1. Statistical Challenges in Agent-Based Computational Modeling László Gulyás (lgulyas@aitia.ai)lgulyas@aitia.ai AITIA International Inc & Lorand Eötvös University, Budapest

2. Gulyás László2 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

3. Gulyás László3 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

4. Gulyás László4 On Agent-Based Modeling (ABM) Main Properties Bottom-Up Individuals with their idiosyncrasies, With their imperfections (e.g., cognitive or computational limitations) Heterogeneous Populations Dynamic Populations Explicit Modeling of Interaction Topologies Examples Santa Fe Institute Artificial Stock Market Discrete Choices on Networks (Social Influence Modeling)

5. Gulyás László5 Praise of ABM Attempt to Create Micro-Macro Links “Micromotives and Macrobehavior” Generative Modeling Approach Realistic Microstructures Explicit Representation of Agents Realistic Computational Abilities Modeling of the Information Flow Tool for Non-Equilibrium Behavior Ability to Study Trajectories

6. Gulyás László6 Critique of ABM (Mis)Uses of Computer Simulation Prediction…………………………(Weather) “Simulation”……………………..(Wright Bros) Thought Experiments /………(Evol of Coop.) Existence Proofs Computational (In)Efficiency Questionable Results / Foundations?

7. Gulyás László7 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

8. Gulyás László8 Example I. The Santa Fe Institute Artificial Stock Market (SFI ASM) ( Arthur et al., 1994, 1997)

9. Gulyás László9 The Santa Fe Institute Artificial Stock Market (1/3) A minimalist model of two assets: “Money”: fixed, risk-free, infinite supply, fixed interest. “Stock”: unknown, risky behavior, finite supply, varying dividend. Artificial traders Developing (learning) trading strategies. In an attempt to maximize their wealth.

10. Gulyás László10 The Santa Fe Institute Artificial Stock Market (2/3) Trading rules of the agents Actions (buy, sell, hold) based on market indicators: Fundamental and Technical Indicators Price > Fundamental Value, or Price < 100-period Moving Average, etc. Reinforced if their ‘advice’ would have yielded profit. A classifier system. A Genetic algorithm Activated in random intervals (individually for each agent). Replaces 10-20% of weakest the rules.

11. Gulyás László11 The Santa Fe Institute Artificial Stock Market (3/3) Two behavioral regimes (depending on learning speed). One (Fundamental Trading) – Theory Consistent with Rational Expectations Equilibrium. Price follows fundamental value of stock. Trading volume is low. Two (Technical/Chartist Trading) – Practice “Chaotic” market behavior. “Bubbles” and “crashes”: price oscillates around FV. Trading volume shows wild oscillations. “In accordance” with actual market behavior.

12. Gulyás László12 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

13. Gulyás László13 ABMs as Stochastic Processes Not modeled processes are typically represented by stochastic elements. ABMs are implemented as Discrete Time Discrete Event simulations.  Markov Processes Often with enormous state-spaces…

14. Gulyás László14 ABM Methodology (101) High dimensionality of the parameter space.  Only sampling is possible.  Establishing results’ independence from pseudo-random number sequences.  Sensitivity analysis, wrt. Parameters Pseudo-Random Number Sequences

15. Gulyás László15 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

16. Gulyás László16 Verification & Validation Challenges The Challenge of ‘Dimension Collapse’ ANTs (John H. Miller) QosCosGrid EMIL Empirical Fitting Micro- and Macro-Level Data Network Data Estimation Problems (Endogeneity)

17. Gulyás László17 Verification & Validation Directions I. Networks Research on Network Data Collection Abstract Network Classes Empirically Grounded Abstract Networks

18. Gulyás László18 Example II. Socio-Dynamic Discrete Choices on Networks in Space (Dugundji & Gulyas, 2002-2006)

20. Gulyás László20 Starting Point Discrete Choice Theory allows prediction based on computed individual choice probabilities for heterogeneous agents’ evaluation of discrete alternatives. Individual choice probabilities are aggregated for policy forecasting.

21. Gulyás László21 Industry Standard in Land Use Transportation Planning Models Ground-breaking work: Ben-Akiva (1973); Lerman (1977) Some operational models: Wegener (1998, IRPUD – Dortmund) Anas (1999, MetroSim – New York City) Hensher (2001, TRESIS – Sydney) Waddell (2002, UrbanSim – Salt Lake City)

22. Gulyás László22 Interdependence of Decision-Makers’ Choices Discrete Choice Theory is fundamentally grounded in individual choice, however... Global versus local versus random interactions Interaction through complex networks Network evolution Problem domain: residential choice behavior and multi-modal transportation planning Social networks, transportation land use networks

23. Gulyás László23 Discrete Choice Model Population of N decision-making agents indexed (1,...,n,...,N) Each agent is faced with a single choice among mutually exclusive elemental alternatives i in the composite choice set C = {C 1,...,C M } For sake of simplicity, we assume that the (composite) choice set does not vary in size or content across agents.

24. Gulyás László24 Nested Logit Models  12...m...M n  Lm 12... J C 1 12... J Cm 12... J C M

25. Gulyás László25 Nested Logit, cont’d. Let U in =V in +  in  be the utility that a given agent n is presumed to associate with a particular alternative i, where V in is the “systematic” utility and  in is an error term Similarly, let U mn =V mn +  mn  be the utility that a given agent n is presumed to associate with a particular choice subset C m Under the assumption of Gumbel distributed disturbances  with scale parameters , the joint probability P n (i,m) that agent n chooses alternative i in subset C m is given as follows:

26. Gulyás László26 Nested Logit, cont’d.

27. Gulyás László27 We introduce (social) network dynamics by allowing the systematic utilities V in and V mn to be linear-in-parameter  first order functions of the proportions x in and x mn of a given decision-maker’s “reference entity” agents making these choices Interaction Effects

28. Gulyás László28 Empirical Dilemma In practice … It can be difficult to reveal the exact details of the relevant network(s) of reference entities influencing the choice of each decision-maker The actual reference entities for a given decision-maker may not be among those in the data sample One solution: studying abstract network classes with an aim towards mathematical understanding of the properties of the model.

29. Gulyás László29 Computational Model in RePast Example time series for 100 agents with f(x) = x for (a) low certainty and (b), (c) high certainty with two distinct random seeds

30. Gulyás László30 Results (Random / Erdős-Rényi network)

31. Gulyás László31 Results (Watts-Strogatz network)

32. Empirical Application Socio-Geographic Network

33. Gulyás László33 Overview of the Data Geographical location is given in terms of the centroid of a traffic analysis zone (TAZ) 381 TAZ centroids in Amsterdam (nr.s 1-381) 48 TAZ centroids in Amstelveen (nr.s 414-461) The data is organized by trip (5368 direct home- work or work-home trips), and grouped by: respondent (2925 respondents who have made these trips) household (2328 households with a respondent who made such a trip) address (2321 addresses where there is a household with a respondent who made such a trip)

34. Gulyás László34 Visualization of Semi-Abstract Socio-Geographic Network

35. Gulyás László35 Socio-Geographic Network  =1.9284,  L =2.5062, Seed 1

36. Gulyás László36 Socio-Geographic Network  =1.9075,  L =1, Seed 2

37. Gulyás László37 Challenge in Estimation Endogeneity!

38. Gulyás László38 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

39. Gulyás László39 Verification & Validation Directions II. Experimental Validation Participatory Simulation The case of the SFI-ASM

40. Gulyás László40 Example III. The Participatory SFI-ASM (Gulyás, Adamcsek and Kiss, 2003, 2004.) Can agents adapt to external trading strategies, just as well as they did to those developed by fellow agents?

41. Gulyás László41 Humans Increase Market Volatility The presence of human traders increased market volatility. The higher percentage of the population was human, the higher the difference was w.r.t. the performance of the fully computational population.

42. Gulyás László42 Participants Learn Fundamental Trading First set of Experiments: Humans initially applied technical trading, but gradually discovered fundamental strategies. The winning human’s strategy was: Buy if price < FV, sell otherwise.

43. Gulyás László43 Artificial Chartist Agents Second set of Experiments: We introduced artificial chartist (technical) agents. Base experiments show: Chartist agents normally increase market volatility. That is, humans are subjected to extreme bubbles and crashes.

44. Gulyás László44 Participants Learn Technical Trading Subjects received a bias towards fundamental indicators. Still, they reported gradually switching for technical strategies after confronting with the ‘chartist’ market.

45. Gulyás László45 Participants Moderate Market Deviations However, chartist human subjects actually modulated the market’s volatility. The market actually show REE-like behavior. The absolute winner’s strategy in this case was a pure technical rule.

46. Gulyás László46 Hypothesis The learning rate again. The participants may have adapted quicker. The effect of human ‘impatience’. Cf. ‘Black Monday’ due to programmed trading. An apparent lesson: learning agents may do no better.

47. Gulyás László47 Overview On Agent-Based Modeling (ABM) Properties, Praise & Critique Example ABMs as Stochastic Processes Source of Randomness Basic ABM Methodology Verification & Validation Challenges & Directions Networks Example Experimental Validation Example Conclusions

48. Gulyás László48 Conclusions A methodology attempting the micro- macro link: ABM. Methodological challenges of ABM Mainly in empirical validation. Some in parameter space sampling. Two new directions discussed Empirical estimation based on semi-abstract networks. Participatory experiments.