On the dynamics of social conflicts: looking for the Black Swan

This paper deals with the modeling of social competition, possibly resulting in the onset of extreme conflicts. More precisely, we discuss models describing the interplay between individual competition for wealth distribution that, when coupled with political stances coming from support or opposition to a government, may give rise to strongly self-enhanced effects. The latter may be thought of as the early stages of massive, unpredictable events known as Black Swans, although no analysis of any fully-developed Black Swan is provided here. Our approach makes use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to game-theoretical tools.

💡 Research Summary

The paper tackles the problem of how ordinary social competition can evolve into extreme, hard‑to‑predict conflicts that resemble the early stages of a Black Swan event. The authors adopt a kinetic‑theory framework for “active particles” and embed game‑theoretic interaction rules to capture the dual drivers of wealth competition and political alignment. Each individual is described by a continuous wealth variable (w\ge0) and a discrete political stance (p\in{+1,-1}) (support or opposition to the government). The whole population is represented by a time‑dependent probability density (f(t,w,p)) that conserves total mass (population) and total wealth.

Microscopic interactions are defined as follows: when two agents meet, they play a payoff matrix (M(p_i,p_j)) that rewards cooperation when political stances coincide and penalises it when they differ. The resulting payoff influences a wealth‑transfer function (\tau(w_i,w_j)), which can be proportional or inversely proportional to the payoff, thereby modelling both “rich‑get‑richer” and “redistributive” scenarios. Political stance changes are governed by a stochastic transition rate (\lambda(p_i\to p_j)) that depends on the opponent’s wealth and the payoff differential, introducing a feedback loop between economic inequality and political polarization.

By averaging over many binary encounters and invoking an entropy‑production principle, the authors derive a nonlinear Boltzmann‑type kinetic equation:

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