1. Sami Al-Suwailem
IRTI - IDB

2. Coined by Brian Arthur (1999)
Attracting more attention
Promising with great potential
Still needs more precise characterization

3. Probably the most fundamental property of Neoclassical Economics (NE)
Convexity can be viewed as an organizing principle of the comparison between NE and CE
Any combination of two points in the set belongs to the same set

4. Convexity precludes novelty by design: combinations always belong to the same set
No innovations or creativity
No learning or R&D
No entrepreneurship

5. Convexity allows only negative feedback; positive feedback is not allowed
Equilibrium, static system
No dynamics, no self-organization

6. Maximization requires convexity
Path-independence: Choice process or act of choice is ignored
No place for emotions, ethics, values, and social relations

7. NE assumes perfectly divisible commodities
Real numbers exclude Diophantine problems
But if commodities are indivisible, we cannot use real numbers
Rational numbers are non-convex
Diophantine problems are not decidable

8. Neoclassical Economics
Complexity Economics
Novelty not allowed
Negative feedback
Maximization
Path-independent
Decidable
Perpetual novelty
Negative and positive
Satisficing
Path-dependent
Undecidable

9. Institutions can be seen as factors for “convexifying” the choice set
Convexity might not be always bad!
A promising line of research

10. Self-organization—structure
Emergence—function

11. Global order via local interactions
Implies positive-feedback—excluded by convexity
Examples:
Bird flocks
Fireflies

12. “The whole is greater than the sum”
Self-organizing system is able to perform functions the sum cannot
Implies novelty—excluded by convexity

13. “Swarm Intelligence”
“Group Genius”
“Wisdom of the Crowds”

14. Both exhibit nonlinear dynamics and universality
Different nature and properties

15. Chaotic Systems
Complex Systems
Indistinguishable from random behavior
Ergodic
Non-adaptive
Basin of attraction computable
Not capable of universal computation
Path-independent
Recognizable patterns and order
Non-ergodic
Adaptive
Basin of attraction not computable
Capable of universal computation
Path-dependent

16. Fireflies, bird flocks, fish schools, …
Agents react to two sources of information:
Environment—exogenous variables
Local neighbors—endogenous variables

17. Each agent has a piece of knowledge regarding target or objective
Relative variables communicate the knowledge to neighbors
As each agent adjusts to its neighbors, the whole group synchronizes to the environment
Knowledge therefore becomes integrated

18. “The problem is thus in no way solved if we can show that all of the facts, if they were known to a single mind … would uniquely determine the solution; instead, we must show how a solution is produced by the interactions of people, each of whom possesses only partial knowledge”

19. Dispersed information zi must be consistent
An aggregator function must exist:
F need not be computable
Agents need not know F but they need to know it does exist

20. If independent variables dominate: stagnant order
If relative variables dominate: chaos
Complexity lies at the edge between order and chaos

21. Relative variables: the “self” part
Independent variables: “organization” part

22. Missing from mainstream NE
Supported by behavioral and social studies
Also by physical sciences (spin glass)
A point of departure of CE from NE
But can be a point for extending NE

23. Consumption is presented as a function of income (and wealth)
How about consumption of local neighbors?
“Social capital”
“Social multiplier”

24. As agents get different incomes, they cannot have equal consumption
How to react to “consumption gap”?
Move to different neighbors—Schelling model
Trade—labor market
Borrow—different modes of finance
Donate—philanthropic institutions

25. Simple (NE):
Complex:
How this affects economic variables?

26. NetLogo 3.1.4
1225 patches (agents); 8 neighbors
1500 periods
30 runs
Income is exogenous, uniformly distributed across agents; normally distributed across time
Gap is closed using interest-free lending

27. Surpluses are managed centrally
Deficits are financed from accumulated surpluses
Loans are extended based on available funds 27

28. Total assets = total cash + total credit
Total cash = cum (total-surplus + total-principal- payment – total-loans)
Net wealth (i) = share in total assets – debt
Share (i) = (acc. surplus) / sum (acc. surplus)
Total credit = total debt
loan-funds = loan-funds + total-surplus + total-principal-payment - total-loan ; this is a measure of cash-stock available for lending before consumption is decided. 28

29. 29

30. surplus
Loanable funds
Loans
Consumption,
wealth
deficit
Desired Consumption

31. Sum (net-wealth) = total cash Sum (shares) = 1
Income + loan – consumption – surplus – installment = 0
If there is interest or markup, then the equation for income becomes:
Income + loan + (interest or markup) – consumption – surplus – installment = 0 31

33. More efficient fund utilization
Smoother consumption
Higher wealth
More efficient fund utilization 33

34. Consumption Simple  = 0 Complex  > 0 Mean 74.5 74.3 Median 73.4
74.0
Std/Mean
0.22
0.19
Max.
127
112
No. below .5 max
354
126

35. Net-wealth Simple  = 0 Complex  > 0 Mean 1,316 1,855 Median 1,245
1,746
Std/Mean
0.55
1.02
Max.
No. below .5 max
972
1,102

36. Wealth and Debt Simple  = 0 Complex  > 0 Wealth 1,439 2,446 Debt
123
591
Net
1,316
1,855

37. Flow of Funds Simple  = 0 Complex  > 0 Acc. surplus 1,439 2,446
Acc. loans
1,838
10,534
Acc. no. of loans
940
1,112
Average loan size
1.96
9.48
Turnover
1.28
4.31

38. Relative behavior smoothes out consumption
Smoothing reduces excessive consumption, thus adding to wealth
Connectedness facilitates channeling funds to deficit agents
Higher net-worth and higher efficiency

39. Relative behavior deserves more attention
Agent-based simulation provides a rich environment for research
Extensions to investment and capital markets