A. Ishii trust and suspicion model with combined update rule

So for our final post on the trust and suspicion model [1], and also for our last post this year (happy new year by the way), we add a trivial extension to this model. Namely we have rebuilt the apps you have already seen, where you can mix both update rules (model types) and have them acting at different intensities. While this does not add much to the model, but it allows to explore even more complex social scenarios.

So just to be safe we want to write down the combined update rule:

\begin{equation} O_{i} (t+1) = O_{i} (t) + \sum_{j=1}^N D_{ij} [ \alpha_{I} O_{j} (t) + \alpha_{II} \Phi(|O_{i} (t)-O_{j} (t)|) ( O_{j} (t) - O_i(t) ) ] \Delta t . \end{equation}

In the above \( \alpha \) values tune intensity of expression of both update rules (original model types). Tune the parameter values in the apps below. Explore the possibilities the combined model offers.

\( N=2 \) app

\( N=3 \) app

\( N=100 \) app

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Acknowledgment. This post was written while reviewing literature relevant to the planned activities in postdoctoral fellowship ''Physical modeling of order-book and opinion dynamics'' (09.3.3-LMT-K-712-02-0026) project. The fellowship is funded by the European Social Fund under the No 09.3.3-LMT-K-712 ''Development of Competences of Scientists, other Researchers and Students through Practical Research Activities'' measure.


  • A. Ishii. Opinion Dynamics Theory Considering Trust and Suspicion in Human Relations. In: Group Decision and Negotiation: Behavior, Models, and Support, Lecture Notes in Business Information Processing, 351: 193-204. Springer, 2019. doi: 10.1007/978-3-030-21711-2_15.