IDEAS home Printed from
   My bibliography  Save this paper

Self-Organized Critical Evolution In Economic Systems That Display Local Complementarities


  • Alexander Arenas

    (Universitat Rovira i Virgili)

  • Fernando Vega-Redondo

    (Universidad de Alicante)

  • Conrad J. Perez

    (Universitat de Barcelona)

  • Albert Diaz-Guilera

    (Universitat de Barcelona)


We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power-laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state. There are clear evidences that social and economic change in modern societies typically come in ``waves'' with seemingly little intertemporal structure. There are many factors that can contribute to such complex evolution but, in essence, any theory able to account for the inherent dynamics of the phenomenon should consider how the stimulus for change spreads by gradual local interaction through a social network as well as the incentives that govern individual behavior. The hope is that, independently of the particular choice for the microscopic rules describing the dynamic behavior of the agents that form an arbitrary system, one should observe some collective trends that could be reflected in terms of macroscopic observables.In this work, our main goal is to define a general scenario that could be useful to understand evolution in socio-economic environments and within such a broad field our concern is related to technological progress. In a general sense, let us consider a population of agents each of them interacting with a group of neighbors in order to carry out projects of mutual interest. From these collaborations agents obtain payoffs which, of course, tend individually to be as large as possible. To be more precise these payoffs should reflect several basic properties. First, they should account for a basic benefit obtained just for having a certain technological level. It might be thought as an index for the technological potential productivity. It is reasonable to assume that the higher the technological level the larger the base payoff will be. Furthermore, it should measure how similar the tools required to undertake a mutual project are. It should favor those collaborations where both technological levels are very similar (high compatibility) and punish any waste of resources derived from a possible mismatch between them. In other words, technological compatibility should induce high values of the payoff function while significant costs should arise from any degree of incompatibility. It is also reasonable to assume that those costs are bounded from below (the bankrupt).The dynamics must be consequent with the aforementioned basic trends. Two main ingredients contribute to the dynamical evolution. One is the interaction with the rest of the population. Each agent should have the possibility to modify her technological level if the benefits derived from this change are increased. With only this term the system might reach a quiescent state where all the agents are happy with their respective technological level, not necessarily the same for all of them. To complete the picture, it is also natural to think of individual mechanisms of technological improvement which could be modeled as a sudden update of the state of a given agent. This change plays the role of a perturbation and admits several interpretations (e.g. local innovation, a shock in payoffs, population renewal, etc.). Immediately, her nearest neighbors check whether an update to a new technological state is more profitable for them. The process can be extended all over the network triggering a wave of change or avalanche till a new quiescent state is reached. Then, the sequence of events is repeated again. Notice that in modern socio-economic environments, the diffusion of information/technology is usually a fast process while advances are developed in a much slower time scale. Therefore, it is reasonable to assume that both processes are defined in different time scales. Other ingredients can also be incorporated into this general framework but, up to now, let us keep this simple picture in mind.We present here a general scenario for the study of the technological evolution in a socio-economic environment. It is quite appealing to realize that in a very general manner the framework described in this paper is able to predict the existence of different regimes depending on the cost associated to the improvement/diffussion of technology and that these regimes can be computed directly from a macroscopic quantity without specifying details about the underlying microscopic dynamics and payoff functions. Even more, we have shown through a simple model that critical behavior is attained in a natural way through a process of self-organization that maximizes a macroscopic observable: the advance rate.

Suggested Citation

  • Alexander Arenas & Fernando Vega-Redondo & Conrad J. Perez & Albert Diaz-Guilera, 2000. "Self-Organized Critical Evolution In Economic Systems That Display Local Complementarities," Computing in Economics and Finance 2000 271, Society for Computational Economics.
  • Handle: RePEc:sce:scecf0:271

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    2. Bosch-Domènech, Antoni & Vriend, Nicolaas J., 2013. "On the role of non-equilibrium focal points as coordination devices," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 52-67.
    3. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    4. Chantal Marlats, 2021. "Reputation effects in stochastic games with two long-lived players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 1-31, February.
    5. Maarten C.W. Janssen, 1997. "Focal Points," Tinbergen Institute Discussion Papers 97-091/1, Tinbergen Institute.
    6. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    7. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
    8. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    9. Burkhard C. Schipper, 2004. "Submodularity and the evolution of Walrasian behavior," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 471-477, August.
    10. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    11. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    12. Conley, John P. & Neilson, William S., 2013. "Endogenous coordination and discoordination games: Multiculturalism and assimilation," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 176-191.
    13. Bernard, Mark & Hett, Florian & Mechtel, Mario, 2016. "Social identity and social free-riding," European Economic Review, Elsevier, vol. 90(C), pages 4-17.
    14. William Tracy, 2014. "Paradox Lost: The Evolution of Strategies in Selten’s Chain Store Game," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 83-103, January.
    15. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
    16. Carlos Alós-Ferrer & Georg Kirchsteiger & Markus Walzl, 2010. "On the Evolution of Market Institutions: The Platform Design Paradox," Economic Journal, Royal Economic Society, vol. 120(543), pages 215-243, March.
    17. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
    18. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    19. T. Guse & B. Hehenkamp, 2006. "The strategic advantage of interdependent preferences in rent-seeking contests," Public Choice, Springer, vol. 129(3), pages 323-352, December.
    20. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf0:271. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.