pith. machine review for the scientific record. sign in

arxiv: 2604.04543 · v1 · submitted 2026-04-06 · 💻 cs.MA · cs.LO

Recognition: no theorem link

Statistical Model Checking of the Island Model: An Established Economic Agent-Based Model of Endogenous Growth

Andrea Vandin (Institute of Economics, Daniele Giachini (Institute of Economics, Ernest Ivanaj (Swiss Finance Institute, Giorgio Fagiolo (Institute of Economics, L'EMbeDS, Sant'Anna School of Advanced Studies), Stefano Blando (Institute of Economics, University of Geneve)

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:49 UTC · model grok-4.3

classification 💻 cs.MA cs.LO
keywords agent-based modelsstatistical model checkingendogenous growthIsland Modelsensitivity analysisexploration-exploitationeconomic simulationWelch t-test
0
0 comments X

The pith

Statistical model checking supplies formal confidence intervals and sensitivity tests for the Island Model of endogenous growth.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how statistical model checking automates the analysis of an established agent-based model that links technological search to economic growth. It reproduces the original stylized facts about exploration versus exploitation with formal statistical bounds rather than informal Monte Carlo runs. The same framework then tests whether moderate exploration rates remain optimal and how growth trajectories shift when returns to scale, skill transfer, or knowledge locality change. A reader would care because this replaces ad-hoc simulation summaries with reproducible, statistically grounded claims about model behavior.

Core claim

Applying Multi-VeStA statistical model checking to the Island Model reproduces its key stylized facts with confidence intervals, confirms that moderate exploration rates maximize growth, and performs a sensitivity analysis on returns to scale, skill transfer, and knowledge locality. Six of seven pairwise parameter comparisons produce statistically distinct growth trajectories under Welch's t-test, while the seventh reveals a saturation effect once knowledge locality reaches a threshold.

What carries the argument

Multi-VeStA statistical model checker applied to the Island Model's agent-based exploration-exploitation dynamics.

If this is right

  • Moderate exploration rates remain the growth-maximizing choice across the tested parameter space.
  • Most parameter alterations produce growth trajectories that are statistically distinguishable from one another.
  • Knowledge locality stops affecting outcomes once a saturation threshold is crossed.
  • Statistical model checking supplies a reproducible pipeline for quantitative claims about agent-based economic models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same checking approach could be applied to other established agent-based models to strengthen or revise their qualitative conclusions.
  • Policy experiments run inside such models could carry explicit statistical statements about robustness rather than point estimates alone.
  • Saturation effects identified in one parameter might prompt targeted experiments on whether similar thresholds exist in related dimensions such as skill transfer.

Load-bearing premise

The reimplementation of the Island Model inside the statistical model checking tool exactly matches the original Fagiolo-Dosi dynamics without introducing new artifacts.

What would settle it

A side-by-side run in which the confidence intervals around growth rates or the optimality ranking of exploration levels from the SMC analysis fail to overlap with the values reported in the original Island Model paper.

Figures

Figures reproduced from arXiv: 2604.04543 by Andrea Vandin (Institute of Economics, Daniele Giachini (Institute of Economics, Ernest Ivanaj (Swiss Finance Institute, Giorgio Fagiolo (Institute of Economics, L'EMbeDS, Sant'Anna School of Advanced Studies), Stefano Blando (Institute of Economics, University of Geneve).

Figure 1
Figure 1. Figure 1: Agent type transitions. Miners are the productive state. Exploration (with probability [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Stagnation vs. sustained growth. When exploration ceases at [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average Growth Rate vs. exploration probability [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows the resulting trajectories. Growth increases monotonically with α. Even a mild de￾gree of increasing returns (α = 1.1) produces markedly higher growth than constant returns (α = 1.0), consistent with the agglomeration effects predicted by the model. The pairwise t-tests ( [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows that even a small amount of skill transfer (ϕ = 0.1) produces visibly higher growth than no transfer (ϕ = 0), with average log(GDP) reaching 8.1 vs. 7.4 at t = 201. This captures the learning￾by-doing mechanism emphasized by Arrow [4]: productivity gains are cumulative and embodied in workers’ experience. The pairwise t-test ( [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of knowledge locality ρ on average log(GDP). Lower ρ (broader knowledge diffusion) promotes growth. Bottom: pairwise t-test results (• = equal means, × = different means). These results demonstrate that MultiVeStA’s counterfactual analysis can effectively detect mean￾ingful differences across parameter configurations. The formal statistical guarantees complement the original analysis of Fagiolo and … view at source ↗
read the original abstract

Agent-based models (ABMs) are increasingly used to study complex economic phenomena such as endogenous growth, but their analysis typically relies on ad-hoc Monte Carlo exercises without formal statistical guarantees. We show how statistical model checking (SMC), and in particular Multi-VeStA, can automate and enrich the analysis of a seminal ABM: the Island Model of Fagiolo and Dosi, which captures the exploration-exploitation trade-off in technological search. We reproduce key stylized facts from the original model with formal confidence intervals, confirm the optimality of moderate exploration rates, and perform a counterfactual sensitivity analysis across returns to scale, skill transfer, and knowledge locality. Using MultiVeStA's built-in Welch's t-test, 6 out of 7 pairwise parameter comparisons yield statistically different growth trajectories, while the exception reveals a saturation effect in knowledge locality. Our results demonstrate that SMC offers a principled, reproducible methodology for the quantitative analysis of agent-based economic models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper applies statistical model checking (SMC) via the Multi-VeStA tool to the Island Model of Fagiolo and Dosi, an established ABM of endogenous growth that captures the exploration-exploitation trade-off in technological search. It reports reproduction of key stylized facts with formal confidence intervals, confirmation that moderate exploration rates are optimal, and a counterfactual sensitivity analysis varying returns to scale, skill transfer, and knowledge locality. Using Multi-VeStA's built-in Welch t-test, the authors find statistically significant differences in growth trajectories for 6 out of 7 pairwise parameter comparisons, with the exception indicating a saturation effect in knowledge locality. The central claim is that SMC supplies a principled, reproducible methodology for quantitative analysis of agent-based economic models.

Significance. If the embedded implementation of the Island Model faithfully reproduces the original Fagiolo-Dosi dynamics, the work would provide a useful demonstration of how SMC tools can replace ad-hoc Monte Carlo exercises with statistically guaranteed procedures for validating stylized facts and conducting sensitivity analysis in economic ABMs. The identification of a saturation effect in knowledge locality and the formal confidence intervals on growth trajectories could serve as a template for other complex ABMs in the field.

major comments (1)
  1. [Abstract] Abstract: The central claim that SMC via Multi-VeStA supplies a 'principled, reproducible methodology' for ABM analysis rests on the unverified assumption that the Island Model implementation inside the SMC framework exactly reproduces the original Fagiolo-Dosi agent search, knowledge spillovers, returns to scale, and locality rules. No quantitative benchmark (e.g., comparison of output distributions, mean growth rates, or variance) against the original model is reported, so any divergence in random-number handling or update rules would directly undermine the reported optimality of moderate exploration rates and the 6/7 statistically significant counterfactual differences.
minor comments (1)
  1. [Abstract] Abstract: The exception among the 7 pairwise comparisons is described only as revealing 'a saturation effect in knowledge locality,' without identifying the specific parameter pair or providing the associated p-value or effect size.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting an important aspect of our validation strategy. We address the concern regarding the implementation fidelity below.

read point-by-point responses

  1. Referee: The central claim that SMC via Multi-VeStA supplies a 'principled, reproducible methodology' for ABM analysis rests on the unverified assumption that the Island Model implementation inside the SMC framework exactly reproduces the original Fagiolo-Dosi agent search, knowledge spillovers, returns to scale, and locality rules. No quantitative benchmark (e.g., comparison of output distributions, mean growth rates, or variance) against the original model is reported, so any divergence in random-number handling or update rules would directly undermine the reported optimality of moderate exploration rates and the 6/7 statistically significant counterfactual differences.

    Authors: We acknowledge the referee's point that a direct quantitative benchmark against the original Fagiolo and Dosi model would provide stronger evidence of faithful reproduction. Our current validation relies on reproducing the key stylized facts (such as the exploration-exploitation trade-off effects and growth patterns) with confidence intervals, which is the common practice in the ABM literature for model validation. However, to address this concern directly, we will revise the manuscript to include a dedicated benchmark section. This will report comparisons of summary statistics like average GDP growth rates, variance in firm sizes, and innovation frequencies from our Multi-VeStA simulations against the values and behaviors described in the original Fagiolo and Dosi (2003) paper. We will also clarify the implementation details, including random number generation and update rules, to ensure transparency. This revision will be incorporated in the next version of the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: SMC application to external established ABM is self-contained

full rationale

The paper applies the pre-existing Multi-VeStA SMC tool to the independently published Island Model of Fagiolo and Dosi. Reproduction of stylized facts uses the tool's built-in confidence intervals and Welch t-tests on model outputs; no parameters are fitted to the reported optimality or sensitivity results and then re-presented as predictions. The model implementation is asserted to match the prior specification without any self-referential equations or definitions that would make the growth trajectories tautological. Self-citation to the original Island Model is to an external, falsifiable benchmark rather than a load-bearing uniqueness theorem or ansatz invented by the present authors. The methodological claim (SMC supplies principled analysis) therefore rests on independent tool behavior and external model dynamics, not on any reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the original Island Model is correctly re-implemented and that SMC properties transfer directly to this stochastic ABM without additional validation steps.

axioms (1)
  • domain assumption Statistical model checking provides formal probabilistic guarantees for properties of stochastic simulation models
    Invoked when applying Multi-VeStA to obtain confidence intervals and t-test results on growth trajectories.

pith-pipeline@v0.9.0 · 5518 in / 1147 out tokens · 54854 ms · 2026-05-10T19:49:33.050384+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

70 extracted references · 68 canonical work pages · 1 internal anchor

  1. [1]

    ACM Transactions on Modeling and Computer Simulation 28(1), pp

    Gul Agha & Karl Palmskog (2018): A Survey of Statistical Model Checking. ACM Transactions on Modeling and Computer Simulation 28(1), pp. 1–39, doi:10.1145/3158668

    work page doi:10.1145/3158668 2018

  2. [2]

    Econo- metrica60(2), 323–351 (1992)

    Philippe Aghion & Peter Howitt (1992): A Model of Growth Through Creative Destruction . Econometrica 60(2), pp. 323–351, doi:10.2307/2951599

    work page doi:10.2307/2951599 1992

  3. [3]

    Studies in Nonlinear Dynamics & Econometrics 16(4), doi:10.1515/1558-3708.1903

    Mikhail Anufriev & Giulio Bottazzi (2012): Asset Pricing with Heterogeneous Investment Horizons. Studies in Nonlinear Dynamics & Econometrics 16(4), doi:10.1515/1558-3708.1903

    work page doi:10.1515/1558-3708.1903 2012

  4. [4]

    The Review of Eco- nomic Studies29(3), 155–173 (1962)

    Kenneth J. Arrow (1962): The Economic Implications of Learning by Doing . The Review of Economic Studies 29(3), pp. 155–173, doi:10.2307/2295952

    work page doi:10.2307/2295952 1962

  5. [5]

    Brian Arthur, John H

    W. Brian Arthur, John H. Holland, Blake LeBaron, Richard Palmer & Paul Tayler (1996): Asset Pricing Under Endogenous Expectations in an Artificial Stock Market . In: The Economy as an Evolving Complex System II, Addison-Wesley, pp. 15–44, doi:10.1201/9780429496639-2

    work page doi:10.1201/9780429496639-2 1996

  6. [6]

    MIT Press (2008)

    Christel Baier & Joost-Pieter Katoen (2008): Principles of model checking . MIT Press, doi:10.1093/comjnl/bxp025

    work page doi:10.1093/comjnl/bxp025 2008

  7. [7]

    Junttila, Alberto Lluch-Lafuente, Massimiliano Mirelli & Andrea Vandin (2022): Formal Analysis of Lending Pools in Decentralized Finance

    Massimo Bartoletti, James Hsin-yu Chiang, Tommi A. Junttila, Alberto Lluch-Lafuente, Massimiliano Mirelli & Andrea Vandin (2022): Formal Analysis of Lending Pools in Decentralized Finance . In Tiziana Margaria & Bernhard Steffen, editors: Leveraging Applications of Formal Methods, Verification and Val- idation. Adaptation and Learning - 11th International...

    work page doi:10.1007/978-3-031-19759-8_21 2022

  8. [8]

    Doyne Farmer, Andreas Flache, Diego Garlaschelli, Andrew G

    Stefano Battiston, J. Doyne Farmer, Andreas Flache, Diego Garlaschelli, Andrew G. Haldane, Hans Heester- beek, Cars Hommes, Carlo Jaeger, Robert May & Marten Scheffer (2016):Complexity Theory and Financial Regulation. Science 351(6275), pp. 818–819, doi:10.1126/science.aad0299

    work page doi:10.1126/science.aad0299 2016

  9. [9]

    IEEE Transactions on Robotics , author=

    Maurice H. ter Beek, Axel Legay, Alberto Lluch-Lafuente & Andrea Vandin (2020):A Framework for Quan- titative Modeling and Analysis of Highly (Re)configurable Systems . IEEE Trans. Software Eng. 46(3), pp. 321–345, doi:10.1109/TSE.2018.2853726

    work page doi:10.1109/tse.2018.2853726 2020

  10. [10]

    ter Beek, Axel Legay, Alberto Lluch-Lafuente & Andrea Vandin (2021): Quantita- tive Security Risk Modeling and Analysis with RisQFLan

    Maurice H. ter Beek, Axel Legay, Alberto Lluch-Lafuente & Andrea Vandin (2021): Quantita- tive Security Risk Modeling and Analysis with RisQFLan . Computers & Security 109, p. 102381, doi:10.1016/j.cose.2021.102381

    work page doi:10.1016/j.cose.2021.102381 2021

  11. [11]

    Lenz Belzner, Rocco De Nicola, Andrea Vandin & Martin Wirsing (2014): Reasoning (on) Service Compo- nent Ensembles in Rewriting Logic. In Shusaku Iida, José Meseguer & Kazuhiro Ogata, editors: Specifica- tion, Algebra, and Software - Essays Dedicated to Kokichi Futatsugi , Lecture Notes in Computer Science 8373, Springer, pp. 188–211, doi:10.1007/978-3-64...

    work page doi:10.1007/978-3-642-54624-2_10 2014

  12. [12]

    Journal of Mathematical Economics 41(1-2), pp

    Giulio Bottazzi, Giovanni Dosi & Igor Rebesco (2005): Institutional architectures and behavioral ecolo- gies in the dynamics of financial markets . Journal of Mathematical Economics 41(1-2), pp. 197–228, doi:10.1016/j.jmateco.2004.02.006

    work page doi:10.1016/j.jmateco.2004.02.006 2005

  13. [13]

    Physica A: Statistical Mechanics and its Applications 471, pp

    Giulio Bottazzi & Daniele Giachini (2017): Wealth and price distribution by diffusive approximation in a repeated prediction market . Physica A: Statistical Mechanics and its Applications 471, pp. 473–479, doi:10.1016/j.physa.2016.12.012. S. Blando et al. 19

    work page doi:10.1016/j.physa.2016.12.012 2017

  14. [14]

    Roberto Bruni, Andrea Corradini, Fabio Gadducci, Alberto Lluch-Lafuente & Andrea Vandin (2015): Mod- elling and analyzing adaptive self-assembly strategies with Maude . Sci. Comput. Program. 99, pp. 75–94, doi:10.1016/j.scico.2013.11.043

    work page doi:10.1016/j.scico.2013.11.043 2015

  15. [15]

    https://doi.org/10.1007/s40821-019-00121-0

    Gianluca Capone, Franco Malerba, Richard R. Nelson, Luigi Orsenigo & Sidney G. Winter (2019): His- tory friendly models: retrospective and future perspectives . Eurasian Business Review 9(1), pp. 1–23, doi:10.1007/s40821-019-00121-0

    work page doi:10.1007/s40821-019-00121-0 2019

  16. [16]

    Journal of Systems and Software 210, doi:10.1016/j.jss.2024.111983

    Roberto Casaluce, Andrea Burattin, Francesca Chiaromonte, Alberto Lluch Lafuente & Andrea Vandin (2024): White-box validation of quantitative product lines by statistical model checking and process min- ing. Journal of Systems and Software 210, doi:10.1016/j.jss.2024.111983

    work page doi:10.1016/j.jss.2024.111983 2024

  17. [17]

    In Cristina Cabanillas, Niels Frederik Garmann-Johnsen & Agnes Koschmider, editors: Business Process Management Workshops, Springer International Publishing, Cham, pp

    Roberto Casaluce, Andrea Burattin, Francesca Chiaromonte & Andrea Vandin (2023): Process Mining Meets Statistical Model Checking: Towards a Novel Approach to Model Validation and Enhancement. In Cristina Cabanillas, Niels Frederik Garmann-Johnsen & Agnes Koschmider, editors: Business Process Management Workshops, Springer International Publishing, Cham, p...

    work page doi:10.1007/978-3-031-25383-6_18 2023

  18. [18]

    Roberto Casaluce, Andrea Burratin, Francesca Chiaromonte, Alberto Lluch-Lafuente & Andrea Vandin (2024): Enhancing Threat Model Validation: A White-Box Approach based on Statistical Model Check- ing and Process Mining. In Bernardo Breve, Giuseppe Desolda, Vincenzo Deufemia & Lucio Davide Spano, editors: Proceedings of the First International Workshop on D...

    2024

  19. [19]

    Usage of Not

    Roberto Casaluce, Max Tschaikowski & Andrea Vandin (2024): White-Box Validation of Collective Adaptive Systems by Statistical Model Checking and Process Mining. In Tiziana Margaria & Bernhard Steffen, editors: Leveraging Applications of Formal Methods, Verification and Validation. REoCAS Colloquium in Honor of Rocco De Nicola - 12th International Symposiu...

    work page doi:10.1007/978-3- 2024

  20. [20]

    Vincenzo Ciancia, Diego Latella, Mieke Massink, Rytis Paskauskas & Andrea Vandin (2016): A Tool-Chain for Statistical Spatio-Temporal Model Checking of Bike Sharing Systems . In Tiziana Margaria & Bernhard Steffen, editors: Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques - 7th International Symposium, ISoLA ...

    work page doi:10.1007/978-3-319-47166- 2016

  21. [21]

    Clarke, Orna Grumberg, Daniel Kroening, Doron A

    Edmund M. Clarke, Orna Grumberg, Daniel Kroening, Doron A. Peled & Helmut Veith (2018): Model checking, 2nd Edition . MIT Press. Available at https://mitpress.mit.edu/books/ model-checking-second-edition

    2018

  22. [22]

    Flavio Corradini, Fabrizio Fornari, Andrea Polini, Barbara Re, Francesco Tiezzi & Andrea Vandin (2021): A formal approach for the analysis of BPMN collaboration models . J. Syst. Softw. 180, p. 111007, doi:10.1016/j.jss.2021.111007

    work page doi:10.1016/j.jss.2021.111007 2021

  23. [23]

    Flavio Corradini, Sara Pettinari, Barbara Re, Lorenzo Rossi & Francesco Tiezzi (2024): A technique for discovering BPMN collaboration diagrams. Softw. Syst. Model.23(6), pp. 1323–1343, doi:10.1007/s10270- 024-01153-5

    work page doi:10.1007/s10270- 2024

  24. [24]

    In: Handbook of Computa- tional Economics, 4, Elsevier, pp

    Herbert Dawid & Domenico Delli Gatti (2018): Agent-Based Macroeconomics. In: Handbook of Computa- tional Economics, 4, Elsevier, pp. 63–156, doi:10.2139/ssrn.3112074

    work page doi:10.2139/ssrn.3112074 2018

  25. [25]

    Technical Report 05-2012, Bielefeld University, doi:10.2139/ssrn.2408969

    Herbert Dawid, Simon Gemkow, Philipp Harting, Sander van der Hoog & Michael Neugart (2012): The EURACE@Unibi Model: An Agent-Based Macroeconomic Model for Economic Policy Analysis . Technical Report 05-2012, Bielefeld University, doi:10.2139/ssrn.2408969. 20 Statistical Model Checking of the Island Model

    work page doi:10.2139/ssrn.2408969 2012

  26. [26]

    Journal of Economic Dynamics and Control34(9), 1748–1767 (2010)

    Giovanni Dosi, Giorgio Fagiolo & Andrea Roventini (2010): Schumpeter Meeting Keynes: A Policy-Friendly Model of Endogenous Growth and Business Cycles. Journal of Economic Dynamics and Control 34(9), pp. 1748–1767, doi:10.1016/j.jedc.2010.06.018

    work page doi:10.1016/j.jedc.2010.06.018 2010

  27. [27]

    Journal of Evolutionary Economics 27(1), 63–90 (2017)

    Giovanni Dosi, Marcelo C. Pereira, Andrea Roventini & Maria Enrica Virgillito (2017): Micro and Macro Policies in the Keynes+Schumpeter Evolutionary Models . Journal of Evolutionary Economics 27(1), pp. 63–90, doi:10.1007/s00191-016-0466-4

    work page doi:10.1007/s00191-016-0466-4 2017

  28. [28]

    Journal of Economic Interaction and Coordination 8(2), pp

    Annalisa Fabretti (2013): On the Problem of Calibrating an Agent Based Model for Financial Markets . Journal of Economic Interaction and Coordination 8(2), pp. 277–293, doi:10.1007/s11403-012-0096-3

    work page doi:10.1007/s11403-012-0096-3 2013

  29. [29]

    Structural Change and Economic Dynamics 14(3), pp

    Giorgio Fagiolo & Giovanni Dosi (2003): Exploitation, Exploration and Innovation in a Model of Endoge- nous Growth with Locally Interacting Agents . Structural Change and Economic Dynamics 14(3), pp. 237– 273, doi:10.1016/s0954-349x(03)00022-5

    work page doi:10.1016/s0954-349x(03)00022-5 2003

  30. [30]

    https://doi.org/10.1007/s11403-019-00258-1, https://doi.org/ 10.1007/s11403-019-00258-1

    Giorgio Fagiolo, Daniele Giachini & Andrea Roventini (2020): Innovation, finance, and economic growth: an agent-based approach . Journal of Economic Interaction and Coordination 15(3), pp. 703–736, doi:10.1007/s11403-019-00258-1

    work page doi:10.1007/s11403-019-00258-1 2020

  31. [31]

    In: Computer Simulation Validation, pp

    Giorgio Fagiolo, Mattia Guerini, Francesco Lamperti, Alessio Moneta & Andrea Roventini (2019): Valida- tion of Agent-Based Models in Economics and Finance . In: Computer Simulation Validation, Springer, pp. 763–787, doi:10.1007/978-3-319-70766-2_31

    work page doi:10.1007/978-3-319-70766-2_31 2019

  32. [32]

    Computational Economics 30(3), pp

    Giorgio Fagiolo, Alessio Moneta & Paul Windrum (2007): A Critical Guide to Empirical Validation of Agent- Based Models in Economics: Methodologies, Procedures, and Open Problems . Computational Economics 30(3), pp. 195–226, doi:10.1007/s10614-007-9104-4

    work page doi:10.1007/s10614-007-9104-4 2007

  33. [33]

    Management Science 47(1), pp

    Lee Fleming (2001): Recombinant Uncertainty in Technological Search . Management Science 47(1), pp. 117–132, doi:10.1287/mnsc.47.1.117.10671

    work page doi:10.1287/mnsc.47.1.117.10671 2001

  34. [34]

    In Björn Johansson & Sanjay Jain, editors: 2018 Winter Simulation Conference, WSC 2018, Gothenburg, Sweden, December 9-12, 2018 , IEEE, pp

    Vashti Galpin, Anastasis Georgoulas, Michele Loreti & Andrea Vandin (2018): Statistical Analysis of CARMA Models: an Advanced Tutorial . In Björn Johansson & Sanjay Jain, editors: 2018 Winter Simulation Conference, WSC 2018, Gothenburg, Sweden, December 9-12, 2018 , IEEE, pp. 395–409, doi:10.1109/WSC.2018.8632456

    work page doi:10.1109/wsc.2018.8632456 2018

  35. [35]

    In: Integrated Formal Methods - 13th International Conference, IFM 2017, Turin, Italy, September 20-22, 2017, Proceedings, pp

    Stephen Gilmore, Daniel Reijsbergen & Andrea Vandin (2017): Transient and Steady-State Statistical Analy- sis for Discrete Event Simulators. In: Integrated Formal Methods - 13th International Conference, IFM 2017, Turin, Italy, September 20-22, 2017, Proceedings, pp. 145–160, doi:10.1007/978-3-319-66845-1_10

    work page doi:10.1007/978-3-319-66845-1_10 2017

  36. [36]

    Stephen Gilmore, Mirco Tribastone & Andrea Vandin (2014): An Analysis Pathway for the Quantitative Evaluation of Public Transport Systems . In Elvira Albert & Emil Sekerinski, editors: Integrated Formal Methods - 11th International Conference, IFM 2014, Bertinoro, Italy, September 9-11, 2014, Proceedings , Lecture Notes in Computer Science 8739, Springer,...

    work page doi:10.1007/978-3-319-10181-1_5 2014

  37. [37]

    In: Hand- book of Computational Economics, vol

    Cars H. Hommes (2006): Heterogeneous Agent Models in Economics and Finance. In: Handbook of Com- putational Economics, 2, Elsevier, pp. 1109–1186, doi:10.1016/s1574-0021(05)02023-x

    work page doi:10.1016/s1574-0021(05)02023-x 2006

  38. [38]

    Jaffe, Manuel Trajtenberg & Rebecca Henderson (1993): Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations

    Adam B. Jaffe, Manuel Trajtenberg & Rebecca Henderson (1993): Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations . The Quarterly Journal of Economics 108(3), pp. 577–598, doi:10.2307/2118401

    work page doi:10.2307/2118401 1993

  39. [39]

    Lucas Jr

    Robert E. Lucas Jr. (1988): On the Mechanics of Economic Development . Journal of Monetary Economics 22(1), pp. 3–42, doi:10.1016/0304-3932(88)90168-7

    work page doi:10.1016/0304-3932(88)90168-7 1988

  40. [40]

    Hanf normal form for first-order logic with unary counting quantifiers

    Joost-Pieter Katoen (2016): The Probabilistic Model Checking Landscape . In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science , LICS ’16, Association for Computing Ma- chinery, New York, NY , USA, p. 31–45, doi:10.1145/2933575.2934574

    work page doi:10.1145/2933575.2934574 2016

  41. [41]

    Kauffman (1993): The Origins of Order: Self-Organization and Selection in Evolution

    Stuart A. Kauffman (1993): The Origins of Order: Self-Organization and Selection in Evolution . Oxford University Press, New York, doi:10.1126/science.260.5113.1531

    work page doi:10.1126/science.260.5113.1531 1993

  42. [42]

    Routledge, London (2011)

    Alan Kirman (2011): Complex Economics: Individual and Collective Rationality . Routledge, London, doi:10.23941/ejpe.v4i2.81. S. Blando et al. 21

    work page doi:10.23941/ejpe.v4i2.81 2011

  43. [43]

    Jack P. C. Kleijnen (2015): Design and Analysis of Simulation Experiments , 2nd edition. Springer, doi:10.1007/978-3-319-18087-8

    work page doi:10.1007/978-3-319-18087-8 2015

  44. [44]

    Journal of Political Economy 99(3), pp

    Paul Krugman (1991): Increasing Returns and Economic Geography . Journal of Political Economy 99(3), pp. 483–499, doi:10.1086/261763

    work page doi:10.1086/261763 1991

  45. [45]

    Journal of Economic Dynamics and Control90, 366–389 (2018)

    Francesco Lamperti, Andrea Roventini & Amir Sani (2018): Agent-based model calibration us- ing machine learning surrogates . Journal of Economic Dynamics and Control 90, pp. 366–389, doi:10.1016/j.jedc.2018.03.011

    work page doi:10.1016/j.jedc.2018.03.011 2018

  46. [46]

    In: Runtime Verification (RV 2010)

    Axel Legay, Benoît Delahaye & Saddek Bensalem (2010): Statistical Model Checking: An Overview . In: Runtime Verification (RV 2010), LNCS 6418, Springer, pp. 122–135, doi:10.1007/978-3-642-16612-9_11

    work page doi:10.1007/978-3-642-16612-9_11 2010

  47. [47]

    Levinthal & James G

    Daniel A. Levinthal & James G. March (1993): The Myopia of Learning . Strategic Management Journal 14(S2), pp. 95–112, doi:10.1002/smj.4250141009

    work page doi:10.1002/smj.4250141009 1993

  48. [48]

    Nature Physics 5(1), pp

    Thomas Lux & Frank Westerhoff (2009): Economics Crisis . Nature Physics 5(1), pp. 2–3, doi:10.1038/nphys1163

    work page doi:10.1038/nphys1163 2009

  49. [49]

    March (1991): Exploration and Exploitation in Organizational Learning

    James G. March (1991): Exploration and Exploitation in Organizational Learning . Organization Science 2(1), pp. 71–87, doi:10.1287/orsc.2.1.71

    work page doi:10.1287/orsc.2.1.71 1991

  50. [50]

    Harvard University Press, Cambridge, MA (1982)

    Richard R. Nelson & Sidney G. Winter (1982): An Evolutionary Theory of Economic Change . Harvard University Press, Cambridge, MA, doi:10.1086/261177

    work page doi:10.1086/261177 1982

  51. [51]

    chinchilla optimal

    Marco Pangallo, Daniele Giachini & Andrea Vandin (2025): Statistical Model Checking of NetLogo Models. CoRR abs/2509.10977, doi:10.48550/ARXIV .2509.10977

    work page internal anchor Pith review doi:10.48550/arxiv 2025

  52. [52]

    Phelps (1969): The New Microeconomics in Inflation and Employment Theory

    Edmund S. Phelps (1969): The New Microeconomics in Inflation and Employment Theory . American Eco- nomic Review 59(2), pp. 147–160, doi:10.1016/B978-0-12-554001-8.50009-0

    work page doi:10.1016/b978-0-12-554001-8.50009-0 1969

  53. [53]

    In: International Conference on High Perfor- mance Computing & Simulation, HPCS 2014, Bologna, Italy, 21-25 July, 2014 , IEEE, pp

    Danilo Pianini, Stefano Sebastio & Andrea Vandin (2014): Distributed statistical analysis of com- plex systems modeled through a chemical metaphor . In: International Conference on High Perfor- mance Computing & Simulation, HPCS 2014, Bologna, Italy, 21-25 July, 2014 , IEEE, pp. 416–423, doi:10.1109/HPCSIM.2014.6903715

    work page doi:10.1109/hpcsim.2014.6903715 2014

  54. [54]

    Romer (1990): Endogenous Technological Change

    Paul M. Romer (1990): Endogenous Technological Change. Journal of Political Economy 98(5), pp. S71– S102, doi:10.1086/261725

    work page doi:10.1086/261725 1990

  55. [55]

    Romer (1994): The Origins of Endogenous Growth

    Paul M. Romer (1994): The Origins of Endogenous Growth . Journal of Economic Perspectives 8(1), pp. 3–22, doi:10.1257/jep.8.1.3

    work page doi:10.1257/jep.8.1.3 1994

  56. [56]

    Wiley, doi:10.1111/j.1751-5823.2008.00062_17.x

    Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana & Stefano Tarantola (2008): Global Sensitivity Analysis: The Primer . Wiley, doi:10.1111/j.1751-5823.2008.00062_17.x

    work page doi:10.1111/j.1751-5823.2008.00062_17.x 2008

  57. [57]

    Schelling (1971): Dynamic Models of Segregation

    Thomas C. Schelling (1971): Dynamic Models of Segregation. Journal of Mathematical Sociology 1(2), pp. 143–186, doi:10.1080/0022250x.1971.9989794

    work page doi:10.1080/0022250x.1971.9989794 1971

  58. [58]

    Performance Evaluation 70(6), pp

    Stefano Sebastio & Andrea Vandin (2013): MultiVeStA: Statistical model checking for discrete event simula- tors. Performance Evaluation 70(6), pp. 457–475, doi:10.4108/icst.valuetools.2013.254377

    work page doi:10.4108/icst.valuetools.2013.254377 2013

  59. [59]

    Computational and Math- ematical Organization Theory23(1), 94–121 (2017)

    Davide Secchi & Raffaello Seri (2017): Controlling for false negatives in agent-based models: a review of power analysis in organizational research. Computational and Mathematical Organization Theory23(1), pp. 94–121, doi:10.1007/s10588-016-9218-0

    work page doi:10.1007/s10588-016-9218-0 2017

  60. [60]

    The Quarterly Journal of Economics69(1), 99–118 (1955)

    Herbert A. Simon (1955): A Behavioral Model of Rational Choice . The Quarterly Journal of Economics 69(1), pp. 99–118, doi:10.2307/1884852

    work page doi:10.2307/1884852 1955

  61. [61]

    Solow (1956): A Contribution to the Theory of Economic Growth

    Robert M. Solow (1956): A Contribution to the Theory of Economic Growth . The Quarterly Journal of Economics 70(1), pp. 65–94, doi:10.2307/1884513

    work page doi:10.2307/1884513 1956

  62. [62]

    Sutton & Andrew G

    Richard S. Sutton & Andrew G. Barto (2018): Reinforcement Learning: An Introduction , second edition. MIT Press, Cambridge, MA, doi:10.1017/s0263574799211174

    work page doi:10.1017/s0263574799211174 2018

  63. [63]

    Judd (2006): Handbook of Computational Economics: Agent-Based Compu- tational Economics

    Leigh Tesfatsion & Kenneth L. Judd (2006): Handbook of Computational Economics: Agent-Based Compu- tational Economics. 2, Elsevier, Amsterdam, doi:10.1109/mci.2008.929849. 22 Statistical Model Checking of the Island Model

    work page doi:10.1109/mci.2008.929849 2006

  64. [64]

    Andrea Vandin (2024): Statistical Model Checking of Python Agent-Based Models: An Integration of Mul- tiVeStA and Mesa. In Bernhard Steffen, editor: Bridging the Gap Between AI and Reality - Second Inter- national Conference, AISoLA 2024, Crete, Greece, October 30 - November 3, 2024, Proceedings , Lecture Notes in Computer Science 15217, Springer, pp. 398...

    work page doi:10.1007/978-3-031-75434-0_26 2024

  65. [65]

    ter Beek, Axel Legay & Alberto Lluch-Lafuente (2018): QFLan: A Tool for the Quantitative Analysis of Highly Reconfigurable Systems

    Andrea Vandin, Maurice H. ter Beek, Axel Legay & Alberto Lluch-Lafuente (2018): QFLan: A Tool for the Quantitative Analysis of Highly Reconfigurable Systems . In Klaus Havelund, Jan Peleska, Bill Roscoe & Erik P. de Vink, editors: Formal Methods - 22nd International Symposium, FM 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK,...

    work page doi:10.1007/978-3-319-95582-7_19 2018

  66. [66]

    Journal of Economic Dynamics and Control143(10 2022)

    Andrea Vandin, Daniele Giachini, Francesco Lamperti & Francesca Chiaromonte (2022): Automated and distributed statistical analysis of economic agent-based models. Journal of Economic Dynamics and Control 143, doi:10.1016/j.jedc.2022.104458

    work page doi:10.1016/j.jedc.2022.104458 2022

  67. [67]

    Sequential Tests of Statistical Hypotheses

    Abraham Wald (1945): Sequential Tests of Statistical Hypotheses . The Annals of Mathematical Statistics 16(2), pp. 117–186, doi:10.1214/aoms/1177731118

    work page doi:10.1214/aoms/1177731118 1945

  68. [68]

    Welch (1947): The Generalization of ‘Student’s’ Problem when Several Different Population Variances are Involved

    Bernard L. Welch (1947): The Generalization of ‘Student’s’ Problem when Several Different Population Variances are Involved. Biometrika 34(1–2), pp. 28–35, doi:10.2307/2332510

    work page doi:10.2307/2332510 1947

  69. [69]

    Journal of Artificial Societies and Social Simulation 10(2), doi:10.1007/s10614- 007-9104-4

    Paul Windrum, Giorgio Fagiolo & Alessio Moneta (2007): Empirical Validation of Agent-Based Models: Alternatives and Prospects. Journal of Artificial Societies and Social Simulation 10(2), doi:10.1007/s10614- 007-9104-4

    work page doi:10.1007/s10614- 2007

  70. [70]

    Wiley Publishing, doi:10.5555/1695886

    Michael Wooldridge (2009): An Introduction to MultiAgent Systems . Wiley Publishing, doi:10.5555/1695886

    work page doi:10.5555/1695886 2009