Social Accumulation of Knowledge

1. Discovery and Diffusion of Knowledge in an Endogenous Social NetworkMyong-Hun Chang and Joe Harrington

2. Social Accumulation of Knowledge • Essential elements of the process • Generation of Ideas by Individuals • Adoption of Ideas by Individuals • Diffusion of Ideas through Social Networks Diffusion Process Social Network

3. Generation of Knowledge • Research: process of searching for better ways of doing things (finding better solution to a problem?) • Decentralized Research  Parallel Search • How is this search carried out by an individual agent? • Innovation (individual learning) • Production of “new” ideas • Imitation (social learning) • Adoption of “existing” ideas of others ( diffusion)

4. Underlying social system: A population of autonomous agents (= problem-solvers), each endowed with a goal unknown to her ex ante • Goal: “Optimal” solution to the given problem • Goals can differ: Diversity in solution due to diversity in local environments • Goals can change: Local environments may be subject to inter-temporal fluctuations  Problems may change

5. Decision-making by individual agents • Should we model them as being hyper-rational with perfect foresight, etc.? • No. The decision environment is too complex. • Full rationality – too demanding • Boundedly rational and engage in myopic search for the unknown goal (local optimum) • Adaptive and capable of learning from past experiences • Search alone (innovation) or search by learning from others (imitation)

6. Research Questions • Individual learning versus social learning via network • How do individuals choose among the two learning mechanisms? • Network as an outcome of interactive choices among individuals as to whom to observe and whom to ignore • What are the determinants of their emergent structure? • Performance at the individual and community level • How does the reliability of communication technology affect the performance? • How does the innovativeness of the population affect the performance?

7. The Model • Social system: Lindividuals • Each individual engages in an operation with Hseparate tasks • For each task, there is a fixed number of possible methods that can be used to perform the task. • A given method is a string of d bits – 0’s and 1’s • 2d possible methods per task

8. An individual iin period t characterized by a binary vector of Hd dimensions: zi(t) • Example: H = 4 and d= 4 • Z1= 1101 0100 1111 1001 • Z2= 0101 1101 0011 1000 • Distance between two vectors • Hamming distance: D(z1, z2) • No. positions for which the corresponding bits differ  D(z1, z2) = 6 for the above vectors

9. There exists a goal vector (binary) of Hddimensions for each agent in t: gi(t) • Unique optimal solution to the problem agent i is facing • Inter-agent diversity • It is possible that gi(t)≠ gj(t) for i ≠ j. • Inter-temporal variability • It is possible that gi(t)≠ gi(t’) for t ≠ t’. • Individuals uninformed about gi(t)ex ante, but engage in “search” to get as close to it as possible.

10. g2(t) g1(t) D(z1(t), g1(t)) g4(t) g3(t) z1(t) D(z4(t), g4(t)) D(z3(t), g3(t)) z4(t) D(z2(t), g2(t)) z3(t) z2(t)

11. Period-t performance of agent i • How close is agent i to his current optimum? • πi(t) = Hd–D(zi(t), gi(t)) • Period-t performance of the social system • Sum of all agent’s performances.

12. Decision-Making Sequence (in t) for an Agent μiin Innovate Choose to Innovate qi(t) 1 - μiin Idle Observe j = 1 pi1(t) i Observe j = 2 pi2(t) Observe j = 3 Observe μiim pij(t) 1 - qi(t) Choose to Imitate Observe j ≠ i piL(t) Observe j = L 1 - μiim Idle

13. If fail to generate an idea or fail to connect to the network, zi(t+1) = zi(t). • Otherwise, there exists an idea, zi’(t), proposed under innovation or imitation such that zi’(t) is adopted iff it gets i closer to gi(t). • Innovation: Randomly chosen method for a randomly chosen task Z1= 1101 0100 1111 1001 Z’1= 1101 0100 1011 1001 • Imitation: Method used by another agent for a randomly chosen task Z1= 1101 0100 1111 1001 Z2= 0101 1101 0011 1000 Z’1= 1101 0100 0011 1001

14. Evolving Choices • Exogenous Probabilities: (μiin, μiim) • Endogenous Probabilities: (qi(t), {pij(t)}j≠i) • (qi(t), {pij(t)}j≠i) evolve via reinforcement learning • A positive outcome realized from a course of action reinforces the likelihood of that same action being chosen again [Experience-Weighted Attraction Learning – Camerer & Ho, Econometrica, 1999]

15. Evolving qi(t) • Attractions for the available courses of action • Biin(t): i’s attraction measure for innovation • Biim(t): i’s attraction measure for imitation • Evolution of the attractions • Biin(t+1)= Biin(t) + 1, if innovation successful in tBiin(t+1)= Biin(t), otherwise • Biim(t+1)= Biim(t) + 1, if imitation successful in tBiim(t+1)= Biim(t), otherwise

16. Biin(t) qi(t) = Biin(t) + Biim(t) Biim(t) 1 - qi(t) = Biin(t) + Biim(t)

17. Evolving pi j(t) • pi j(t): Probability with which i observes j in t • ∑j≠ipi j(t) = 1 for all i • Aij(t): agent i’s attraction to another agent j • Evolution of the attractions • Aij(t+1) = Aij(t) + 1, if i successfully imitated j in tAij(t+1) = Aij(t), otherwisefor all j ≠ i and for all i.

18. Aij(t) pij(t) = ∑i≠jAij(t) for all j ≠ i and for all i.

19. social network of agent i {pij(t)}j≠i

20. Agents with Uniform Learning Capabilities • μiin = μin for all i (innovativeness) • μiim = μim for all i (reliability of the network) • Improved productivity in innovation: a rise in μin • Improved communication: a rise in μim

21. Initial Conditions at t = 0 • All agents have equal probabilities of innovation vs. imitation: qi(0) = 1- qi(0) = .5 for all i • All agents have equal probabilities of observing all other agents in the population: pij(t) = 1/(L-1) for all j≠i, for all i

22. Goals, Groups, and Networks • Similarity or diversity in the objectives drive the formation of networks • Partition the population into a fixed number of groups • Agents belonging to the same group tend to have more similar goals – i.e., working on similar problems – than those belonging to different groups. • Two sources for social learning • Another agent in the same group • Another agent in a different group • Efficacy of social learning dependent on the tightness of goals within a given group relative to the tightness of the goals between different groups.

23. How are the goals specified?

25. Goal Diversity • Intra-group diversity: κ • Inter-group diversity: X

26. Shift Dynamics for the Goals • gi(t) stays the same with probability σ and changes with probability (1-σ). • If gi(t+1) is different from gi(t), it is chosen from the set of points that lie both within the Hamming distance ρ of gi(t) and within Hamming distance κ of the original group seed vector gk.

27. Parameters – {σ, ρ, κ, X} • σ • The greater is σ, the more stable is an agent’s goal vector. • ρ • The greater is ρ, the more variable is the change in an agent’s goal vector. • κ • The higher is κ, the lower is the intra-group goal congruence. • X • The higher is X, the greater is the inter-group goal diversity.

28. Specs for Computational Experiments • 20 agents • 4 groups • 24 tasks, each with 4 bits • 16 methods in each task • Search space contains over 7.9 x 1028 possibilities • Biin(0)=Biim(0)=1 for all i • Aij(0)=1 for all i and all j ≠i • Horizon: 20,000 periods

29. Baseline Parameter Values • μim = μin = 0.5 • σ = 0.75 • ρ = 4 • κ = 16 • X = 16

30. Performance Time Series (Baseline)

31. Steady-State Values of Endogenous Variables • Average over the 5,000 periods from t=15,001 to t=20,000 • Let’s look at the learning patterns: pi j(t) • Do agents choose their learning partners randomly? • Or do they learn from a small subset of other agents? • Do agents go to those who also come to them? • MUTUAL LEARNING? Are pi j(t) and pji(t) correlated?

32. pi j(t) and pji(t)

33. Mutuality in Learning • Correlation positive for all parameter values • Correlation increases in X • The greater the inter-group diversity in goals  The stronger the mutuality in learning • Correlation decreases in κ • The lower the intra-group diversity  The stronger the mutuality in learning

34. Okay, but who is learning from whom? What drives the tendency for mutual learning? Can we be more specific? How about tracking the evolution of the imitation probabilities? - Very complex. 20 agents, each with probabilities of observing 19 other agents in each period (380 probabilities per period over the horizon of 20,000 periods).

35. Visualization of pij(t)s 20 13 i (observer) 9 1 1 9 18 20 j (observed)

36. Four groups • Group 1 = {1, 2, 3, 4, 5} • Group 2 = {6, 7, 8, 9, 10} • Group 3 = {11, 12, 13, 14, 15} • Group 4 = {16, 17, 18, 19, 20} • At t=0, everyone observes everyone else with an equal probability.

37. Steady-state pij(t)s averaged over 20 replications

38. Learning is mutual and more active among agents sharing similar goals. • Intra-group mutual learning is more intensive when the groups are more segregated and isolated from one another.

39. What about the aggregate performance of the social system? How is it affected by various parameters?

40. Comparative Dynamics • How is performance influenced by • Reliability of the communication technology supporting the network – μim? • Productivity of agents engaging in innovation – μin? • How is the above relationship affected by features of the environment? • Turbulence in the task environments – σ and ρ • Inter-agent goal diversity – X and κ • Focus on steady-state (t=15,000 to t=20,000) – Long run properties of the system

41. σ = 0.75; ρ = 4; κ = 16; X = 16 The rate of innovation declines in μim

42. σ = 0.75; ρ = 4; κ = 16; X = 16 Performance of the social system rises in μim

43. Is this universal? • Does the steady-state performance always rise in the reliability of communication technology? • Try: • Lower μin to .25 • Agents less productive at innovation • Lower κ to 4 • Degree of intra-group goal congruence higher

44. μin = .25σ = 0.75; ρ = 4; κ = 4; X = 16

45. An improvement in communication technology can lead to a deterioration in performance. • Is this a general property? Do we observe this for different parameter configurations? • YES

46. Property 1 • When the reliability of the network is sufficiently low, steady-state performance is increasing in reliability. • When the reliability of the network is sufficiently high AND- task environment is sufficiently volatile (σ low, ρ high)- goal diversity among groups is sufficiently great (X high)- intra-group goal diversity is sufficiently low (κ low)performance decreases in reliability.

47. More reliable network (higher μim) Imitation substituted for innovation Faster diffusion of ideas Formation of more structured network Agents in a network (and in a group) become more alike (homogenization of the networks) LACK OF DIVERSITYIN THE SYSTEM!!!

48. More stable environment • Lack of diversity is not a problem • Faster social learning is more critical (speeding up convergence to local optima) • Volatile environment • Agents must modify their tasks continually to solve new problems. • As network becomes more reliable, imitation crowds out innovation and the ensuing lack of diversity makes it less likely that there will be useful ideas that serve the new environment.

49. What about the role of inter-group diversity (X)? • Low X  the optima of agents from different groups overlap to a greater extent  social learning is more global (agents observe other agents in different groups more frequently)  inter-agent diversity survives over time  superior adaptability to changing environment

50. Summary • Simple improvement in the reliability of the network may harm long-run performance. • Enhanced communication technology can induce too much imitation  Loss of diversity in responding to future environments • An individual’s capacity to carry on independent innovation is crucial in supplying the necessary fuel for the effective operation of the social network.