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Strong random correlations in networks of heterogeneous agents

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Abstract

Correlations and other collective phenomena are considered in a schematic model of pairwise interacting, competing and collaborating agents facing a binary choice and situated at the nodes of the complete graph and a 2-dimensional regular lattice, respectively. The agents may be subjected to an idiosyncratic or common external influence and also some random noise. The system’s stochastic dynamics is studied by numerical simulations. It displays the characteristics of punctuated, multiple equilibria, sensitivity to small details, and path dependence. The dynamics is so slow that one can meaningfully speak of quasi-equilibrium states. Performing measurements of correlations between the agents choices we find that they are random both as to their sign and absolute value, but their distribution is very broad when the interaction dominates both the noise and the external field. This means that random but strong correlations appear with large probability. In the two dimensional model this also implies that the correlations on average fall off with distance very slowly: the system is essentially non-local, small changes at one end may have a strong impact at the other. The strong, random correlations tend to organize a large fraction of the agents into strongly correlated clusters that act together. If we think of this model as a metaphor of social or economic agents or bank networks, the systemic risk implications of this tendency are clear: any impact on even a single strongly correlated agent will not be confined to a small set but will spread, in an unforeseeable manner, to the whole system via the strong random correlations.

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Notes

  1. Note how different this concept of equilibrium is from that in economics.

  2. An obvious example is the following: If the agents occupy the nodes of a bipartite graph, they can be divided into two subsets such that every agent belonging to subset A is directly linked only to agents belonging to subset B and vice versa. Then each subset can be updated simultaneously, still applying the update rule Eq. (2), which evidently results in a tremendous gain in simulation time. We have actually used this method in the case of the square lattice, and checked that it leads to the same result as the sequential update, provided the latter is run for a large number of sweeps. An arbitrary redefinition of the rules of the game may, of course, lead to arbitrarily different results, including the flip-flop type of behaviour if one decided to update every agent simultaneously.

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Acknowledgments

We are obliged to Alan Kirman for critically reading the manuscript. This work has been supported by the European Union under Grant Agreement No. FP7-ICT-255987-FOC-II Project; by the Institute for New Economic Thinking under Grant Agreement ID: INO1200019; by the European Union and the European Social Fund under Grant Agreement No. TÁMOP 4.2.1./B-09/KMR-2010-0003; and by the National Innovation Office under Grant No. KCKHA005.

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Authors and Affiliations

  1. Parmenides Foundation, Pullach b., Munich, Germany

    Imre Kondor

  2. Eötvös Loránd University, Budapest, Hungary

    István Csabai, Gábor Papp, Enys Mones, Gábor Czimbalmos & Máté Cs. Sándor

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  1. Imre Kondor
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  2. István Csabai
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  6. Máté Cs. Sándor
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Correspondence to Imre Kondor.

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Kondor, I., Csabai, I., Papp, G. et al. Strong random correlations in networks of heterogeneous agents. J Econ Interact Coord 9, 203–232 (2014). https://doi.org/10.1007/s11403-014-0125-5

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