groningen September 15, 2006 16 Network measures IndicatorDescription DensityThe proportion of in the network Full triadsThe proportion of full triads CentralizationThe standard deviation of the proportion of ties each actor has. The measure is standardized, such that all values are between 0 (min.) and 1 (max.) for networks with six actors SegmentationThe proportion of dyads with at least distance 3 of all dyads that have at least distance 2. We chose the maximal value 1 for disconnected networks and -1 for complete networks.

17. Predictions: Differences across Contexts DensityProportion of full triads CentralizationSegmentation Low costs1) Coleman 2) Neutral 3) Burt 1) Coleman 2) Neutral 3) Burt 1) Neutral 2) Coleman 3) Burt 1) Burt, Neutral 2) Coleman High cost1) Coleman 2) Neutral, Burt 1) Coleman 2) Neutral, Burt No rank order1) Coleman 2) Neutral, Burt 1= highest (e.g., highest expected density), 3=lowest (e.g., lowest expected density)

18. QMSS seminar Groningen September 15, 2006 18 Experiment Predictions were tested by means of a computerized laboratory experiment Equipment: Z-Tree (Fishbacher, 1999) ORSEE recruitment system (Greiner, 2004) ELSE laboratory We vary quadratic costs (2 levels), context (3 versions)

19. QMSS seminar Groningen September 15, 2006 19 Experiment: General Set-Up 18 participants in each session, total 108 subjects in 6 session Participants had to interact in all three network formation contexts under one of the two costs functions Two costs functions and order of network formation contexts varied across sessions Every participant was match anonymously with five other participants three times for each condition Every condition is repeated nine times within sessions and three times between sessions.

20. QMSS seminar Groningen September 15, 2006 20 Experiment: “The Game” 10 periods of 30 seconds each Everybody could click on others in the group to indicate that they want a link If the other also clicked, a tie was formed All clicks were shown instantly to all others in the group After every 30 second period, subjects obtained a number of points corresponding to their network position Maximum possible payoff: €16.80, maximum earned: €15.80, minimum earned: €10.80, average earned: €14.20

22. QMSS seminar Groningen September 15, 2006 22 Data Analysis Network dynamics for 27 networks in each of the 6 conditions We consider a network converged to a stable structure if the same configuration chosen in three consecutive periods Analysis: Comparison rank orders Testing point-predictions of network characteristics (one-sample z-test)

23. QMSS seminar Groningen September 15, 2006 23 General Results Proportion ‘Stable’ Networks Proportion ‘Stable’ Networks that are also Pairwise Stable Low Costs Neutral.815 (22 of 27)1.000 (22 of 22) Burt.519 (14 of 27)1.000 (14 of 14) Coleman.926 (25 of 27).600 (15 of 25) High Costs Neutral.963 (26 of 27)1.000 (26 of 26) Burt.815 (22 of 27).864 (19 of 22) Coleman.778 (21 of 27).857 (18 of 21) Overall.802 (130 of 162).877 (114 of 130)

24. Predicted Rank OrderObserved Rank Order Confirmation Hypotheses? Low Costs Density1) Coleman 2) Neutral 3) Burt Yes Proportion of Full Triads 1) Coleman 2) Neutral 3) Burt Yes Centralization1) Neutral 2) Coleman 3) Burt1) Coleman, Neutral 2) Burt*? Segmentation1) Burt, Neutral 2) Coleman Yes High Costs Density1) Coleman 2) Neutral, BurtNo rank order? Proportion of Full Triads 1) Coleman 2) Neutral, Burt Yes CentralizationNo rank order1) Coleman 2) Burt**, Neutral? Segmentation1) Coleman 2) Burt, Neutral Yes Testing rank orders of network measures

25. QMSS seminar Groningen September 15, 2006 25 Rank Orders across Contexts Most of our hypotheses confirmed. Limited confirmation where also theoretical differences are small Burt networks: relatively sparse networks, low amount of full triads, highly decentralized Coleman networks: dense networks, high amount of full triads, tend to segment when the costs of ties are becoming too high Hence, emerging networks to a large extent contingent on social context in which they are embedded

26. Proportion of full triadsSegmentation Low CostsEM (SD) OM (SD) z-testEM (SD) OM (SD) z-test Neutral.362 (.047).395 (.034) 3.29*.040 (.196).045 (.213) 0.12 Burt.031 (.046).000 (.000) -2.52*.000 (.000).000 (.000) 0.00 Coleman.930 (.174).906 (.126) -0.69-.720 (.696) -.600 (.500) 0.86 High Costs Neutral.014 (.035).012 (.033) -0.29.627 (.332).428 (.230) -3.06* Burt.000 (.000).000 (.000) 0.00.577 (.322).328 (.042) -3.63* Coleman.081 (.061).114 (.036) 2.48*.870 (.265).972 (.086) 1.76 Testing Point-Predictions

27. QMSS seminar Groningen September 15, 2006 27 Observed vs. predicted scores Observed scores are often close to the predicted ones, but often do not exactly match Discrepancy due the fact that for each condition one stable structure seems even more dominant than predicted Learning effects Inequality adverseness

28. QMSS seminar Groningen September 15, 2006 28 Conclusion and discussion Adaptive model in combination with the stability criterion seems to predict behavior reasonably well Empirically stable networks are very often the theoretically stable networks Main structural differences in network characteristics emerge as predicted Precise likelihood of different stable networks more difficult to predict. Possible additions: Stricter stability concepts Additional selection arguments: inequality aversion Some limitations All actors are the same No hybrid utility functions