Agent-Based Approach for Growing Adaptive Organizations

1. GROWING ADAPTIVE ORGANIZATIONS: An Agent-Based Computational Approach Dr. Joshua M. Epstein, The Brookings Institution and Santa Fe Institute June 2008

2. The Neoclassical Firm • Production Function Q=F(K,L) • Prices of inputs and outputs exogenously determined. • Solve the constrained -maximization problem for optimal inputs K*, L* • No Managerial Structure • Solve for inputs • We will fix the inputs and solve for a management structure…indeed, a whole history of them.

3. Different Motivating Questions • What is an Adaptive Organization? • What Would Constitute Optimal Structural Adaptation in A Dynamic Environment? • Can One “Grow” Optimally Adaptive Organizations From The Bottom-Up?

4. No Known Model That Grows Optimally Adaptive Enterprises • Large Literature (Beginning with Coase, 1937). • Few Models Grow Internal Organizational Structures From The Bottom-Up • …Much Less, Structures That Adapt • …Much Less, That Adapt Optimally in Dynamic Environments

5. Goal of the Research • Develop an Agent-Based Model in Which Enterprises Endogenously Adapt to Dynamic Environments • Given Simple Behavioral Rules. • Determine Optimal Rules and • Display the Histories of Structural Adaptation they Generate. • We’ll Encode Rule Sets in a Kind of Genome and Compute…

6. …The Optimal Genome • User sets • Goal (max profit, market share, mixes) • Time horizon • Environmental dynamic • Cost structure (wages, labor) • Model searches the entire space of genomes (cultures) and returns • The optimal one • The induced optimal history of structural adaptation (as a movie)

7. Basic Model Structure • The Environment is a Dynamic Pattern (Flux) of “Opportunities” (or Threats), Depicted as a Flow of Red Dots Moving Left to Right Toward the “Market” of the Enterprise: 32 Contiguous Cells, Depicted as a Vertical Array. The Market is Manned By • The Enterprise’s Labor Force of (at most 32)Workers, Depicted as Blue Squares, Each of Which Controls Just the Cell He Occupies. • For an Enterprise to Have No Red Penetrations; Blue Squares Would Have To Be Positioned To Intercept Every Incident Red Dot.

8. Function of Management • Workers (Blue Squares) Cannot Move Themselves. • The Task of Management (Blue Circles) is to Allocate Them Effectively. • A Level n Manager Can Shift Workers Around the 2nCells He Controls (i.e., Each L1 Controls a 2-Cell Segment; Each L2 Controls a 4-Cell Segment, and So On Up to the Very Top: e.g., the Level 5 CEO, Who Can Shift Labor Anywhere Across the Market)

9. Single Labor Allocation Rule, L. • Within The Manager’s Span of Control, He: • Identifies All Labor Not Currently Intercepting: Call That List 1 • Identifies Undefended Sites Subject to Imminent Penetration: Call That List 2 • Chooses A Random Laborer From List 1 and Moves Him to a Random Site From List 2. • Repeat until List 1 or List 2 is empty. • “Grab anybody leaning on his rake and throw him at a problem.”

10. 0 2 1 The Basic Problem Labor force of 3 is sufficient, but Level 1 Management Not Adequate to Block Cell 3 Penetration. Two Pure Approaches: [1] Hierarchy. Level 2 Management Created to Shift Free Resource Up From Cell 2 to Cell 3. [2] Trade. Level 1 Manager “Posts” Labor Demand in His Layer. Level 1 Managers with Surplus Respond

11. Penetration Thresholds • The Level-n Manager Controls a Market Segment of 2n Cells. • The Manager Re-Allocates Labor Over This Market Segment to Block Penetrations. • He Counts [Total Penetrations/ Memory]= P. • He Has Penetration Thresholds Tmin and Tmax (Tolerance for Missed Opportunities)

12. Mechanics of The Rise and Fall of Hierarchy (Trade Turned Off). • UPWARD: If P >= Tmax, Then (with prob 1-upward inertia) a Level-(n+1) Manager is Created Above Him. (Interpretations: Military, Spot Market, Promotion) • Control Passes to This Higher Level Manager (Responsible for a Segment of Width 2n+1), who Applies L. • DOWNWARD: If P <Tmin (The Threshold That Brought Him Into Play), He is Deleted (with prob 1-downward inertia) from the Structure, and Control Reverts to his Subordinates. • Currently, The Tmax of a Subordinate Equals the Tmin of his Immediate Superior. • Lowest have no min; top has no max

13. Mechanics of Internal Trade • A Manager Suffering Above-T Penetrations Can Post a Demand for Labor: D=P-T. • Managers of the Same Level May Transfer Labor if They Have a Excess Supply: S=(L-I)-(P-T). • There May Be “Horizontal” Inertia in Demand or Supply: i [0,1]. • Transaction Activities, Negotiations, Contracts, Hoarding, All Contribute to H-Inertia. • Labor Transport Costs The Same For Horizontal or Vertical

14. Trade Rules • DEMAND: If P>Tmax, then (with Prob 1 minus D-inertia), post excess D (P-Tmax) to layer. • SUPPLY: With Prob 1 minus S-inertia, transfer to the posting agent Min[His excess D, your excess S] • If Internal Trade Fails to Meet Demand, The UPWARD Hierarchy Rule is Applied and a Higher Level Manager May Be Created, as Before. • Trade is Attempted First. • Hierarchy As Failure of Internal Trade—a Kind of Market Failure

15. The Genome (Culture) Relevant Management Layers Hierarchy: Penetration Threshold t 1 2 3 4 __ Upward Inertia u 1 2 3 4 __ Downward Inertia d __ 2 3 4 5 Trade: Demand Inertia h 1 2 3 4 __ Supply Inertial 1 2 3 4 __ G={t1,t2,t3,t4,u1,u2,u3,u4,d2,d3,d4,d5,h1,h2,h3,h4,l1,l2,l3,l4}

16. Godel Number First L primes, each raised to g(i)

17. Graphics • Opportunity Flux of Red Dots • Workers are Blue Squares • Intercepts are White Dots • Penetrations are Yellow Dots • Managers With Workers in Their Span of Authority are Solid Blue Dots • Managers Controlling No Workers are Hollow Blue Dots • Corollary: Solid Managers Become Hollow When Superiors are Activated

18. Run 1. Emergence and Persistence of Hierarchy • Opportunity Flux (Attack) Concentrated in South • Firm’s Resources (Defense) Concentrated in North • Low Penetration Thresholds • Low Upward Inertia • High Downward inertia

19. The Genome for Immediate and Permanent Hierarchy 1 2 3 4 5 Hierarchy: Penetration Threshold t 0 0 0 0 __ Upward Inertia u 0 0 0 0 __ Downward Inertia d __ # # # 1 Trade: Demand Inertia h 1 1 1 1 __ Supply Inertia l 0 0 0 0 __ Relevant Management Layers G={0,0,0,0,0,0,0,0,#,#,#,1,1,1,1,1,0,0,0,0}

20. Run 2. Emergence and Dissolution of Hierarchy • Same Attack and Initial Labor Allocation as in Run 1 • All Thresholds Also As Before, Except • Low Downward Inertia

21. The Genome for Immediate but Dissolving Hierarchy 1 2 3 4 5 Hierarchy: Penetration Threshold t 0 0 0 0 __ Upward Inertia u 0 0 0 0 __ Downward Inertia d __ 0 0 0 0 Trade: Demand Inertia h 1 1 1 1 __ Supply Inertia l 0 0 0 0 __ Relevant Management Layers G={0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0}

22. Run 3: Split Attack • Separated Attacks in the North and South • Defenses Concentrated in Center • Same Genome as in Run 2 • What History of Structural Adaptation Unfolds?

23. Different (Fixed) Genomes Generate Different Adaptive Histories in Dynamic Environments

24. Observations Regarding Runs 1 –3 • Self-Organized; Bottom-Up; No Central Direction. • Each Fixed Genome (Vector of Agent Thresholds and Inertias) Generates an Entire History of Structural Adaptation to a Dynamic Environment (Same Genome in Different Environments Generates Different Histories) • Specific Agent Parameters Encode a Path of Realized Adaptations Through A Structural Repertiore. (What is “The” Firm?) • So Far, No Costs or Objective Functions, so No Ranking Possible • So Far, No Internal Trade

25. The Genome for Pure Trade 1 2 3 4 5 Hierarchy: Penetration Threshold t 0 0 0 0 __ Upward Inertia u 1 # # # __ Downward Inertia d __ # # # # Trade: Demand Inertia h 0 0 0 0 __ Supply Inertia l 0 1 1 1 __ Relevant Management Layers G={0,0,0,0,1,#,#,#,#,#,#,#,0,0,0,0,1,1,1,1}

26. Pure Trade Runs • Run 4=The Run 1 Attack Handled Through Trade With Zero H-inertia. • Run 5=The Run 3 Attack Handled Through Trade With Zero H-inertia. (Note Global Reallocations)

27. Introducing A Challenging Environmental Dynamic • Run 6: Performance of Pure Trade • Run 7: Performance of Pure Hierarchy Long range re-allocation by a decentralized series of myopic L-applications [T] vs a single centralized global L-application [H].

28. General Trade Offs • Benefit: Hierarchy Prevents Penetrations • Cost: Salaries Increase with Management Level • So There are Trade Offs • What Levels of Penetration And Hierarchy Maximize • Profit? • Market Share? • Combinations of the Two?

29. Optimal Adaptive Histories.Introducing a General Objective Function F(t) = R(t) – W(t) – T(t) – kP(t) R=Revenue=Value of Intercepts W=Wage Bill=(W· M) wi = wage at layer i=c(i+1)³ mi = number of agents in layer i T=Transaction Costs of Trade P=Penetration Cost k=0  Profit-Maximizer k=1 Market-Share Maximizer k=0.5 Hybrid

30. The Central Question • Enterprises Face Dynamic Environments • Each Fixed Genome (each 20-Vector of Thresholds and Inertias, etc) Will Generate Some History of Structural Adaptation • But, For A Given Objective Function (k-Value), What Genome Will Produce the Optimal History of Structural Adaptation? • And what does that look like?

31. Evolutionary Framing • The Unit of Selection is the Genome • Selection Pressures are • Specified Objective Function F (revenue/intercept, costs/penetration, k-value) • Specified Environmental Dynamic (Over a Specified Time horizon T) • The Genome’s Fitness is

32. More Formally… • Specify the environmental dynamic, objective function (k-value), and time horizon T. • Each G generates a history of structural adaptation and corresponding stream of net returns: F(t;G). We seek:

33. Cool Methods (Taught at SFI) • Genetic Algorithms • Simulated Annealing • Uncool Method

34. Cool Methods (Taught at SFI) • Genetic Algorithms • Simulated Annealing • Uncool Method • Cheat, by shrinking the search space • Search it by brute force…

35. Combinatorial Optimization • Sweep Parameter Space (“All” Genomes) • For Each Genome Vector, Record Cumulative Returns Over The Time Horizon (500 Periods) • For k=0.0 (Profit), 0.5, and 1.0 (Market), Return that Genome (the Vector of Parameter Values) That Maximizes the Objective Function • Apply Those Values and “Watch” The Optimal History of Structural Adaptation • First, What Do You Predict—Pure Cases First?

36. Pure Cases: Same Dynamic Environment • K=0Profit Maximization. What’s Optimal? • K=1Market Share Maximization. What’s Optimal?

37. Results • K=0Profit Maximization. Solution is Pure Trade, Substantial Penetration (Sacrifice Market Share, but Avoid Costs of Hierarchy) • K=1Market Share Maximization. Solution is Immediate Pure Hierarchy (Sacrifice Profit, but Avoid Penetrations). Explains Military • What About The Hybrid Case K=0.5? • K=0, no hierarchy • K=1, max hierarchy • K=0.5, medium hierarchy?

38. The Hybrid Case: k=0.5. Top Three Performers • Winner. Smooth Oscillatory Structures in Which Local Hierarchies of Level 4 Emerge and Dissolve With Period 10, Up and Down the Market: Travelling Wave. (Runner-Up Very Similar) • Third Place. Square Wave (On-Off) of Maximum Amplitude 5 and Period 30. (More Effective Than Winner, But More Costly)

39. What is the Winner’s “Design?” • Not a Particular Structure, Since Adaptive. • Not a Particular Sequence of Structures, Since Different Environmental Dynamics Yield Different Sequences for the Same Enterprise. • Rather…

40. “Design” Must Be… • …The Complete Adaptive Repertoire Encoded in the Enterprise’s Genome. • What is Beethoven’s Fifth?

41. Competition • Ring of firms • Penetrations of j are opportunities for (j+1). • Randomize order

42. Friedman • Divide the market? • Evolve to maximize profit?

43. Issues • Robustness. How sensitive to • Salaries/transaction costs • Cost of collapsing hierarchy • Particular dynamic? • Why so much hierarchy? • Good for global shifting in volatile env, but ubiquitous in stable settings • What if info degrades as it ascends?

44. Empirical Research • Data • Does model “fit” data? Don’t know. • Lousy model of real firms, because real firms are lousy at adapting • Lousy model because it’s lousy • Reform of systems (CDC Public Health Proposal)

45. Summary Developed an Agent-Based Model in Which Hierarchies and Internal Trading Regimes Emerge Endogenously. Generated Structural Adaptation to a Range of Dynamic Environments. Introduced Objective Functions, and for a Variety of These, Determined Optimal Genomes and Histories of StructuralAdaptation in a Particular Dynamic Environment. Variable Geometry Firm Optimized.

46. Overall Conclusion Agent-based computational modeling is an extremely powerful tool, with wide-ranging applications. We looked at: --Civil Violence --Disease Dynamics --Organizational Adaptation Please add more…and please consider me a colleague in doing so! jepstein@brookings.edu

47. Thank you

48. K-mgr Algorithm P>T_max? Y N I:T L K+1 mgr K-1 mgr P>T_max? K mgr N Y I:H P<T_min? Y N L I:T N P<T_min? Y I:H

49. Commercial Applications • Immersive Training Environment • Distance Learning (Web) • Sloan Foundation • NIH • Legacy • ModelU Consulting Service. • Gene Sequencing (What is your culture?) • Gene Therapy (What should it be?)