Abstract

“Self-organized criticality” (SOC) is the mechanism by which complex systems are spontaneously driven towards, or even across, a} critical point \textit{at the edge between stability and chaos. These special points are characterized by fat-tailed fluctuations and long-memory correlations. Such a scenario can explain why insignificant perturbations may generate large disruptions, through the propagation of “avalanches” across the system. This short review discusses how SOC could offer a plausible solution to the excess volatility puzzle in financial markets and the analogue “small shocks, large business cycle puzzle” for the economy at large, as initially surmised by Per Bak et al. (1993) and, in a different language, by Hyman Minsky. I argue that in general the quest for efficiency and the necessity of resilience may be mutually incompatible and require specific policy considerations.

Bibliography

Acemoglu, D., V. M. Carvalho, A. Ozdaglar, and A. Tahbaz-Salehi. 2012. “The Network Origins of Aggregate Fluctuations.” Econometrica 80 (5): 1977–2016. https://doi.org/10.3982/ECTA9623.

Alfi, V., L. Pietronero, and A. Zaccaria. 2009. “Self-Organization for the Stylized Facts and Finite-Size Effects in a Financial-Market Model.” Europhysics Letters 86 (5):58003. https://doi.org/10.1209/0295-5075/86/58003.

Amir, R., I. Evstigneev, T. Hens, and K. Schenk-Hoppé. 2005. “Market Selection and Survival of Investment Strategies.” Journal of Mathematical Economics 41 (1-2): 105–122. https://EconPapers.repec.org/RePEc:eee:mateco:v:41:y:2005:i:1-2:p:105-122.

Aspelmeier, T. 2008. “Bond Chaos in the Sherrington-Kirkpatrick Model.” Journal of Physics A: Mathematical and Theoretical 41 (20): 205005. https://doi.org/10.1088/1751-8113/41/20/205005.

Aspelmeier, T., and M. A. Moore. 2019. “Realizable Solutions of the Thouless-Anderson-Palmer Equations.” Physical Review E 100 (3): 032127. https://doi.org/10.1103/PhysRevE.100.032127.

Atalay, E., A. Hortacsu, J. Roberts, and C. Syverson. 2011. “Network Structure of Production.” Proceedings of the National Academy of Sciences 108 (13): 5199–5202. https://doi.org/10.1073/pnas.1015564108.

Aubrun, C., R. Morel, M. Benzaquen, and J.-P. Bouchaud. 2024. Riding Wavelets: A Method to Discover New Classes of Price Jumps. ArXiv preprint:2404.16467. https://doi.org/10.48550/arXiv.2404.16467.

Axtell, R. L. 2001. “Zipf Distribution of US Firm Sizes.” Science 293 (5536): 1818–1820. https://doi.org/10.1126/science.106208.

Bacry, E., I. Mastromatteo, and J.-F. Muzy. 2015. “Hawkes Processes in Finance.” Market Microstructure and Liquidity 1 (01): 1550005. https://doi.org/10.1142/S2382626615500057.

Bak, P. 2013. How Nature Works: The Science of Self-Organized Criticality. New York, NY: Copernicus. https://doi.org/10.1007/978-1-4757-5426-1.

Bak, P., K. Chen, J. Scheinkman, and M. Woodford. 1993. “Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics.” Ricerche Economiche 47 (1): 3–30. https://doi.org/10.1016/0035-5054(93)90023-V.

Bak, P., and M. Paczuski. 1997. “Mass Extinctions vs. Uniformitarianism in Biological Evolution.” In Physics of Biological Systems: From Molecules to Species, edited by H. Flyvbjerg, J. Hertz, M. H. Jensen, O. G. Mouritsen, and K. Sneppen, 341–356. Berlin, Germany: Springer.

Bak, P., C. Tang, and K. Wiesenfeld. 1987. “Self-Organized Criticality: An Explanation of the 1/f Noise.” Physical Review Letters 59 (4): 381–384. https://doi.org/10.1103/PhysRevLett.59.381.

Baqaee, D. R., and E. Farhi. 2019. “The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten’s Theorem.” Econometrica 87 (4): 1155–1203. https://doi.org/10.3982/ECTA15202.

—. 2020. “Productivity and Misallocation in General Equilibrium.” The Quarterly Journal of Economics 135 (1): 105–163. https://doi.org/10.1093/qje/qjz030.

Bayer, C., P. K. Friz, M. Fukasawa, J. Gatheral, A. Jacquier, and M. Rosenbaum, eds. 2023. Rough Volatility. Philadelphia, PA: SIAM. https://doi.org/10.1137/1.9781611977783.

Bernanke, B. S., M. Gertler, and S. Gilchrist. 1996. “The Financial Accelerator and the Flight to Quality.” The Review of Economics and Statistics 78 (1): 1–15. https://doi.org/10.2307/2109844.

Bialek, W., A. Cavagna, I. Giardina, T. Mora, O. Pohl, E. Silvestri, M. Viale, and A. M. Walczak. 2014. “Social Interactions Dominate Speed Control in Poising Natural Flocks Near Criticality.” Proceedings of the National Academy of Sciences 111 (20): 7212–7217. https://doi.org/10.1073/pnas.132404511.

Biroli, G., G. Bunin, and C. Cammarota. 2018. “Marginally Stable Equilibria in Critical Ecosystems.” New Journal of Physics 20 (8): 083051. https://doi.org/10.1088/1367-2630/aada58.

Blanc, P., J. Donier, and J.-P. Bouchaud. 2017. “Quadratic Hawkes Processes for Financial Prices.” Quantitative Finance 17 (2): 171–188. https://doi.org/10.1080/14697688.2016.1193215.

Bochud, T., and D. Challet. 2007. “Optimal Approximations of Power Laws with Exponentials: Application to Volatility Models with Long Memory.” Quantitative Finance 7 (6): 585–589. https://doi.org/10.1080/14697680701278291.

Bouchaud, J.-P. 2001. “Power Laws in Economics and Finance: Some Ideas from Physics.” Quantitative Finance 1 (1): 105. https://doi.org/10.1088/1469-7688/1/1/307.

—. 2011. “The Endogenous Dynamics of Markets: Price Impact, Feedback Loops and Instabilities.” In Lessons from the Credit Crisis, 345–74. New York, NY: Risk Publications.

—. 2021. “Radical Complexity.” Entropy 23 (12): 1676. https://doi.org/10.3390/e23121676.

Bouchaud, J.-P., J. Bonart, J. Donier, and M. Gould. 2018. “The Impact of Market Orders.” In Trades, Quotes and Prices: Financial Markets Under the Microscope, edited by J.-P. Bouchaud, J. Bonart, J. Donier, and M. Gould, 208–228. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/9781316659335.017.

Bouchaud, J.-P., and D. Challet. 2017. “Why Have Asset Price Properties Changed so Little in 200 Years?” In Econophysics and Sociophysics: Recent Progress and Future Directions, edited by F. Abergel, H. Aoyama, B. K. Chakrabarti, A. Chakraborti, N. Deo, D. Raina, and I. Vodenska, 3–17. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-47705-3_1.

Bouchaud, J.-P., S. Ciliberti, Y. Lempérière, A. Majewski, P. Seager, and K. S. Ronia. 2017. Black was Right: Price is Within a Factor 2 of Value. arXiv preprint:1711.04717. https://doi.org/10.48550/arXiv.1711.04717.

Bouchaud, J.-P., J. D. Farmer, and F. Lillo. 2009. “How Markets Slowly Digest Changes in Supply and Demand.” In Handbook of Financial Markets: Dynamics and Evolution, edited by T. Hens and K. R. Schenk-Hoppé, 57–160. Amsterdam, Netherlands: Elsevier. https://doi.org/10.1016/B978 -012374258-2.50006-3.

Bouchaud, J.-P., Y. Gefen, M. Potters, and M. Wyart. 2003. “Fluctuations and Response in Financial Markets: The Subtle Nature of Random Price Changes.” Quantitative Finance 4 (2): 176. https://doi.org/10.1080/14697680400000022.

Bouchaud, J.-P., and M. Mézard. 2000. “Wealth Condensation in a Simple Model of Economy.” Physica A: Statistical Mechanics and its Applications 282 (3–4): 536–545. https://doi.org/10.1016/S0378-4371(00)00205-3.

Bouchaud, J.-P., and M. Potters. 2003. Theory of Financial Risks. Vol. 12. Cambridge, UK: Cambridge University Press.

Brémaud, P., and L. Massoulié. 2001. “Hawkes Branching Point Processes without Ancestors.” Journal of Applied Probability 38 (1): 122–135. https://doi.org/10.1239/jap/996986648.

Brock, W. A., and C. H. Hommes. 1998. “Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model.” Journal of Economic Dynamics and Control 22 (8-9): 1235–1274. https://doi.org/10.1016/S0165-1889(98)00011-6.

Brunnermeier, M. K., and L. H. Pedersen. 2009. “Market Liquidity and Funding Liquidity.” The Review of Financial Studies 22 (6): 2201–2238. https://doi.org/10.1093/rfs/hhn098.

Bunin, G. 2017. “Ecological Communities with Lotka–Volterra Dynamics.” Physical Review E 95 (4): 042414. https://doi.org/10.1103/PhysRevE.95.042414.

Cabrera, J. L., and J. G. Milton. 2004. “Human Stick Balancing: Tuning Lévy Flights to Improve Balance Control.” Chaos: An Interdisciplinary Journal of Nonlinear Science 14 (3): 691–698. https://doi.org/10.1063/1.1785453.

. 2012. “Stick Balancing, Falls and Dragon-Kings.” The European Physical Journal Special Topics 205 (1): 231–241. https://doi.org/10.1140/epjst/e2012-01573-7.

Caccioli, F., P. Barucca, and T. Kobayashi. 2018. “Network Models of Financial Systemic Risk: A Review.” Journal of Computational Social Science 1:81–114. https://doi.org/10.1007/s42001-017-0008-3.

Caccioli, F., J.-P. Bouchaud, and D. Farmer. 2012. “Impact-Adjusted Valuation and the Criticality of Leverage.” Risk 25 (12): 74–77. https://doi.org/10.1080/14697688.2022.2039755.

Caccioli, F., J. D. Farmer, N. Foti, and D. Rockmore. 2015. “Overlapping Portfolios, Contagion, and Financial Stability.” Journal of Economic Dynamics and Control 51:50–63. https://doi.org/10.1016/j.jedc.2014.09.041.

Caccioli, F., M. Marsili, and P. Vivo. 2009. “Eroding Market Stability by Proliferation of Financial Instruments.” The European Physical Journal B 71:467–479. https://doi.org/10.1140/epjb/e2009-00316-y.

Carlson, J. M., and J. Doyle. 1999. “Highly Optimized Tolerance: A Mechanism for Power Laws in Designed Systems.” Physical Review E 60 (2): 1412. https://doi.org/10.1103/PhysRevE.60.1412.

Carvalho, V. M., and A. Tahbaz-Salehi. 2019. “Production Networks: A Primer.” Annual Review of Economics 11:635–663. https://doi.org/10.1146/annureveconomics-080218-030212.

Castellano, C., and R. Pastor-Satorras. 2017. “Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects.” Physical Review X 7 (4): 041024. https://doi.org/10.1103/PhysRevX.7.041024.

Cavagna, A., I. Giardina, and G. Parisi. 1998. “Stationary Points of the Thouless–Anderson–Palmer Free Energy.” Physical Review B 57 (18): 11251. https://doi.org/10.1103/PhysRevB.57.11251.

Challet, D., and M. Marsili. 2003. “Criticality and Market Efficiency in a Simple Realistic Model of the Stock Market.” Physical Review E 68 (3): 036132. https://doi.org/10.1103/PhysRevE.68.036132.

Challet, D., M. Marsili, and Y.-C. Zhang. 2004. Minority Games: Interacting Agents in Financial Markets. Oxford, UK: Oxford University Press.

Cherkashin, D., J. D. Farmer, and S. Lloyd. 2009. “The Reality Game.” Journal of Economic Dynamics and Control 33 (5): 1091–1105. https://doi.org/10.1016/j.jedc.2009.02.002.

Chialvo, D. R. 2010. “Emergent Complex Neural Dynamics.” Nature Physics 6 (10): 744–750. https://doi.org/10.1038/nphys1803.

Chiarella, C. 1992. “The Dynamics of Speculative Behaviour.” Annals of Operations Research 37 (1): 101–123. https://doi.org/10.1007/BF02071051.

Chicheportiche, R., and J.-P. Bouchaud. 2014. “The Fine-Structure of Volatility Feedback I: Multi-Scale Self-Reflexivity.” Physica A: Statistical Mechanics and its Applications 410:174–195. https://doi.org/10.1016/j.physa.2014.05.007.

Cochrane, J. H. 1994. “Shocks: A Comment.” Carnegie–Rochester Conference Series on Public Policy 41:295–364. https://doi.org/10.1016/0167-2231(94)00025-5.

Colon, C., and J.-P. Bouchaud. 2022. “The Radical Complexity of Rewiring Supplier–Buyer Networks.” Available at SSRN 4300311.

Colon, C., and M. Ghil. 2017. “Economic Networks: Heterogeneity-Induced Vulnerability and Loss of Synchronization.” Chaos: An Interdisciplinary Journal of Nonlinear Science 27 (12): 126703. https://doi.org/10.1063/1.5017851.

Cont, R. 2001. “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.” Quantitative Finance 1 (2): 223. https://doi.org/10.1080/713665670.

Cont, R., and L. Wagalath. 2013. “Running for the Exit: Distressed Selling and Endogenous Correlation in Financial Markets.” Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics 23 (4): 718–741. https://doi.org/10.1111/j.1467-9965.2011.00510.x.

Cutler, D. M., J. M. Poterba, and L. H. Summers. 1988. What Moves Stock Prices? Technical Report 2538. Cambridge, MA: National Bureau of Economic Research. https://doi.org/10.3386/w2538.

Dall’Amico, L., A. Fosset, J.-P. Bouchaud, and M. Benzaquen. 2019. “How Does Latent Liquidity get Revealed in the Limit Order Book?” Journal of Statistical Mechanics: Theory and Experiment 2019 (1): 013404. https://doi.org/10.1088/1742-5468/aaf10e.

De Arcangelis, L., C. Perrone-Capano, and H. J. Herrmann. 2006. “Self-Organized Criticality Model for Brain Plasticity.” Physical Review Letters 96 (2): 028107. https://doi.org/10.1103/PhysRevLett.96.028107.

Dekker, M. M., and D. Panja. 2021. “Cascading Dominates Large-Scale Disruptions in Transport Over Complex Networks.” PLoS One 16 (1): e0246077. https://doi.org/10.1371/journal.pone.0246077.

Dessertaine, T., J. Moran, M. Benzaquen, and J.-P. Bouchaud. 2022. “Out-of-Equilibrium Dynamics and Excess Volatility in Firm Networks.” Journal of Economic Dynamics and Control 138: 104362. https://doi.org/10.1016/j.jedc.2022.104362.

di Santo, S., R. Burioni, A. Vezzani, and M. A. Munoz. 2016. “Self-Organized Bistability Associated with First-Order Phase Transitions.” Physical Review Letters 116 (24): 240601. https://doi.org/10.1103/PhysRevLett.116.240601.

Engle, R. F. 1982. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica: Journal of the Econometric Society, 987–1007. https://www.jstor.org/stable/1912773.

Engle, R. F. 2001. “GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics.” Journal of Economic Perspectives 15 (4): 157–168. https://doi.org/10.1257/jep.15.4.157.

Fair, R. C. 2002. “Events that Shook the Market.” The Journal of Business 75 (4): 713–731. https://doi.org/10.1086/341640.

Farmer, J. D. 2002. “Market Force, Ecology and Evolution.” Industrial and Corporate Change 11 (5): 895–953. https://doi.org/10.1093/icc/11.5.895.

Farmer, J. D. 2024. Making Sense of Chaos: A Better Economics for a Better World. New Haven, CT: Yale University Press.

Farmer, J. D., and F. Lillo. 2004. “On the Origin of Power-Law Tails in Price Fluctuations.” Quantitative Finance 4 (1): 7–11. https://doi.org/10.1088/1469-7688/4/1/C01.

Filimonov, V., D. Bicchetti, N. Maystre, and D. Sornette. 2014. “Quantification of the High Level of Endogeneity and of Structural Regime Shifts in Commodity Markets.” Journal of International Money and Finance 42: 174–192. https://doi.org/10.1016/j.jimonfin.2013.08.010.

Fisher, D. S., and D. A. Huse. 1991. “Directed Paths in a Random Potential.” Physical Review B 43 (13): 10728–10742. https://doi.org/10.1103/PhysRevB.43.10728.

Fisher, F. M. 1989. Disequilibrium Foundations of Equilibrium Economics. Cambridge, UK: Cambridge University Press.

Flaschel, P. 2010. “The Classical Growth Cycle: Reformulation, Simulation and Some Facts.” In Topics in Classical Micro- and Macroeconomics, 435–463. Amsterdam, Netherlands: Springer. https://doi.org/10.1007/978-3-642-00324-0_20.

Fosset, A., J.-P. Bouchaud, and M. Benzaquen. 2020. “Endogenous Liquidity Crises.” Journal of Statistical Mechanics: Theory and Experiment 2020 (6): 063401. https://doi.org/10.1088/1742-5468/ab7c64.

Fosset, A., J.-P. Bouchaud, and M. Benzaquen. 2022. “Non-Parametric Estimation of Quadratic Hawkes Processes for Order Book Events.” The European Journal of Finance 28 (7): 663–678. https://doi.org/10.1080/1351847X.2021.1917441.

Franz, S., G. Parisi, M. Sevelev, P. Urbani, and F. Zamponi. 2017. “Universality of the SAT–UNSAT (Jamming) Threshold in Non-Convex Continuous Constraint Satisfaction Problems.” SciPost Physics 2: 019. https://doi.org/10.21468/SciPostPhys.2.3.019.

Frisch, U. 1995. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9781139170666.

Gabaix, X. 2009. “Power Laws in Economics and Finance.” Annual Review of Economics 1 (1): 255–294. https://doi.org/10.1146/annurev.economics.050708.142940.

Gabaix, X. 2011. “The Granular Origins of Aggregate Fluctuations.” Econometrica 79 (3): 733–772. https://doi.org/10.3982/ECTA8769.

Gabaix, X., P. Gopikrishnan, V. Plerou, and H. E. Stanley. 2003. “A Theory of Power-Law Distributions in Financial Market Fluctuations.” Nature 423 (6937): 267–270. https://doi.org/10.1038/nature01624.

Gabaix, X., P. Gopikrishnan, V. Plerou, and H. E. Stanley. 2006. “Institutional Investors and Stock Market Volatility.” The Quarterly Journal of Economics 121 (2): 461–504. https://www.jstor.org/stable/25098798.

Gai, P., and S. Kapadia. 2010. “Contagion in Financial Networks.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466 (2120): 2401–2423. https://doi.org/10.1098/rspa.2009.0410.

Garnier-Brun, J., M. Benzaquen, and J.-P. Bouchaud. 2024. “Unlearnable Games and ‘Satisficing’ Decisions: A Simple Model for a Complex World.” Physical Review X 14 (2): 021039. https://doi.org/10.1103/PhysRevX.14.021039.

Garnier-Brun, J., M. Benzaquen, S. Ciliberti, and J.-P. Bouchaud. 2021. “A New Spin on Optimal Portfolios and Ecological Equilibria.” Journal of Statistical Mechanics: Theory and Experiment 2021 (9): 093408. https://doi.org/10.1088/1742-5468/ac21d9.

Giardina, I., and J.-P. Bouchaud. 2003. “Bubbles, Crashes and Intermittency in Agent Based Market Models.” The European Physical Journal B—Condensed Matter and Complex Systems 31: 421–437. https://doi.org/10.1140/epjb/e2003-00050-6.

Gillemot, L., J. D. Farmer, and F. Lillo. 2006. “There’s More to Volatility than Volume.” Quantitative Finance 6 (5): 371–384. https://doi.org/10.1080/14697680600835688.

Glosten, L. R., and P. R. Milgrom. 1985. “Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders.” Journal of Financial Economics 14 (1): 71–100. https://doi.org/10.1016/0304-405X(85)90044-3.

Grossman, S. J., and J. E. Stiglitz. 1980. “On the Impossibility of Informationally Efficient Markets.” The American Economic Review 70 (3): 393–408. https://www.jstor.org/stable/1805228.

Gualdi, S., J.-P. Bouchaud, G. Cencetti, M. Tarzia, and F. Zamponi. 2015a. “Endogenous Crisis Waves: Stochastic Model with Synchronized Collective Behavior.” Physical Review Letters 114 (8): 088701. https://doi.org/10.1103/PhysRevLett.114.088701.

Gualdi, S., M. Tarzia, F. Zamponi, and J.-P. Bouchaud. 2015b. “Tipping Points in Macroeconomic Agent-Based Models.” Journal of Economic Dynamics and Control 50: 29–61. https://doi.org/10.1016/j.jedc.2014.08.003.

Haldane, A. G., and R. M. May. 2011. “Systemic Risk in Banking Ecosystems.” Nature 469 (7330): 351–355. https://doi.org/10.1038/nature09659.

Hardiman, S. J., N. Bercot, and J.-P. Bouchaud. 2013. “Critical Reflexivity in Financial Markets: a Hawkes Process Analysis.” The European Physical Journal B 86: 1–9. https://doi.org/10.1140/epjb/e2013-40107-3.

Hardiman, S. J., and J.-P. Bouchaud. 2014. “Branching-Ratio Approximation for the Self-Exciting Hawkes Process.” Physical Review E 90 (6): 062807. https://doi.org/10.1103/PhysRevE.90.062807.

Harras, G., C. J. Tessone, and D. Sornette. 2012. “Noise-Induced Volatility of Collective Dynamics.” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 85 (1): 011150. https://doi.org/10.1103/PhysRevE.85.011150.

Harris, T. E. 1963. The Theory of Branching Processes. Vol. 6. Berlin, Germany: Springer.

Hawkins, D., and H. A. Simon. 1949. “Note: Some Conditions of Macroeconomic Stability.” Econometrica, Journal of the Econometric Society, 245–248. https://www.jstor.org/stable/1905526.

Herskovic, B., B. Kelly, H. Lustig, and S. Van Nieuwerburgh. 2020. “Firm Volatility in Granular Networks.” Journal of Political Economy 128 (11): 4097–4162. https://doi.org/10.1086/710345.

Hynes, W., B. D. Trump, A. Kirman, A. Haldane, and I. Linkov. 2022. “Systemic Resilience in Economics.” Nature Physics 18 (4): 381–384. https://doi.org/10.1038/s41567-022-01581-4.

Jensen, H. J. 1998. Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Vol. 10. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9780511622717.

Joulin, A., A. Lefevre, D. Grunberg, and J.-P. Bouchaud. 2008. “Stock Price Jumps: News and Volume Play a Minor Role.” Wilmott Magazine 46. https://doi.org/10.48550/arXiv.0803.1769.

Kaplan, G., B. Moll, and G. L. Violante. 2018. “Monetary Policy According to HANK.” American Economic Review 108 (3): 697–743. https://doi.org/10.1257/aer.20160042.

Keeler, J. D., and J. D. Farmer. 1986. “Robust Space–Time Intermittency and 1f Noise.” Physica D: Nonlinear Phenomena 23 (1–3): 413–435. https://doi.org/10.1016/0167-2789(86)90148-X.

Khandani, A. E., and A. W. Lo. 2007. “What Happened to the Quants in August 2007? Evidence from Factors and Transactions Data.” Journal of Financial Markets 14 (1): 1–46. https://doi.org/10.1016/j.finmar.2010.07.005.

Kinouchi, O., R. Pazzini, and M. Copelli. 2020. “Mechanisms of Self-Organized Quasicriticality in Neuronal Network Models.” Frontiers in Physics 8: 583213. https://doi.org/10.3389/fphy.2020.583213.

Krząkała, F., and J.-P. Bouchaud. 2005. “Disorder Chaos in Spin Glasses.” Europhysics Letters 72 (3): 472. https://doi.org/10.1209/epl/i2005-10256-2.

Kyle, A. S. 1985. “Continuous Auctions and Insider Trading.” Econometrica: Journal of the Econometric Society, 1315–1335. https://www.jstor.org/stable/1913210.

Laval, J. A. 2023. “Self-Organized Criticality of Traffic Flow: Implications for Congestion Management Technologies.” Transportation Research Part C: Emerging Technologies 149: 104056. https://doi.org/10.1016/j.trc.2023.104056.

Leal, L., H. Mateen, M. Nirei, and J. A. Scheinkman. 2021. Repricing Avalanches in the Billion-Prices Data. Technical report. National Bureau of Economic Research. https://www.nber.org/papers/w29236.

LeRoy, S. F. 2008. “Excess Volatility Tests.” In The New Palgrave Dictionary of Economics, 2nd ed., vol. 13. London, UK: Palgrave Macmillan. https://doi.org/10.1057/978-1-349-95121-5_2307-1.

LeRoy, S. F., and R. D. Porter. 1981. “The Present-Value Relation: Tests Based on Implied Variance Bounds.” Econometrica: Journal of the Econometric Society, 555–574. https://doi.org/10.2307/1911512.

Lillo, F., S. Mike, and J. D. Farmer. 2005. “Theory for Long Memory in Supply and Demand.” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 71 (6): 066122. https://doi.org/10.1103/PhysRevE.71.066122.

Lombardi, F., H. J. Herrmann, and L. de Arcangelis. 2017. “Balance of Excitation and Inhibition Determines 1/f Power Spectrum in Neuronal Networks.” Chaos: An Interdisciplinary Journal of Nonlinear Science 27 (4). https://doi.org/10.1063/1.4979043.

Lombardi, F., O. Shriki, H. J. Herrmann, and L. de Arcangelis. 2021. “Long-Range Temporal Correlations in the Broadband Resting State Activity of the Human Brain Revealed by Neuronal Avalanches.” Neurocomputing 461: 657–666. https://doi.org/10.1016/j.neucom.2020.05.126.

Long, Jr., J. B., and C. I. Plosser. 1983. “Real Business Cycles.” Journal of Political Economy 91 (1): 39–69. https://www.jstor.org/stable/1840430.

Lux, T. 2021. “Can Heterogeneous Agent Models Explain the Alleged Mispricing of the S&P 500?” Quantitative Finance 21 (9): 1413–1433. https://doi.org/10.1080/14697688.2021.1909744.

Lux, T., and M. Marchesi. 1999. “Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market.” Nature 397 (6719): 498–500. https://doi.org/10.1038/17290.

Majewski, A. A., S. Ciliberti, and J.-P. Bouchaud. 2020. “Co-existence of Trend and Value in Financial Markets: Estimating an Extended Chiarella Model.” Journal of Economic Dynamics and Control 112: 103791. https://doi.org/10.1016/j.jedc.2019.103791.

Marcaccioli, R., J.-P. Bouchaud, and M. Benzaquen. 2022. “Exogenous and Endogenous Price Jumps Belong to Different Dynamical Classes.” Journal of Statistical Mechanics: Theory and Experiment 2022 (2): 023403. https://doi.org/10.1088/1742-5468/ac498c.

Marsili, M. 2014. “Complexity and Financial Stability in a Large Random Economy.” Quantitative Finance 14 (9): 1663–1675. https://doi.org/10.1080/14697688.2013.765061.

May, R. M. 1972. “Will a Large Complex System Be Stable?” Nature 238 (5364): 413–414. https://doi.org/10.1038/238413a0.

Mazzarisi, O., and M. Smerlak. 2024. Beyond May: Complexity-Stability Relationships in Disordered Dynamical Systems. ArXiv preprint: 2403.11014. https://doi.org/10.48550/arXiv.2403.11014.

Minsky, H. P. 2015. Can ‘It’ Happen Again?: Essays on Instability and Finance. New York, NY: Routledge. https://doi.org/10.4324/9781315705972.

Minsky, H. P., and H. Kaufman. 2008. Stabilizing an Unstable Economy. Vol. 1. New York, NY: McGraw-Hill.

Moran, J., and J.-P. Bouchaud. 2019. “May’s Instability in Large Economies.” Physical Review E 100 (3): 032307. https://doi.org/10.1103/PhysRevE.100.032307.

Moran, J., F. P. Pijpers, U. Weitzel, J.-P. Bouchaud, and D. Panja. 2023. Critical Fragility in Socio-Technical Systems. ArXiv preprint: 2307.03546. https://doi.org/10.48550/arXiv.2307.03546.

Moran, J., M. Romeijnders, P. Le Doussal, F. P. Pijpers, U. Weitzel, D. Panja, and J.-P. Bouchaud. 2024. “Timeliness Criticality in Complex Systems.” Nature Physics 20: 1352–1358. https://doi.org/10.1038/s41567-024-02525-w.

Moran, J., A. Secchi, and J.-P. Bouchaud. 2024. Revisiting Granular Models of Firm Growth. https://doi.org/10.48550/arXiv.2404.15226.

Müller, M., and M. Wyart. 2015. “Marginal Stability in Structural, Spin, and Electron Glasses.” Annual Review of Condensed Matter Physics 6 (1): 177–200. https://doi.org/10.1146/annurev-conmatphys-031214-014614.

Muzy, J., J.-F. Delour, and E. Bacry. 2000. “Modelling Fluctuations of Financial Time Series: From Cascade Process to Stochastic Volatility Model.” The European Physical Journal B—Condensed Matter and Complex Systems 17: 537–548. https://doi.org/10.1007/s100510070131.

Muzy, J.-F., R. Baïle, and E. Bacry. 2013. “Random Cascade Model in the Limit of Infinite Integral Scale as the Exponential of a Nonstationary 1/f Noise: Application to Volatility Fluctuations in Stock Markets.” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 87 (4): 042813. https://doi.org/10.1103/PhysRevE.87.042813.

Nirei, M., and J. A. Scheinkman. 2024. “Repricing Avalanches.” Journal of Political Economy 132 (4): 1327–1388. https://doi.org/10.1086/727286.

Osorio, I., M. G. Frei, D. Sornette, J. Milton, and Y.-C. Lai. 2010. “Epileptic Seizures: Quakes of the Brain?” Physical Review E 82 (2): 021919. https://doi.org/10.1103/PhysRevE.82.021919.

Palmer, R. G., W. B. Arthur, J. H. Holland, B. LeBaron, and P. Tayler. 1994. “Artificial Economic Life: A Simple Model of a Stockmarket.” Physica D: Nonlinear Phenomena 75 (1–3): 264–274. https://doi.org/10.1016/0167-2789(94)90287-9.

Parisi, G. 1999. “Complex Systems: A Physicist’s Viewpoint.” Physica A: Statistical Mechanics and its Applications 263 (1–4): 557–564. https://doi.org/10.1016/S0378-4371(98)00524-X.

Parisi, G. 2007. “Physics Complexity and Biology.” Advances in Complex Systems 10 (supp02): 223–232. https://doi.org/10.1142/S021952590700132X.

Patil, N., and J.-P. Bouchaud. 2024. Emergent Inequalities in a Primitive Agent-Based Good-Exchange Model. ArXiv preprint: 2405.18116. https://doi.org/10.48550/arXiv.2405.18116.

Patzelt, F., and K. Pawelzik. 2011. “Criticality of Adaptive Control Dynamics.” Physical Review Letters 107 (23): 238103. https://doi.org/10.1103/PhysRevLett.107.238103.

Patzelt, F., and K. Pawelzik. 2013. “An Inherent Instability of Efficient Markets.” Scientific Reports 3 (1): 2784. https://doi.org/10.1038/srep02784.

Perotti, J. I., O. V. Billoni, F. A. Tamarit, D. R. Chialvo, and S. A. Cannas. 2009. “Emergent Self-Organized Complex Network Topology out of Stability Constraints.” Physical Review Letters 103 (10): 108701. https://doi.org/10.1103/PhysRevLett.103.108701.

Sachs, M. K., M. R. Yoder, D. L. Turcotte, J. B. Rundle, and B. D. Malamud. 2012. “Black Swans, Power Laws, and Dragon-Kings: Earthquakes, Volcanic Eruptions, Landslides, Wildfires, Floods, and SOC Models.” The European Physical Journal Special Topics 205: 167–182. https://doi.org/10.1140/epjst/e2012-01569-3.

Sato, Y., and K. Kanazawa. 2023. “Inferring Microscopic Financial Information from the Long Memory in Market-Order Flow: A Quantitative Test of the Lillo-Mike-Farmer Model.” Physical Review Letters 131 (19): 197401. https://doi.org/10.1103/PhysRevLett.131.197401.

Scheinkman, J. A., and M. Woodford. 1994. “Self-Organized Criticality and Economic Fluctuations.” The American Economic Review 84 (2): 417–421. https://www.jstor.org/stable/2117870.

Schmitt, N., and F. Westerhoff. 2021. “Trend Followers, Contrarians and Fundamentalists: Explaining the Dynamics of Financial Markets.” Journal of Economic Behavior & Organization 192: 117–136. https://doi.org/10.1016/j.jebo.2021.10.006.

Scholl, M. P., A. Calinescu, and J. D. Farmer. 2021. “How Market Ecology Explains Market Malfunction.” Proceedings of the National Academy of Sciences 118 (26): e2015574118. https://doi.org/10.1073/pnas.2015574118.

Schwarzkopf, Y., and J. D. Farmer. 2010. “Empirical Study of the Tails of Mutual Fund Size.” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 81 (6): 066113. https://doi.org/10.1103/PhysRevE.81.066113.

Sethna, J. P., K. A. Dahmen, and C. R. Myers. 2001. “Crackling Noise.” Nature 410 (6825): 242–250. https://doi.org/10.1038/35065675.

Sharma, D., J.-P. Bouchaud, M. Tarzia, and F. Zamponi. 2021. “Good Speciation and Endogenous Business Cycles in a Constraint Satisfaction Macroeconomic Model.” Journal of Statistical Mechanics: Theory and Experiment 2021 (6): 063403. https://doi.org/10.1088/1742-5468/ac014a.

Shiller, R. J. 1981. “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?” American Economic Review 71 (3): 421–436. https : //www.jstor.org/stable/1802789.

Shiller, R. J. 1987. “The Volatility of Stock Market Prices.” Science 235 (4784): 33–37. https://doi.org/10.1126/science.235.4784.3.

Sornette, A., and D. Sornette. 1989. “Self-Organized Criticality and Earthquakes.” Europhysics Letters 9 (3): 197. https://doi.org/10.1209/0295-5075/9/3/002.

Sornette, D. 1994. “Sweeping of an Instability: an Alternative to Self-Organized Criticality to get Powerlaws without Parameter Tuning.” Journal de Physique I 4 (2): 209–221. https://doi.org/10.1051/jp1:1994133.

Sornette, D. 2006. “Endogenous Versus Exogenous Origins of Crises.” In Extreme Events in Nature and Society, edited by S. Albeverio, V. Jentsch, and H. Kantz, 95–119. Berlin, Germany: Springer. https://doi.org/10.1007/3-540-28611-X_5.

Sornette, D., and G. Ouillon. 2012. “Dragon-Kings: Mechanisms, Statistical Methods and Empirical Evidence.” The European Physical Journal Special Topics 205 (1): 1–26. https://doi.org/10.1140/epjst/e2012-01559-5.

Squartini, T., I. Van Lelyveld, and D. Garlaschelli. 2013. “Early-Warning Signals of Topological Collapse in Interbank Networks.” Scientific Reports 3 (1): 1–9. https://doi.org/10.1038/srep03357.

Sterman, J. 1989. “Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment.” Management Science 35 (3): 321–339. https://doi.org/10.1287/mnsc.35.3.321.

Stone, L. 2018. “The Feasibility and Stability of Large Complex Biological Networks: A Random Matrix Approach.” Scientific Reports 8 (1): 1–12. https://doi.org/10.1038/s41598-018-26486-2.

Taleb, N. N. 2014. Antifragile: Things that Gain from Disorder. Vol. 3. New York, NY: Random House.

Thurner, S., J. D. Farmer, and J. Geanakoplos. 2012. “Leverage Causes Fat Tails and Clustered Volatility.” Quantitative Finance 12 (5): 695–707. https://doi.org/10.1080/14697688.2012.674301.

Watkins, N. W., G. Pruessner, S. C. Chapman, N. B. Crosby, and H. J. Jensen. 2016. “25 Years of Self-Organized Criticality: Concepts and Controversies.” Space Science Reviews 198: 3–44. https://doi.org/10.1007/s11214-015-0155-x.

Wehrli, A., and D. Sornette. 2022. “The Excess Volatility Puzzle Explained by Financial Noise Amplification from Endogenous Feedbacks.” Scientific Reports 12: 18895. https://doi.org/10.1038/s41598-022-20879-0.

Wheatley, S., A. Wehrli, and D. Sornette. 2019. “The Endo–Exo Problem in High Frequency Financial Price Fluctuations and Rejecting Criticality.” Quantitative Finance 19 (7): 1165–1178. https://doi.org/10.1080/14697688.2018.1550266.

Wyart, M., J.-P. Bouchaud, J. Kockelkoren, M. Potters, and M. Vettorazzo. 2008. “Relation Between Bid–Ask Spread, Impact and Volatility in Order-Driven Markets.” Quantitative Finance 8 (1): 41–57. https://doi.org/10.1080/14697680701344515.

Zumbach, G., and P. Lynch. 2001. “Heterogeneous Volatility Cascade in Financial Markets.” Physica A: Statistical Mechanics and its Applications 298 (3–4): 521–529. https://doi.org/10.1016/S0378-4371(01)00249-7.

BACK TO The Economy as an Evolving Complex System IV