From Nonequilibrium to Equilibrium: Insights from a Two-Population Occupation Model

Jerome Garnier-Brun, Ruben Zakine and Michael Benzaquen

Papers from arXiv.org

Abstract: In socioeconomic systems, nonequilibrium dynamics naturally stem from the generically non-reciprocal interactions between self-interested agents, whereas equilibrium descriptions often only apply to scenarios where individuals act with the common good in mind. We bridge these two contrasting paradigms by studying a Sakoda-Schelling occupation model with both individualistic and altruistic agents, who, in isolation, follow nonequilibrium and equilibrium dynamics respectively. We investigate how the relative fraction of these two populations impacts the behavior of the system. In particular, we find that when fluctuations in the agents' decision-making process are small (high rationality), a very moderate amount of altruistic agents mitigates the sub-optimal concentration of individualists in dense clusters. In the regime where fluctuations carry more weight (low rationality), on the other hand, altruism progressively allows the agents to coordinate in a way that is significantly more robust, which we understand by reducing the model to a single effective population studied through the lens of active matter physics. We highlight that localizing the altruistic intervention at the right point in space may be paramount for its effectiveness.

Date: 2024-12
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