# Influence of long-range interactions on strategy selection in crowd

Source: [Influence of long-range interactions on strategy selection in crowd](<https://www.sota2.com/research/paper/68fa2d4b1e209131ce858425>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:12:04.426Z

Authors: K. Malarz, M. J. Krawczyk, K. Kulakowski

Published: 2013-10-30T14:47:20.000Z

## Abstract

An order--disorder phase transition is observed for Ising-like systems even for arbitrarily chosen probabilities of spins flips \[K. Malarz et al, Int. J. Mod. Phys. C 22, 719 (2011)\]. For such athermal dynamics one must define $(z+1)$ spin flips probabilities $w(n)$, where $z$ is a number of the nearest-neighbours for given regular lattice and $n=0,\\cdots,z$ indicates the number of nearest spins with the same value as the considered spin. Recently, such dynamics has been successfully applied for the simulation of a cooperative and competitive strategy selection by pedestrians in crowd \[P. Gawro\\'nski et al, Acta Phys. Pol. A 123, 522 (2013)\]. For the triangular lattice ($z=6$) and flips probabilities dependence on a single control parameter $x$ chosen as $w(0)=1$, $w(1)=3x$, $w(2)=2x$, $w(3)=x$, $w(4)=x/2$, $w(5)=x/4$, $w(6)=x/6$ the ordered phase (where most of pedestrians adopt the same strategy) vanishes for $x\>x\_C\\approx 0.429$. In order to introduce long-range interactions between pedestrians the bonds of triangular lattice are randomly rewired with the probability $p$. The amount of rewired bonds can be interpreted as the probability of communicating by mobile phones. The critical value of control parameter $x\_C$ increases monotonically with the number of rewired links $M=pzN/2$ from $x\_C(p=0)\\approx 0.429$ to $x\_C(p=1)\\approx 0.81$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1310.8175>)

[PDF](<https://arxiv.org/pdf/1310.8175.pdf>)